The following is a collection of questions that the instructor has given as either exam questions or 'sample exam' questions in the past. They are collected here for two purposes: (a) to provide you with some idea of the sorts of questions he might ask in future exams, and (b) to provide him with an easy way to incorporate such questions into the homework. 
Table of Contents:
Coulomb's Law 
Electric Potential and Capacitance 
Electric Current, Resistance, and Circuits 
Magnetism 
Magnetic Induction 
AC Circuits 
Geometric Optics 
Physical Optics 
Relativity 
Modern Physics 

Selected Solutions 


ELECTRIC FORCE, FIELDS, AND DIPOLES
Coulomb's Law
1. A proton (q=1.6 × 10-19C, m-1.6 × 10-27 kg), floats in the air, levitated by the repulsive force of another proton below it. How close are they, if there are no other relevant forces around?

2. A 3mC charge of mass 0.050 kg floats motionless above a 60nC charge.  There are no strings attached to the charge on top.  At what height is it floating if there are no other relevant forces around?

E-field
3. Which two of the following four quantities would be zero halfway between +3nC charge and a -3nC charge?
a) the E-field
b) the force on a test charge at that point
c) the electric potential
d) the potential energy of a test charge at that point

4. Two positive 3microC charges sit as shown in Fig. J: one on the y-axis at y=3cm, the other on the negative x-axis at x=-2cm.
a) Sketch the lines of electric force in the vicinity of the two charges. Use at least four lines coming out of (or going in to) each charge.
b) Calculate the magnitude of the electric field at the origin.

5. A 10-4kg, 3microC charge is suspended from a 10cm string in a region where the E-field has a magnitude of 250N/C and points horizontally. At what angle will the charge hang in equilibrium? B. Sketch the electric field lines around a +2nC charge and a -1nC charge.

6. Consider a +9nC charge and a -6nC charge, 3mm to its right.
a) What is the magnitude and direction of the electric field halfway between the two charges?
b) What is the magnitude and direction of the electric field halfway between the two charges if the -6nC is replaced by +6nC?
c) What is the magnitude and direction of the force would a -1nC charge experience halfway between the two charges of part b?

7. An electron, Q=-1.6´ 10-19C, is positioned at x=-2cm on the x axis. A proton sits at x=-2cm, y=-2cm. What is the magnitude and direction of the electric field at the origin?

8. Find the magnitude of the electric field at the origin, given its proximity to the following source charges:
Q1=+5nC, at x=10cm on the y-axis
Q2=-2nC, at x=6cm on the x-axis.
Indicate on a sketch the direction of the electric field.

9. A 10g mass, with a -3nC charge on it, hangs at an angle of 10 from the vertical, because of the presence of a uniform horizontal electric field. Let's say that it hangs toward the right hand side of the page.
a) What is the magnitude of the electric field?
b) What is the direction of the field?

10. You are setting up a classroom demonstration of electric forces and you have a 5 microgram pithball attached to a nearly massless string. You know that you can easily generate a horizontal 100V/m electric field near the pith ball. How much charge must you put on the ball to get it to hang at a 75o angle, measured relative to the horizontal?

11. A +3
mC charge sits at the origin, a -2mC charge sits on the x-axis at x=2cm. Calculate the magnitude and direction of the electric field 2cm above the negative charge.

12. Sketch the electric field lines for four equal positive charges at the four corners of a square.

13. Calculate the magnitude and direction of the force on charge C, if charge A (-6
mC) is located at the origin, charge B (+1.5mC) is located at x=3cm, and charge C (-2mC) is located at x=5cm.

14. One +2
mC charge sits on the x-axis at x=-3cm, and a -3mC charge sits on the y-axis at y= +2 cm.
a) What is the magnitude and direction of the electric field at the origin?
b) What is the magnitude and direction of the force a -5nC charge sitting at the origin would feel?

Dipoles
15. A molecule which has a dipole moment of 8.2×10-30 Cm is parallel to an electric field of 37000V/m. How much energy is required to flip the molecule until it is antiparallel to the field?

16. An electric dipole lies in an electromagnetic field, and the dipole moment points perpendicular to the field.  Which one of the following is FALSE?
a) _____ The dipole will continue to point in that direction if no other forces act on it.
b) _____ The net force on the dipole is zero.
c) _____ The electrostatic potential energy of the dipole is zero.
d) _____ The net charge of the dipole is zero.

17. A water molecule, which has a dipole moment of 6.2×10-30Cm, is in a 150V/m electric field inside a microwave oven.
a)  How much energy is needed to completely flip the dipole?
b)  If the oven consumes 1kW of power, what is the maximum number of dipole flips that can occur per second?

18. An electric dipole consists of two 1microC charges on the y-axis. The positive charge is at y=+0.5mm, the negative charge is at y=-0.5mm.
a) Calculate the electric field at x=10mm, y=0.
b) This dipole sits in a uniform external electric field. What must Ey be in order for the potential energy of the dipole to be 1014eV?

19. An electric dipole consists of two charges of magnitude lnC, each located lcm away from the origin on the y-axis. The positive charge is at y=+lcm.
a) What is the dipole moment of this dipole?
b) What is the magnitude and direction of the electric field at y= lrn?

ELECTRIC POTENTIAL AND CAPACITANCE

Electric potential
1. For the charge distribution below, with -7nC located at (x,y)=(3m,0) and +6nC located at (0,2m),
a)  calculate the  magnitude and direction of the electric field at the origin.
b)  Using the results of part (a), calculate the magnitude and direction of the force that would act on a 2microC charge at the origin.
c)  Calculate the electric potential at the origin.
d)  How much energy would it take to move a 2microC charge from infinitely far away (V=0) to the origin?

2. Consider two charges --- a +6mC charge at x=6m, y=0, and a -3mC charge at y=3m, x=0  ---- which act on a -2nC charge at the origin,
a)  Calculate the magnitude and direction of the force on the -2nC charge.
b)  Calculate the magnitude and direction of the electric field on the same charge.
c)  Calculate the electric potential on the -2nC charge.

3. Which two of the following four quantities would be zero halfway between two +1nC charges?
a)  the E-field
b)  the force on a test charge at that point
c)  the electric potential
d)  the potential energy of a test charge at that point

4. Four charges of equal magnitude (2 positive, 2 negative) are arranged in a square, with the postive charges at the top left and bottom right.
a)  Sketch the lines of electric force in the vicinity of the square.  Use at least four lines coming out of (or going in to) each charge.
b)  Calculate the potential at the point midway between the top two charges. The charges each have magnitude 6mC, and are each 2mm away from the nearest neighbors.

5. We had a formula for each of the following expressions except one.  Which one? What units would it have?
a) _____  kQ/r3              b) _____  kQ/r2               c) _____  kQq/r2             d) _____ kQ/r

6. Which of the following is FALSE?
a) _____ Electric potential is the electrical potential energy per charge.
b) _____ The electrostatic field is the electrostatic force per charge.
c) _____ Positive charges released from rest will move from higher to lower potential.
d) _____ An electron will always travel from the lower to higher electric potential.
e) _____The electrostatic force on a charge always points in the direction of the E-field.

7. For the charge distribution below, with +5mC located at (x,y)=(-1m,0) and -6mC located at (0,2m),
a) Calculate the magnitude and direction of the electric field at the origin.
b) Using the results of part (a), calculate the force that would act on a 2mC charge at the origin.
c)  Calculate the electric potential at the origin.
d)  How much energy would it take to move a 2mC charge from infinitely far away (V=0) to the origin?

8. Show that the two units of electric field ( V/m and N/C ) are equivalent.

9. A +6microC charge lies on the x-axis at x=+3mm, and a -6mC charge lies at x=-3mm.
a)  Calculate the electric potential at the origin.
b)  Calculate the potential at x=0.01mm. (Do not round off till the final step!)
c)  From a) and b), estimate the E-field near the origin.
d)  Calculate the E-field at x=0 directly.

10. A special constant electric-field chamber, 0.8m to a side, has been created in which the field inside is a uniform 1000V/m, pointing in the positive x-direction.
a) What is the potential difference between the wall at x=0m and the wall at x=0.8m?
b) Which wall is at the higher potential?
c) If a +3nC charge is now added to the x-axis at x=0.4m, for what point on the x-axis is the E-field zero?

11. A +3mC charge sits on the y-axis at y=+1m. A -3mC charge sits on the y-axis at y=-1m.
a) Calculate the electric potential at the origin.
b) Calculate the electric potential at y=+1cm.
c) and d) Calculate Ey at the origin in two different ways.

12. Consider force, electric field, electric potential energy, and potential.
a) Name something significant that electric field and potential have in common that they don't share with either force or potential energy.
b) Name something significant that potential and potential energy have in common that they don't share with either force or electric field. (The letter 'p' does not count.)

13. A water molecule, with a dipole moment of 6.2´ 10-30C× m is sitting in a 250N/C electric field.
a) At what angle
q is the potential energy of the dipole the largest? the smallest?
b) At what angle
q is the magnitude of the torque acting on it the largest? the smallest?
c) How much energy is needed to flip the molecule from its lowest potential energy to its largest?

14. Find the electric potential at the origin, given the existence of the following source charges:
Q1=+2
mC, at x=3m on the x-axis,
Q2=-3
mC, at y=-2m on the y-axis
Sketch on your page the direction, from the origin, of increasing potential.

15. Given what we know about lines of electric force, and about equipotential lines, describe the shape of the equipotential lines far away from a +3nC and a -2nC, which are both very close together.

16. Sketch the equipotential lines around a +1pC charge and a -1pC charge.

17. A special constant-electric-field chamber, 0.8m to a side, has been created in which the field inside is a uniform l000V/m, pointing in the positive x-direction.
a) What is the potential difference between the wall at x=0m and the wall at x=0.8m?
b) Which wall is at the higher potential?
c) If a +3nC charge is now added to the x-axis at x=0.4m, for what point on the x-axis is the E-field zero?

18. A +3
mC charge sits on the y-axis at y=+1m. A -3mC charge sits on the y-axis at y=-1m.
a) Calculate the electric potential at the origin.
b) Calculate the electric potential at y=+lcm.
c) and d) Calculate Ey at the origin in two different ways.

19. A dipole consists of a +3nC charge on the y-axis at y=lmm and a -3nC charge on the y-axis at y=-lmm. a) Calculate the electric potential at x=l.000m and 1.001m.
b) Estimate the electric field from the two values in (a).
c) What is the dipole moment of this pair of charges?


20. Consider a point charge of 33nC situated at the origin.
a) Calculate the electric potential at x=1.99m and x=2.01m.
b) Use this result to estimate Ex at x=2m.
c) Calculate Ex directly.
d) What is Ey at x=2m?

21 A water molecule has a 6.2´ 10-30C× m dipole moment.
a) What is the distance between the time-averaged position of the positive and negative charges (both are single charges) which make up the dipole?
b) There is typically about a 100V/m electric field near the ground, which points vertically. How much energy does it take to flip the dipole moments for 18g of water (Avogadro's number, which equals 6.02´ 1023 ) from being aligned with this field to pointing opposite the field?

22. A point charge of +33
mC sits at the origin.
a) Calculate the magnitude and direction of the electric field at a point 5cm away on the positive x-axis.
b) Calculate the electric potential at x=4.999cm and at 5.001cm.
c) Use the results of part (b) to estimate Ex at x=5.000cm.

23. Consider force, electric field, electric potential energy, and potential.
a) Name something significant that electric field and potential have in common that they don't share with either force or potential energy.
b) Name something significant that potential and potential energy have in common that they don't share with either force or electric field. (The letter 'p' does not count.)

24. A water molecule, with a dipole moment of 6.2´ 10-30C× m is sitting in a 250N/C electric field.
a) At what angle
q is the potential energy of the dipole the largest? the smallest?
b) At what angle
qis the magnitude of the torque acting on it the largest? the smallest?
c) How much energy is needed to flip the molecule from its lowest potential energy to its largest?

25. Find the electric potential at the origin, given the existence of the following source charges:
Q1=+2
mC, at x=3m on the x-axis,
Q2=-3
mC, at y=-2m on the y-axis
Sketch on your page the direction, from the origin, of increasing potential.

26. Given what we know about lines of electric force, and about equipotential lines, describe the shape of the equipotential lines far away from a +3nC and a -2nC, which are both very close together.

27. Sketch the equipotential lines around a +1pC charge and a -1pC charge.

28. A special constant-electric-field chamber, 0.8m to a side, has been created in which the field inside is a uniform l000V/m, pointing in the positive x-direction.
a) What is the potential difference between the wall at x=0m and the wall at x=0.8m?
b) Which wall is at the higher potential?
c) If a +3nC charge is now added to the x-axis at x=0.4m, for what point on the x-axis is the E-field zero?

29. A +3
mC charge sits on the y-axis at y=+1m. A -3mC charge sits on the y-axis at y=-1m.
a) Calculate the electric potential at the origin.
b) Calculate the electric potential at y=+lcm.
c) and d) Calculate Ey at the origin in two different ways.

30. A dipole consists of a +3nC charge on the y-axis at y=lmm and a -3nC charge on the y-axis at y=-lmm.
a) Calculate the electric potential at x=l.000m and 1.001m.
b) Estimate the electric field from the two values in (a).
c) What is the dipole moment of this pair of charges?

31. Consider a point charge of 33nC situated at the origin.
a) Calculate the electric potential at x=1.99m and x=2.01m.
b) Use this result to estimate Ex at x=2m.
c) Calculate Ex directly.
d) What is Ey at x=2m?

32. A water molecule has a 6.2´ 10-30C× m dipole moment.
a) What is the distance between the time-averaged position of the positive and negative charges (both are single charges) which make up the dipole?
b) There is typically about a 100V/m electric field near the ground, which points vertically. How much energy does it take to flip the dipole moments for 18g of water (Avogadro's number, which equals 6.02´ 1023 ) from being aligned with this field to pointing opposite the field?

33. A point charge of +33
mC sits at the origin.
a) Calculate the magnitude and direction of the electric field at a point 5cm away on the positive x-axis.
b) Calculate the electric potential at x=4.999cm and at 5.001cm.
c) Use the results of part (b) to estimate Ex at x=5.000cm.

Capacitance
34. Two capacitor plates are charged to an electric field of 35 kV/m.  The plates are 3mm apart.
a)  How much work is required to move an electron from one plate to another?  (q=1.6×1019C)
b)  What minimum voltage must be applied across the plates to get sparks to jump the gap?

35. A parallel-plate capacitor has a plate separation of 0.08 mm (about the thickness of one sheet of paper), and a capacitance of 47microF. If the E-field in the middle of the capacitor is 10V/m,
a)  what is the voltage across the plates?
b)  what is the charge on the plates?

36. Show that capacitance times the square of voltage has units of energy.

37. 110V are placed across two parallel capacitor plates.
a)  Given that the dielectric strength of air is 3 MV/m, how close can you position the plates before they discharge?
b)  If the capacitance is 12microF, how much charge will the capacitor hold if there are 110V across the plates?
c)  What is the electric field inside the capacitor in part (b) if the plates are 1.5 mm apart?

38. Two pieces of aluminum foil, separated by a 0.1mm air gap, form a 3nF capacitor.
a) What is the area of the plates?
If 9V is applied across the capacitor,
b) What is the charge on the positively charged piece of foil?
c) Will the capacitor spark?

39. For purposes of calculating how much charge you need to shock someone with a spark, we can approximate your finger as being a sphere with about a 0.8cm radius.
a) What is the capacitance of your finger?
b) If you can get a spark to fly 2.5cm, how large a potential is them between your finger and the doorknob?
c) How much charge do you need on your finger to get a lcm spark?
d) If you place your open palm 2.5cm from the body of a car, and the palm has an area of 300rn2, what is the capacitance of the palm/car system?

ELECTRIC CURRENT, RESISTANCE, CIRCUITS

Current
1. I need a resistor of 25kohm for a circuit I am building, but all I have are a pile of 100k-ohm resistors.  How can I construct a network that has a net 25k-ohm resistance?  Is it a parallel or a series network?

2. The unit of electrical current is the
a) _____ coulomb.     b) _____ henry.         c) _____ ampere.        d) _____ volt.     e) _____ farad.

3. A 3microF capacitor is charged by connecting it to a 12V battery.
a) What is the final charge on the positive plate of the capacitor?
b) If the charging circuit was designed to not exceed 10mA current at any time, what is the shortest amount of time it could have taken to fully charge the capcitor?
c) If the capacitor sparked at the instant it became fully charged, and if it is a parallel plate capacitor, what is the area of the plates?

4. A cloud is 1km above the ground and holds 40C of charge.
a) If lightning is produced during a rainstorm, what was the minimum potential difference between cloud and ground?
b) If the entire cloud discharged during a 2ms lightning strike, what was the average current during the strike?
c) What is the resistance of the ionized air?
d) If the cloud and ground can be modeled as a parallel-plate capacitor, what is the area of ground that the cloud covers?

5. A 12V battery delivers a very large current to your car when starting the car. If the car's circuit behaves like a 0.04
W resistor,
a) How much energy is dissipated in the circuit during the half-second it takes the car to turn on?
b) How much potential energy does a single electron lose in going from one battery terminal to the other? (Give your answer in two different units of energy)

6. A 2A current running through a resistor causes it to dissipate 50W.
a) What is the resistor's resistance?
b) How many hours would it take for Avogadro's number of electrons (6.0´ 1023) to flow through the resistor?
c) In order for the same resistor to dissipate twice the power, what current must run through it?

Ohm's law
7. A resistor, R, is connected to a voltage source, V, which causes a current, I, to pass through the resistor.
a)  If the resistor is halved to R/2, how much voltage is needed to get the same current I?
b) If, instead of as in (a), the voltage is tripled to 3V, what resistance will give us a current of I?
Power
8. A 50 microF capacitor is connected to 120V.
a) How much charge collects on the positive plate of the electrode?
b) If a 0.03ohm resistor is connected across the terminals, and the capacitor almost completely discharges in about 3 msec, what is the average current flow through the resistor?
c) What is the average power dissipation in the resistor?

9. If we put a given voltage across a resistor, what must be done to the voltage to halve the power dissipated by the resistor?

10. A pickle, connected to 110V, puts out about 170W of heat and light while it is glowing.
a) What is the current going through the pickle?
b) What is the resistance of the pickle?

11. A 2m length of wire of 25
mm radius has a resistance of 40W.
a) What is the electric field in the wire if it carries a current of 100mA?
b) What is the resistivity of the wire?

Equivalent resitance
12. A single Christmas tree bulb has a resistance of 1000ohm. What is the net resistance of a string of 40 bulbs in parallel?

13. A resistor rated at 1/4W is placed across the terminals of a 9V battery.
a)  What resistance will cause the resistor to dissipate 1/4 W?
b)  Is the answer to (a) a minimum or a maximum value of resistance?
c)  If we string five such resistors end-to-end in a circuit, how much current will the 9V battery allow?
d)  How much power will the string of resistors dissipate?

14. You cannot always say what the resistance of an object is unless you specify which two points you are going to measure the resistance across. Consider a network in which all the resistors are 100ohm, consisting of four resistors connected end-to-end in a closed loop, with A, B, C, and D being consecutive points between resistors.
a) Calculate the resistance if you connect your resistance meter between points A and C.
b) Calculate the resistance if you connect your resistance meter between points A and B.

15. You are given a 20ohm, 1.0mA full-scale galvanometer and a 1Mohm resistor. Put the resistor in series to make a meter.
a) Is the meter an ammeter or a voltmeter?             b) What is its full scale reading?
c) What is the meter's net resistance?                    d) What is the total power dissipated by the meter when it is reading full scale?

16. You are given a 22
W, 1.0mA full-scale galvanometer and a 1MW resistor. Put the resistor in series to make a meter.
a) Is the meter an ammeter or a voltmeter?.
b) What is its full scale reading?
c) What is the meter's net resistance?
d) What is the total power dissipated by the meter when it is reading full scale?

RC circuits
17. Sketch the voltage across a capacitor as a function of time if it starts out with a charge on its plates and is shorted out across a resistor at a time t=0.

18. An ideal capacitor will hold its charge indefinitely. However, the charge on an actual capacitor may leak out because of a conducting path which resembles a resistor in parallel to the capacitor. Consider a 220microF capacitor which has a time constant of 24hr, initially charged to 12V.
a) What value of resistance will give a time constant of 24hr?

b) Fill out the folowing table with the values given at the times given.
                        t=0                             t=108hr                                     t=infinity
VR
VC
I
Q

19. The metal in a lm wire has a resistivity of 30
mW× m.
a) What must be the radius of the wire in order to have R=20W?
b) The wire is connected to a 35mF capacitor. Find the time it takes for the capacitor to charge to 63% of its final charge when connected to a 12V battery?
c) What is the current through the wire at the time you calculated in (b)?

20. An ideal capacitor will hold its charge indefinitely. However, the charge on an actual capacitor may leak out because of a conducting path which resembles a resistor in parallel to the capacitor. Consider a 220
mF capacitor which has a time constant of 24hr, initially charged to 12V.
a) What value of resistance will give a time constant of 24hr?
b) For t=0, 108hr, and infinity, calculate VR, VC, I, and Q.

21. A 12V battery charges a 100
mF capacitor through a 10kW resistor.
a) How long does it take for the capacitor to charge to 95% of its final value?
b) What is the charge on the capacitor after one time constant?
c) If it is a parallel-plate capacitor, with the plates separated by 0.01mm, what is its dipole moment after it is fully charged?

22. A 9V battery is connected to an uncharged 0.1
mF capacitor and a 20MW resistor.
a) What is the initial current when the circuit is initially closed?
At t=1 second, what are
b) the current in the circuit?
c) the charge across the capacitor?
d) the voltage across the resistor?
e) the voltage across the capacitor?

23. Sketch the following voltages vs time:
a) VR for a charging RC circuit
b) VR for a discharging RC circuit
c) VC for a charging RC circuit
d) VR+VC for a discharging RC circuit

24. A 330pF capacitor is connected to a 15V power supply.
a) Calculate the charge on either plate when the capacitor is fully charged.
b) If charge is allowed to flow from one plate thrgugh a ll0k
W resistor to the other plate, what is the current the instant that this connection is made?

MAGNETISM:

Sources
1. The magnetic field lines inside the Earth point approximately from North to South along the Earth's axis of rotation. This field is created by current flowing inside the crust. If these currents flow like current flows in a loop, describe the direction of the current flow.

2. In a TV set or computer display, electrons are fired at the screen from behind. These charges in motion can be thought of as a current, so describe the direction of the magnetic field they create, as viewed by someone watching the screen.

3. One microamp flows along the x-axis from x=¥ to x=-¥ . 3mA flows along the z-axis from z=¥ to z=-¥ . What are the x, y, and z components of the magnetic field at x=30cm, y=40cm, z=0?

4. This paper forms the xy plane. Consider a wire at x=y=0 carrying 5A into the paper, and another wire at x=-20cm, y=0, carrying 3A out of the paper. Calculate the magnitude and direction of the magnetic field at a point P, at x=0, y=20cm.

Forces
5. An airplane, which has picked up a net positive charge by brushing against some clouds, flies over the North Magnetic Pole, located in a remote part of Canada. If the plane crosses the Pole (where the field points down) flying West to East, what is the direction of the magnetic force acting on the plane?

6. A wire of 0.33m length carries a current of 2A.
a) Calculate the magnitude of the magnetic field at a distance of 4cm from the wire.
b) Show, on a diagram the direction of the magnetic field.
c) If another wire of the same length, located 4cm away, also carries 2A and the current runs in a direction parallel to the current in the other wire, what is the force on this second wire? Is it attracted or repelled from the first wire?

7. The Earth's magnetic field is created by current flowing inside.
a) If these currents flow like current in a loop, and if the crust has a radius of 3Mm, and if the magnetic field is about 50microT in the center of the loop, how much current is flowing inside the Earth?
b) How fast must an electron (q=-1.60×10-19C, m=9.11×10-31kg) travel at the Earth's surface for the maximum magnetic force on it to equal its weight?

8. A compass needle with a magnetic dipole moment of 0.13Am2 sits inside a circular coil of 150 loops of wire arranged with a radius of 18cm.
a) What field is needed to provide a torque of 0.12Nm to the needle?
b) What current will produce this field?
c) Draw a figure of how the coil must be situated if the compass lies flat on the top of a desk and the torque is sufficient to twist the needle to point East.

9. The power cord of a light bulb consists of two wires of 1cm diameter located 2cm apart.
a) If the toaster draws 2A of current, what is the magnetic field at one of the wires, caused by the current in the other?
b) What is the force between two 60cm segments of the wire?

10. A 2.3A current flows through two identical parallel wires. If the current flows due East in both and one wire is 0.3m North of the other,
a) Give the magnitude and direction of the magnetic field due to the North wire at the location of the South wire.
b) Give the magnitude and direction of the force per unit length on the South wire due to the Northern one.

11. Consider a 15cm diameter coil of 100 loops of wire lying in the plane of this page, carrying a current of 2A (traveling clockwise). A straight wire running from left to right, also in the plane of the page, carries 1A.
a) What is the magnetic field in the center of the coil?
b) What is the magnitude of the force on the straight wire? You may assume that the magnetic field due to the coil is uniform inside the coil, and that it is zero outside the coil.
c) What is the direction of the force on the straight wire?

12. You are standing 10m underneath a single 700kV, 100MW power line, in which the current is flowing to the East. You are also facing East.
a) What is the magnitude of the magnetic field at your location due to this current?
b) Does this field point up, down, to your left or right, or ahead of or behind you?
c) What magnitude force would a 1km length of this wire feel due to a local magnetic field of 50mT pointing 60° below North?

MAGNETIC INDUCTION

Lenz' law
1. A circular coil lies in the plane of this page. A magnetic field points out of the page. If the coil is tilted in any different direction, will the induced current flow clockwise or counter-clockwise?

2. A square loop of wire sits flat on top of a table. If there is a magnetic field inside the loop that points straight up, describe the current (as viewed from someone looking down on the loop) that is induced in the coil if the coil is quickly 'squished' to zero area.

3. A circular coil lies in the plane of this page. A current I1 flows counterclockwise in this coil. A long straight wire, situated above the plane of this page, passes above the center of this coil, with its current, I2, travelling toward the top of the page. What is the direction of the resulting force on the straight wire?

4. Current in a long straight wire travels from left to right in the plane of this page. A magnetic field points from the lower lefthand corner of this page toward the upper righthand corner. If the current is caused by negatively charged electrons, what is the direction of the force on the wire?

5. An iron bar sits atop two metal rails in the plane of this page that are joined in a semicircle on the right hand side so that the rail and the iron bar form the letter D. A magnetic field points out of the page.
a) Which direction does the induced E-field in the bar point if the iron bar is dragged to the right?
b) Is the induced current in the bar and rails clockwise or counterclockwise?

6. Current flows to the right in a wire in the plane of this page. A circular loop of wire, also in this plane, is closer to the bottom of the page.
a) What is the direction of the magnetic field inside the loop, produced by the current in the wire?
b) If the current is suddenly decreased, is the induced current in the wire clockwise or counterclockwise?

7. Two wires lie parallel to the plane of this page. In one, the current, I1, flows from left to right. The other wire lies below it, with the current, I2, flowing from the bottom lefthand corner to the top righthand corner.
a) What is the direction of the magnetic field due to I1 as felt by the wire carrying I2?
b) What is the direction of the resulting force on I2 due to I1?

Faraday's law
8. Two sets of circular coils of wire sit inside each other. The outer coil consists of 100 loops of wire of 50cm radius. The inner coil consists of 50 loops with a cross-sectional area of 1300cm2.
a) If both loops are lying flat on a table, and if 2.3A flows through the outer coil, then what is the magnetic field at the center of the coil?
b) What is the magnetic flux through the inner coil? What simplifying assumption did you need to make?
c) If the outer coil is rotated through 60o in 2s, what is the voltage induced in the inner coil?

9. The magnetic field on planet X is estimated to be 0.03T, 600 times larger than on the Earth, and is found to point 70o above the horizon.
a) What is the magnitude of the force exerted by the filed on a 1km long vertical power line on Planet X, which carries 100A of current?
b) If the 1km stretch of wire is folded into a single square loop, what is the magnetic moment of this loop?
c) If the loop lies flat on the ground, calculate the effect of the B-field on it.

10. A turbine converts the rotary motion of a loop of wire into a 60Hz AC signal. At some instant in time, the normal of the loop is at an angle of 30o relative relative to a constant magnetic field. The loop has 20 turns of wire on a 0.35m2 frame, and sits inside a 1.7T field.
a) What is the magnetic flux in the loop?
b) If the coil is rotated so that the normal is at an angle of 45o a time 0.69ms later, what is the average induced voltage during this time period?
c) If the coil has a resistance of 100ohm , what is the average current that the turbine can generage in this time interval?

11. A coil consisting of 350 loops sits in the plane of this paper with a magnetic field pointing out of the page. The coil has a diameter of 10cm and a total resistance of 200ohm. The magnetic field increases from 2T to 3T.
a) How quickly must the field change in order to produce a 1mA current in the coil?
b) What is the direction of the current?

12. Consider a 15cm diameter coil of 100 loops of wire lying in the plane of this page, carrying a current of 2A (traveling clockwise). A straight wire running from left to right, also in the plane of the page, carries 1A.
a) What is the B-field in the center of the coil?
b) What is the magnitude of the force on the straight wire? You may assume that the magnetic field due to the coil is uniform inside the coil, and that it is zero outside the coil.
c) What is the direction of the force on the straight wire?

13. A 10cm radius coil sits in the plane of your paper on top of a long wire heading East (to the right of your page).
a) If a current of 3.7A flows clockwise through the loop, what is the magnitude and direction of the magnetic field at the section of the wire below the center of the loop?
b) What is the magnitude and direction of the force on the 20cm length of wire fight below the loop if its current is 2. 1 A due East? (Assume the field inside the coil is uniform.)

14. A coil of wire of radius 10cm lies in the plane of your paper. A 0.95T field points into the paper.
a) What is the magnitude of the magnetic flux through the coil?
b) If the coil is squashed to zero area within 0.5s, what is the induced voltage?
c) If the coil is rotated 200 in 0.05s, what is the induced voltage?
d) What is the direction of the current that flows in this loop in part (c)?

15. A coil consisting of 350 loops sits in the plane of this paper with a magnetic field pointing out of the page. The coil has a diameter of l0cm and a total resistance of 200
W. The magnetic field increases from 2T to 3T.
a) How quickly must the field change in order to produce a lmA current in the coil?
b) What is the direction of the current?

16. A 2.03A current travels through a horizontal power line 10.2m above your head, with the current flowing from West to East.
a) Determine the direction of the magnetic field at your location. Be specific: don't answer 'left' or 'right', but rather 'up', 'down', 'North', 'South', 'East', 'West', or something similar.
b) What is the magnitude of the magnetic field at your location?
c) If you are holding a 1m2 coil of 3 windings and 0.023 ohms, so that the coil is in a horizontal plane, 1.02m below the wire, what is the magnetic flux through the coil?
d) What is the maximum average current you can induce through this coil by rotating its position in 1 second?

17. A 4cm diameter coil of 30 windings sits in the plane of this page. A magnetic field of 2.0T faces into the page. The B-field is increased to 3.4T, inducing a 0.030A current in the coil.
a) What is the direction of the induced current?
b) How quickly was the field increased, if the coil has a resistance of 0.32 ohms?
c) What is the magnetic field at the center of the coil due to this induced current?

18. Consider a circular coil in the plane of this page. A current, I2, travels counterclockwise in the coil. A current, I1, travels from left to right in a straight wire above the coil (between you and the coil).
a) What is the direction of the force on the segment of the straight wire directly above the coil?
b) If I1 increases, does the induced current in the coil travel clockwise, counterclockwise, or is there no induced current?

Inductors
19. A 25mH inductor is connected in series with a 20ohm load, a switch, and a 12V emf. At t=0 the switch is closed.
a) Sketch the current in the circuit as a function of time.
b) What are the initial and final values of current in the circuit?
c) What is the initial and final voltage across the inductor?
d) What is the time constant of the circuit?
e) Calculate the current at t=2.5ms.

20. A 32mH inductor is in series with a 10k
W resistor. No current flows through them. Then, at t=0, a 12V battery is connected across the two.
a) What is the time constant of the circuit?
b) What is the current through the circuit at t=0, after one time constant, and at infinity?
c) Imagine replacing the inductor with a capacitor. If the current in this new circuit behaves the same as in part (b), what is the capacitance?

21. An inductor of 30mH is in series with a 12V DC source, a switch, and a 1k
W resistor. At t=0, the switch is closed.
a) After a sufficiently long time has passed, what will the current in the circuit be?
b) How long does it take to get 93% of the way from the initial current to this final value?
c) After a time much longer than that in part (b) has passed, the switch is turned to a new position so that the inductor and resistor are in series only with each other. How long does it take for the current to change by a factor of 2?

AC CIRCUITS:
1. Line voltage is about 110V at 60Hz in the US and Canada.
a) What is the maximum voltage that comes out of the wall socket at any instant of time?
b) What is the resistance of a 4-slice, 1600W toaster?
c) What is the capacitance that will allow the same current to flow when plugged into the wall socket?

2. (Multiple choice) Consider a DC power source in series with a switch, a resistor, an inductor, and a capacitor. Close the switch. The final value of current (as t goes to infinity)...
a) depends only on the resistor            b) is zero because of the capacitor             c) is large becasue of the inductor
d) is resonant                                    e) depends on R, L, and C

3. A 100ohm resistor is connected to a 60Hz power supply. The power supply has a peak voltage of 35V.
a) What are the peak and rms values of the current?
b) What are the peak and average values for the power dissipated by the resistor?
c) What inductance could one substitute for the resistor and get the same current flow?

4. An 8ohm speaker is driven by a 50W amplifier.
a) What is the peak current in the speaker?
b) What size capacitor will give the same peak current at 60Hz?
c) What size inductor will give the same peak current at 60Hz?

5. What is the root-mean-square of the following voltages: 0V, 10V, -10V, 0V, -5V, 5V?

6. An 8
W resistor, a 1.9mH inductor, and a 30mF capacitor are all connected in series to form a bandpass filter.
a) At what frequency do the reactances of the capacitor and inductor match?
b) Which reactance is bigger at 20Hz? What is its value there?
c) Which reactance is bigger at 20kFIz? What is its value there?

7. A lightbulb is rated at 500W at 115V (AC).
a) What is the maximm current through it?
b) What is the maximm voltage across it?
c) What is the maximum power dissipated by it?

8. An 8
W speaker is driven by a 50W amplifier.
a) What is the peak current in the speaker?.
b) What size capacitor will give the same peak current at 60Hz?
c) What size inductor will give the same peak current at 60Hz?

9. A 12V [DC] battery has an internal resistance of 1 ohms. Its terminals are connected to an 8 ohm resistor.
a) What is the terminal voltage of the battery?
b) What power is dissipated by the 8 ohm resistor?
If the DC battery is replaced by a 12V AC source, also with a 1 ohm internal resistance,
c) what is the maximum current delivered by the AC source?
d) What is the rms current delivered?

10. You have purchased a clothes drier that is rated at 1500W at 220V.
a) If the voltage supplied to the drier is at a maximum at t=0, write an expression for the voltage as a function of time. Specify whether your expression is in radians or degrees.
b) What is the maximum momentary power dissipated by the drier?
c) Write an expression for the current as a function of time. Again, specify whether your expression is in radians or degrees.
d) What is the current at t=0.01s?

11. An LRC circuit has a resonant frequency of 3183Hz. At some other frequency, it is noted that the inductor has a reactance of 12
W and the capacitor of 8W.
a) Is this frequency higher or lower than resonance?
b) What is the reactance of the inductor at resonance?
c) What are L and C?

12. A lightbulb is rated for 60W at 110V.
a) What are the peak values of the following quantities: Voltage, current, power, resistance?
b) For which of the following quantities is it appropriate to speak of an RMS value: Voltage, current, power, resistance?

13. Tinkering with your radio, you find that the capacitance in the tuning circuit (in MKS units) equals the inductance when you are listening to your favorite FM station at 106.3 MHz.
a) What is L?
b) What is C?
c) What is the inductive reactance at resonance?
d) If the resistance of the wire in the tuning circuit is 0.03
W, what is the impedance of the circuit at resonance?

14. An audio amplifier, equivalent to an audio oscillator with an 8.20
W resistor in parallel, delivers alternating voltages at audio frequencies to the speaker. If the source puts out an alternating voltage with an amplitude of 15.0V, and the speaker is equivalent to a resistance of 20.4W, what is the time-averaged power input to the speaker?

Transformers
15. (Multiple choice) A neon sign transformer operates at 60Hz and produces a secondary voltage of 9500V when 120V is applied to the primary coils. If the primary has 280 turns, the secondary has how many coils?
_____34000_____22000_____12000_____7800_____850?

16. Electric power is sent long distances over 700kV power lines.
a) Is 700kV the amplitude, the peak-to-peak, or the rms voltage?
b) Calculate the other two quantities referred to in part (a).
c) If a particular 700kV power line carries power from a 1GW power plant to consumers whose outlets are at 120V, how much total current do the consumers use? Transformers convert the 700kV to 120V.
d) How many residential customers (limited by their 150A fuse boxes) can this power plant serve?

17. A 3GW power plant is to 700kV power lines, which are connected to transformers that step it down to 110V.
a) What is the peak voltage across the power lines?
b) What is the maximum instantaneous power delivered by the power lines?
c) What is the average power delivered by the power lines?
d) What is the turns ratio of the transformers?
e) What is the total current delivered to the customers?

18. A 3GW power plant is connected to 700kV power lines, which are connected to transformers that step it down to ll0V.
a) What is the peak voltage across the power lines?
b) What is the maximum instantaneous power delivered by the power lines?
c) What is the turns ratio of the transformers?
d) What is the total current delivered to the customers?

19. Consider an AC transformer which converts 120V to 6V, and which has 20 coils on the secondary.
a) How many coils does the primary have?
If the secondary delivers 0.20A to some resistor,
b) what is the maximum current at the primary? The rms current?
c) What is the maximum power consumption at the resistor?

20. A 12V car battery has been connected to the primary of a transformer with a turns ratio of 20:1 (primary turns to secondary). After the system achieves a steady-state condition, one measures 3A flowing through the primary windings.
a) What is the voltage across the secondary windings?
b) What is the current flow through the secondary?
The battery is replaced with an AC voltage with 120V peak voltage. The maximum current flow in the primary is 3A.
c) What is the rms current through the secondary?

GEOMETRIC OPTICS
1. (Multiple choice) How long should it take light to travel the distance between the U.S. and Europe (about 5000km) underwater? The index of refraction for water is about 1.33.
_____22ms_____17ms_____17ms_____13ms_____10ms

2. A physics student stands with her eyes 1.8m above the ground at one end of a lake. On the opposite shore, 700m away, stands a tree.
a) If an image of the top of the tree appears in the lake at an angle 4.2o below the horizon, how tall is the tree?
b) What is the angle of refraction of this image of the treetop as it enters the water at point P if n=1.33 for water?

3. I am looking at a fish swimming below the surface of a lake.
a) If the light entering my eye from the fish travels at an angle of 60o above the horizon in the air, at what angle does that ray travel under the water? The index of refraction for water is 1.33.
b) Sketch two rays leaving the fish at this angle and exiting the surface of the water.
c) If the fish appears to be 25cm below the water's surface, how far below is it really? Find where the two rays leaving the water in part (b) would meet if you followed them back below the surface. This is where the fish appears to be.

4. Light enters a prism perpendicular to one face, and hits the next surface with an incident angle of 30o.
a) What is the angle between the two prism faces? (this is known as the apex angle of the prism.)
b) The ray of light enters the air again at an angle 15o away from the direction it entered the first surface. What is the index of refraction in the prism?
c) For a different wavelength of light, the index of refraction is exactly 1.500. How much is the incident beam deflected by going through the prism?

5. A piece of optical fiber consists of a cylindrical 'core' inside a concentric cylinder of 'cladding'. This particular fiber has a numerical aperture of 0.20, meaning that rays entering the core from the end of the fiber at angles less than
q such that sinq=0.20 will travel through the core and always be reflected at the boundary with the cladding. The index of refraction of the core is exactly 1.5.
a) At what angle, relative to the axis of the fiber, do rays travel inside the core?
b) At what angle, relative to the normal, do these rays reach the cladding?
c) What is the index of refraction of the cladding? Include enough significant figures to distinguish your answer from 1.5.

6. Light enters a prism perpendicular to one face, and hits the next surface with an incident angle of 30.
a) What is the angle between the two surfaces? (this is known as the apex angle of the prism.)
b) The ray of light enters the air again at an angle 5 away from the direction it entered the first surface. What is the index of refraction in the prism?
c) For a different wavelength of light, the index of refraction is exactly 1.500. How much is the incident beam deflected by going through the prism?

7. Ulexite, a clear borate mineral which crystallizes in a fibrous form resembling a bundle of optical fibers, has an index of refraction which depends on the direction of travel (and polarization). Along its three axes, n=1.491, 1.504, and 1.521. The speed of light in a vacuum is 2.9979´ 108m/s.
a) What is the fastest that light can travel inside ulexite?
b) What is the longest amount of time light can take to travel 3mm in ulexite?
c) If light travelling in the 1.521 direction hits the boundary with another crystal for which n=1.491, what angle in the first material leads to total internal reflection?

8. Two kids standing at the edge of a pier are dropping identical stones in a pond 3m apart every 2 seconds. The waves from the stones travel at 1.3m/s.
a) What is the wavelength of the disturbances caused by the stones?
b) At what angle(s) (relative to a line perpendicular to the pier) is the water least disturbed by the stones (i.e. the ripples are smallest in amplitude)?
c) If the kids continue to drop stones at the same frequency, but alternate, so that one stone is dropped by a kid every second, would the water in the direction perpendicular to the pier be calm or "choppy"?

Lenses
9. A diverging lens which has focal points at 2m from the lens is placed 6m from an object.
a) Use the appropriate equations to locate the image.
b) Calculate the magnification.
c) Is the image real or virtual?
d) Sketch a ray-tracing diagram, making sure to draw the three principal rays. It is not necessary for the sketch to be of drafting quality, but it should be clear which ray is which and what points each ray passes through.

10. An object is held 50cm away from a lens which forms a virtual image 37cm from the lens on the same side of the lens as the object.
a) What is the focal length of the lens?             b) Is this a converging lens or a diverging lens?
c) What is the magnification of the object?

11. Which of the following are true? (more than one answer)
_____ Lenses work because of refraction.
_____ Refraction occurs because the speed of light is different in different media.
_____ It is impossible for a diverging lens to create a real image from a real object.
_____ It is impossible for a converging lens to create a virtual image.
_____ The focal length of a convex mirror is positive.

12. How many of the following are true? (There is more than one answer.)
_____ Lenses work because of refraction.
_____ Refraction occurs because the speed of light is different in different media.
_____ It is impossible for a diverging lens to create a real image from a real object.
_____ It is impossible for a converging lens to create a virtual image.
_____ The focal length of a convex mirror is positive.

13. What is the focal length of a magnifying glass that produces a magnification of 4.00 when held 7.00cm from an object? Show a ray diagram (with all of the principal rays), and solve exactly.

14. A shopper standing 5.00 m from a convex security mirror sees her image with a magnification of 0.333. (a) Where is the image?
(b) Solve for the focal length of the mirror exactly, and show all of the principal rays in a ray diagram.

15. Another car is 20m behind yours. The rearview mirror creates a virtual image of this car which is 30m in front of your car.
a) Draw a ray diagram and trace the three principal rays.
b) What is the focal length of this mirror?
c) What is the magnification of the mirror?

Human vision
16. A nearsighted person has an uncorrected near point of 12cm and an uncorrected far point of 25cm.
a) What will the patient's prescription read? (What quantity, units, etc.?)
b) When the patient is wearing her new glasses, what range of distances can she focus on? (from what distance to what distance?)

17. A nearsighted patient has a far point of 1.3m.
a) Calculate the focal length of the appropriate corrective lenses for the patient.
b) Calculate the strength of these glasses.
c) If the patient's uncorrected near point is 12 cm, what is it with the glasses on?

18. An optometrist prescribes you a pair of glasses of -6.00 diopters. What condition will these glasses correct? If the glasses listed above replace your old prescription of -6.10 diopters, are your eyes getting better or worse?

19. A newborn is said to be able to focus on objects about 30 cm away.
a) If this is his far point, prescribe glasses for him, assuming that he wants to be able to read the newspaper, 25cm away.
b) If the baby's eyeball is 2.5 cm from front to back, what is the focal length of his eyeball when he focuses at an object 30 cm away, it if causes an image to form on the back of his eyeball?

20. Answer true or false these questions about optical systems:
a) _____ Nearsightedness may be due to having too strong a lens in one's eye.
b) _____ Farsightedness may be due to having too short an eyeball.
c) _____ For a magnifying glass, the angle subtended by the object on the retina is the same as the angle subtended by the image on the retina.
d) _____ The image made by the objective of a microscopy is the best object for the eyepiece.
e) _____ Magnifying glasses or microscopes work by bringing images as close as possible to the eye.

21. A magnifying glass is  used to look at a grasshopper.
a) If it says "8×" on the magnifying glass, and if it is used to put an image of the insect at your focal point, then how much larger will this image be than the object?
b) What is the focal length of the lens?
c) If your near point is at 25 cm, then how close must the insect be to the glass to get the image to appear at your near point?

22. A normal human can focus on objects between about 25cm and infinity.
a) Calculate maximum and minimum values of the strength of the eye's lens, given that an image is formed on the retina 2.5 cm behind the lens?
b) By what percentage does the strength change during accommodation?

23. Your instructor is badly myopic and needs -8D glasses to see well.
a) How far can he see clearly without the glasses?
b) What is his uncorrected near point if his corrected near point is 25cm?
c) Draw a ray diagram for this last case, showing the principal rays, the object and image.

24. A nearsighted person has an uncorrected near point of 12cm and an uncorrected far point of 25cm.
a) What will the patient's prescription read? (What quantity, units, etc.?)
b) When the patient is wearing her new glasses, what range of distances can she focus on? (from what distance to what distance?)

25. You are an optometrist. A patient comes into your office requiring bifocals. The strength of the lenses are +l.5D and -1.5D.
a) What is your patient's uncorrected near point?
b) What is your patient's uncorrected far point?

PHYSICAL OPTICS:
1. Fill in the blanks with an appropriate choice. (There may be more than one correct answer.)
The phenomenon of ______________ is the most compelling demonstration that light is a transverse wave.
The process by which the eye changes its 'focus' is called _________________.
Reflected light is shifted 180o when ________________________________________________.

2. A beam of 3cm microwaves hit a metal screen with two vertical 5cm wide slits in it. The slits are side-by-side and have a 5cm divider between them. Microwaves are a form of electromagnetic radiation, and are reflected by metals.
a) If one of the slits was covered, what would be the angular width of the central diffraction maximum?
b) How many interference maxima are there? (Be sure to include the zeroth maximum if there is one, and maxima on both sides of it.)
c) How many interference maxima are there inside the central diffraction maximum? (Include maxima on either side of the center, and include the center if appropriate. Include the maximum at the edge of the central diffraction maximum, if there is one.)

3. Answer the following true/false questions:
_______Rainbows are examples of Rayleigh scattering.
_______If unpolarized light enters a polarizer, the intensity of transmitted light is independent of the angle at which the polarizer is held.
_______Colors observed in looking at soap bubbles are examples of dispersion.

4. Answer true or false these questions about physical optics:
a) _____ Clouds ar white because of Rayleigh scattering.
b) _____ If unpolarized light enters a polarizer, the intensity of light leaving the polarizer depends on the angle at which the polarizer is held
c) _____ The positions of the intensity maxima from a many-slit interference pattern are the same as the positions of the maxima from a two-slit pattern.
d) _____ One does not hear intensity maximum and minima from two audio speakers less than, say, 10m because the interference maxima would be too close together.
e) _____ One does not see diffraction around a picket fence because the spacing between the pickets is too big.

5. Light enters a prism normal to one surface and leaves another surface tilted 30o with respect to the first surface.  The index of refraction for red light (700 nm) is 1.334.
a) At what angle (relative to the second normal) does the light leave the second surface?
b) What must be the index of reflection for violet light (400 nm) in order for it to be bent 5o more than the red?
c) What would be the distance between lines in a diffraction grating in order to give the same angular distance between red and violet in the first-order maxima?  (Notice: for such small angles, sinA - sinB = sin(A-B).)

6. Consider the note "A" (f = 440 Hz) entering an acoustically insulated room (no echoes) from two doors. Each door is 1.2m wide.  Sound travels from the doors to a stage 20m away. The speed of sound in the room is 340 m/s.
a) What is the wavelength of the sound?
b) What is the width of the central diffraction maximum on the stage?
c) If the fifth interference maximum is also the second diffraction minimum, then what is the distance between the centers of the two doors?

7. Which of the following effects (more than one answer) reveal the wave nature of light?
_____ Polarization_____ Dispersion _____ Diffraction _____ Interference _____ Refraction

8. A diffraction grating has 5000 lines per cm.
a) At what angle is red light of 650 nm wavelength bent for the first interference maximum?
b) How many such maxima would occur between 0o and 90o?

9. Circle each of the following which are examples (or results) of Rayleigh scattering:
a) clouds.......................................................b) the sky on a cloudless day
c) your exhaled breath on a cold day............d) red sunsets

10. Two 1-m wide doorways in a physics lecture room are located with their centers 6m apart.  A stereo in the hallway plays a work by Philip Glass which consists of a 980 Hz tone repeated over and over.
a)  If one door is closed, and if we can ignore reflections, what is the smallest angle from the other doorway where you can sit and hear nothing?  The speed of sound is about 340 m/s.
b) If both doors are open, what is the smallest angle at which you could sit and hear nothing?

11. A microscopic layer of some transparent material with an index of refraction of 1.50 sits on the surface of a lake (n=1.33).
a) Does this system resemble an 'oil slick' or a 'soap bubble' as far as interference effects are concerned?
b) If the layer were  perfectly thin, how would it appear if you looked at it at normal incidence? (What kinds of light would reflect off it well, which would not reflect well)?
c) If the layer instead has a finite thickness, it will have some colored sheen to it. If green, 550nm light is seen in normal reflection off the film, what is the minimum thickness of the layer?
d) For the same thickness as calculated in (c), what visible wavelengths, if any, will destructively interfere on normal reflection?

12. Light of 280
mm shines through two identical slits of finite width. The slits are each lmm wide and are 3mm apart.
a) At what angle is the first dark diffraction band?
b) Which interference maximum or minimum (state which one) occurs at this angle?
c) How many bright interference bands occur within the 'central diffraction maximum'? Don't include the answer to part (b), even if it qualifies as a bright band.

13. A microscopic layer of some transparent material with an index of refraction of 1.50 sits on the surface of a lake (n =1.33).
a) Does this system resemble an 'oil slick' or a 'soap bubble' as far as interference effects are concerned?
b) If the layer were perfectly thin, how would it appear if you looked at it at normal incidence? (What kinds of light would reflect off it well, which would not reflect well)?
c) If the layer instead has a finite thickness, it will have some colored sheen to it. If green, 550nm light is seen in normal reflection off the film, what is the minimum thickness of the layer?
d) For the same thickness as calculated in (b), what visible wavelengths will perfectly destructively interfere on normal reflection?

14. Fill in the blanks with an appropriate choice. (There may be more than one correct answer.)
The phenomenon of________________is the most compelling demonstration that light is a transverse
wave.
The process by which the eye changes its 'focus' is called_______________.
Light is shifted 180 when it reflects off___________________.

15. A beam of 3cm microwaves hit a metal screen with two vertical 15cm wide slits in it. The slits are side-by-side and have a l0cm divider between them. Microwaves are a form of electromagnetic radiation, and are reflected by metals.
a) If one of the slits was covered, what is the width of the central diffraction maximum on a screen lm away?
b) How many interference maxima are there? (Be sure to include the zeroth maximum if there is one, and maxima on both sides of it.)
c) How many interference maxima are there inside the central diffraction maximum? (Include maxima on either side of the center, and include the center if appropriate. Include the maximum at the edge of the central diffraction maximum, if there is one.)

16. Answer the following true/false questions:
--Rainbows are examples of Rayleigh scattering.
--If unpolarized light enters a polarizer, the intensity of transmitted light is independent of the angle at which the polarizer is held.
--Colors observed in looking at soap bubbles are examples of dispersion.

17. A microscopic layer of some transparent material with an index of refraction of 1.65 sits on the surface of a lake (n=1.33).
a) Does this system resemble an 'oil slick' or a 'soap bubble' as far as interference effects are concerned?
b) If the layer were perfectly thin, how would it appear if you looked at it at normal incidence? (What kinds of light would reflect off it well, which would not reflect well)?
c) If the layer instead has a finite thickness, it will have some colored sheen to it. If red, 650nm light is seen in normal reflection off the film, what is the minimum thickness of the layer?
d) For the same thickness as calculated in (c), what visible wavelengths, if any, will destructively interfere on normal reflection?

18. A pair of slits produces a light pattern on a distant screen which is a combination of 2-slit interference and single-slit diffraction. Describe one attribute of the pattern that is a result of interference and one attribute which is the result of diffraction. How can one tell by looking at the pattern that the slit separation is larger than the individual slit widths?

19. A beam of 4cm microwaves hit a metal screen with two vertical 5cm wide slits in it. The slits are side-by-side and have a 10cm divider between them. Microwaves are a form of electromagnetic radiation, and are reflected by metals.
a) If one of the slits was covered, what would be the angular half-width of the central diffraction maximum?
b) How many interference maxima are there? (Be sure to include the zeroth maximum if there is one, and maxima on both sides of it.)
c) How many interference maxima are there inside the central diffraction maximum? (Include maxima on either side of the center, and include the center if appropriate. Include the maximum at the edge of the central diffraction maximum, if there is one.)

20. A layer of water (n2=1.33) sits on a glass slide (n3=1.50).
a) Does this system behave as a "soap bubble" or an "oil slick"? Why?
b) If the layer of water is exactly one micron thick, what visible wavelengths (400-700nm) will reflect most intensely?
c) What visible wavelengths will reflect least intensely?

21. 632.8nm HeNe light is incident on a single slit of width 1.5
mm.
a) At what positive angles,
q, relative to the stit does a dark band occur?
b) If a pattern of bright and dark fringes is observed on a screen 10cm form the slit, how wide is the central bright fringe on the screen?

RELATIVITY:
1. Two spaceships approach each other as each passes a nearby planet at 0.99c, that is, the speed of each spaceship relative to the planet is 0.99c.
a) At what speed do these ships approach each other?
b) The pilot on spaceship A is dieting, and measures him/herself to be about 70kg. What do the people in spaceship B measure for the dieting pilot's mass?
c) The same pilot is 25cm thick from front to back. What do the passengers on the other spaceship measure, assuming the pilot is facing in the direction of travel?
d) Energy and mass are equivalent, so we can express energy in terms of rest mass. How much energy must have been exerted at some point to accelerate this spaceship from rest on the nearby planet? Please give your answer in units of moc2, the rest energy.

2. Answer true or false these questions about relativity:
a) _____ If an astronaut travels toward a distant star at 0.99c, she will observe her twin who remains on Earth appear to age less rapidly than she.
b) _____ If an astronaut travels toward a distant star at 0.99c, her twin who remains on Earth will observe her to age less rapidly than she.
c) _____ One implication of Einstein's second postulate is that, if you shine light through water, its speed will be independent of whether the light is moving.
d) _____ The starship Enterprise hurtles through space at 0.999c. It would be common for people to celebrate their 300th birthdays, given today's medical technology.
e) _____ There is no inertial reference fram for which a meter stick appears twice as long.

3. Answer true or false these questions about relativity:
a) _____ The Earth is, strictly speaking, not an inertial reference frame.
b) _____ If we could speed up a clock to travel at the speed of light, it would appear to a stationary observer to not be running.
c) _____ There exists an inertial reference frame in which you would hear the sound of a baseball hitting a ball before you would see it.
d) _____ If a 4m long car travels through a 4m long garage, a person in the garage sees the car as shorter than the garage.  (The car fits inside.
e) _____ If a 4m long car travels through a 4m long garage, the driver sees the garage as shorter than the car.  (The car doesn't fit inside.)

4. An astronaut Larry, aged 20, leaves his twin Laura on earth while he travels to Alpha Centauri, from which it takes light 4 years to travel. Larry wants to get there and back for Laura's 30th birthday, so he travels at 0.8c.
a)  How far does Larry measure the distance to Alpha Centauri?
b)  How much older is Larry when he returns?
c)  Larry and Laura remain in radio contact.  How much faster or slower does Larry observe Laura's clocks to be running?
d)  From part (c), what would Larry expect Laura's age to be when he returned, given the rate of Laura's clocks? (The difference between this number and 10 years is accounted for by the fact that as Larry turns around at Alpha Centauri, he has to accelerate, and so is no longer in an inertial reference fram.  During the time it takes him to turn around, Laura ages quite rapidly.

5. If the Sun were an inertial reference frame, would the Earth also be one?  Would the Moon?  Explain.

6. The Klingons are chasing the Starship Enterprise at 0.7c, relative to a nearby planet, while the Enterprise is travelling at 0.6c relative to the same planet.
a) How fast do the Klingons measure themselves to be closing in on the Enterprise?
b) An observer on the planet measures the distance between ships to be 5 light minutes.  How far do the Klingons measure it ot be?
c) How long do the Klingons measure for the time needed to catch the Enterprise and how long do the 'ground observers' measure?

7. Two astronauts, Pat and Mike, pass each other in identical spaceships.  Pat sees the Moon approaching her ship at 0.90c, and Mike approaching at 0.99c.
a)  For Pat, what is the ratio of the height of the Moon to its width?
b)  What is the speed of Mike's vessel, relative to the Moon?
c)  If Pat measures her vessel to be 300m long, how long will Mike measure it to be?

8. A spacecraft travels between Earth and Mars.  Which observer -- one on Earth or one on the spaceship -- will measure the 'proper time' for the length of the trip?  Which one measures the proper length for the distance between the planets?

9. The oppossum ('marsupialis virginiania', for example) is about 90 cm long and lives only about one year, owing to its almost total lack of defense against predators.  The raccoon ('procyon lotor') has a length of about 83 cm and lives an average of about 10 years.  (Hence the expression -- "I ain't seen you in a 'coon's age.')
a) If a ground-based raccoon sees a spaceship full of 'possum that seem to have a mean lifespan befitting a raccoon, how fast is the spaceship moving relative to the ground?
b) What length does the 'coon measure for the typical length of a 'possum?  (Neither animal is particularly noted for its eyesight.)
c) What is length of the raccoon as viewed from the spaceship?

10. An Earthside observer, Pat, watches an astronaut, Mike, pass by in a spaceship. Meanwhile a missile is fired from Earth. What variable names would you give each of the following quantities?  (No equations, please!)
a) Mike's velocity as measured by Pat
b) the velocity of the missile as measured by Mike
c) Mike's measurement of his own ship

11. Two spaceships approach the Earth from opposite directions.  If each one approaches the Earth at 0.9c, their relative speed is
a) zero................b) between zero and 0.9c.................. c) between 0.9c and c...............d) between c and 1.8c.......e) 1.8c

12. Two spaceships approach each other at 0.95c.  Spaceship A is traveling at 0.8c relative to a nearby planet.
a) What is the velocity of Spaceship B, relative to the planet?
b) The science officer aboard Ship A measures the ship's mass to be 2.3 × 107 kg.  What does her colleague on the planet measure for Ship A's mass?
c) The chief engineer on Ship A measures Ship B to be 24m long.  What does someone on Ship B measure for its length?

13. The new Air Force F32 bomber cruises at 0.01c. Its manufacturer says that this speedy number is exactly 10m long and has exactly 8000kg mass.
a) What does ground control measure for its length when it is flying overhead?
b) What does ground control measure for its mass when it is flying overhead?
c) What is its kinetic energy? (Do not use the classical formula)
d) If the bomber uses a matter-antimatter drive which converts directly into energy, how much mass needed to be converted to achieve its final kinetic energy?

14. Two spaceships approach Earth from opposite directions, each travelling at 0.5c relative to the Earth.
a) At what rate are the two spaceships approaching each other?.
There are three observers in this problem, the captain of one ship, the captain of the other ship, and an observer on the Earth. Each spaceship is manufactured to be 300m long.
b) Which observer measures the longest length for the length of the ship? How long is that?
c) Which observer measures the shortest length for the ship? How long is that?

15. One object of lkg slams into another object at rest. The first particle goes from travelling at 0.9c to the right to travelling at 0.5c to the right. The second object ends up travelling at 0.4c to the right
a) What is the initial momentum of the first object?
b) What is that object's total initial energy?
c) What is the mass of the second object, if the total momentum is conserved?

16. The new Air Force F32 bomber cruises at 0.01c. Its manufacturer says that this speedy number is l0m long and has an 8000kg mass.
a) What does ground control measure for its length when it is flying overhead?
b) What does ground control measure for its mass when it is flying overhead?
c) What is its kinetic energy? (Do not use the classical formula)
d) If the bomber uses a matter-antimatter drive which converts directly into energy, how much mass needed to be converted to achieve its final kinetic energy?

17. Two spaceships approach each other as each passes a nearby planet at 0.99c, that is, the speed of each spaceship relative to the planet is 0.99c.
a) At what speed do these ships approach each other?
b) The pilot on spaceship A is dieting, and measures him/herself to be about 70kg. What do the people in spaceship B measure for the dieting pilot's mass?
c) The same pilot is 25cm thick from front to back. What do the passengers on the other spaceship measure, assuming the pilot is facing in the direction of travel?
d) Energy and mass are equivalent, so we can express energy in terms of rest mass. How much energy must have been exerted at some point to accelerate this spaceship from rest (relative to the planet)? Please give your answer in units of moc2, the rest energy.

18. Two identical space utility vehicles, built to specifications of 91.4m and 43000kg, find themselves approaching on Intergalactic Highway I90. Your vehicle is doing 0.6c (relative to the Earth), which is the legal speed limit on the expressway in congested areas. Your laser Doppler meter gives the approaching craft's speed as 0.9c.
a) Is the approaching craft violating the speed limit? What is its speed, relative to the Earth?
b) What does your navigation system measure for the other craft's length and mass?
c) What does the other craft measure for your length and mass?
d) Which craft does an observer on Earth measure as shorter, and which as heavier?

19. A 2kg mass is accelerated by a constant 3N force. What is the acceleration of the object when v=0.9c?

20. A space cruiser approaching the Earth at 0.6c fires a nuclear torpedo at New York City. New Yorkers measure the closing speed of the torpedo to be 0.99c.
a) What is the muzzle velocity of the torpedo?
b) If scientists in New York calculate that they have twenty minutes until impact, how much time will elapse on the torpedo's clock between its launch and its landing?

21. Two spaceships approach each other at 0.90c. Spaceship A is traveling at 0.60c relative to a nearby planet.
a) What is the velocity of Spaceship B, relative to the planet?
b) The science officer aboard Ship A measures the ship's mass to be 1.00´ 107 kg. What does her colleague on the planet measure for Ship A's mass?
c) The chief engineer on Ship A measures Ship B to be 100m long. What does someone on Ship B measure for its length?

22. A muon is an unstable particle that has a lifetime of 2.20microsecond in its rest frame. If it is travelling at 0.990c relative to the ground,
(a) What does the Earth-bound observer measure for its lifetime?
(b) How far does the muon "think" it travels before disintegrating?
(c) How far does the Earth-bound observer think it travelled?
(d) How can parts (b) and (c) be consistent?

23. Two particles have rest masses of 90MeV/c2 each. Initially, one of them is at rest in the lab frame, and the other is approaching it at 0.5c.
a) What is the rest mass of the particles in MKS units?
b) What is the total initial energy of the moving particle in the lab frame in MeV?
c) Classically, we might imagine the two particles suffering an inelastic collision in which they both move in the same direction with v=0.25c. Show relativistically that this cannot happen.

MODERN PHYSICS:
1. The human body has a temperature of 37C (310K, 98.6F). Making the appropriate assumptions about the body,
a) What can you say about the peak region of radiation emitted by the human body?
b) If you run a fever of 103F (40C), by what percentage does the amount of radiation emitted by your body increase?

2. The Sun has an inner temperature of about l08K. Its surface temperature is such that its radiant output is in the visible -- let's say 550nm.
a) What is the Sun's surface temperature?
b) The Earth's surface temperature averages about 300K. A global change of about 10K would probably be disastrous to life as we know it. If this change in temperature is due to a decrease in the sunlight hitting the Earth, what percentage decrease would have to occur to see this large a global cooling?

3. Two identical objects are in the same surroundings at 0° C. One is at a temperature of 500K, and the other is at 400K. Find the ratio of the net power emitted by the hotter object to the net power emitted by the cooler object.

4. In a laboratory experiment designed to duplicate Thomson's determination of e/m, a beam of 6.00´ 107m/s electrons enters a 5.00mT magnetic field. The beam moves perpendicular to the field in a path having a 7cm radius of curvature. Determine e/m from these observations. Is this value consistent with the accepted value?

5. In a Millikan oil drop experiment, a 500V potential difference is applied to plates separated by 2.20cm.
a) How many electrons of charge does an oil drop of 1.07´ 10-14kg have, if it is suspended motionless between the plates?
b) What is the diameter of the drop, if it has a density of 0.9g/cc?

Planck
6. The energy of a visible photon of light is
a) less than 1 eV                 b) between leV and 13.6 eV                c) 13.6 eV                d) greater than 13.6 eV

7. A flashlight at rest is released in space by a careless astronaut. The light is emitting 10W of light, with an average wavelength of 580nm.
a) What is the energy of a photon of this wavelength?
b) What is the momentum of such a photon?
c) What is the rate at which these photons are produced?

8. A 20keV electron, from inside a TV set, has a mass of 9.11´ 10-31kg.
a) What is its wavelength?
b) What is the wavelength of a photon of the same energy?
c) Which of these two has the larger momentum?
Bohr
9. Quantum theory should explain large objects as well as small ones. According to Bohr's model, electrons in an atom occupy certain stable orbits of well-defined radius. Man-made satellites, however, are observed to spiral continuously into the Earth before crashing. If this observation can be reconciled with quantum theory, what does this say about the quantum number, n, and spacing between orbits for the satelite?

10. The most energetic photon that can come from an atomic transition in a hydrogen atom is nearest
a) 1 Angstrom                b) 1 nm                c) 10 nm                d) 100 nm

11. Is the energy of a photon emitted as a hydrogen atom goes from one state of very high quantum state to the next lower state much larger or much smaller than l0eV7

12. A hydrogen atom emits a photon of approximately 13.2eV energy.
a) What is the frequency of the photon?
b) What was the initial quantum number of the atom?

13. Is the wavelength of a photon emitted as a hydrogen atom goes from one state of very high quantum state to the next lower state too long or too short to be seen by the human eye?

14. Just as most astronomical objects have not yet been named, so too with the spectral lines for the hydrogen atom. Let's imagine that we want to name one such series after my mom -- the 'Leedom series'. Let's choose a set of lines that nobody has probably yet claimed, the transitions in which the electron winds up in the n=983 level.
a) Write an expression for the wavelength of any arbitrary line in the 'Leedom series'. Include enough information so that someone not familiar with the Balmer or any other series can calculate those wavelengths.
b) What are the shortest and longest possible wavelengths in this series?

15. A hypothetical atom has 5 levels, the highest one at E5=0. The Lyman series of this atom consists of the following wavelengths: 517nm, 1033nm, and 3100nm. Calculate E1 through E4.

16. What are the limits in energy of...
a) the hydrogen Paschen series?
b) the hydrogen nf=5 series?
c) Do these two series overlap?

17. The kinetic energy of a molecule in the Sun's chromosphere (its outer layer) is 0.50eV. This not enough to ionize a hydrogen atom in its ground state, but it will ionize a more energetic hydrogen atom.
a) What is the quantum number, n, of the lowest-lying energy state of hydrogen that can be ionized by 0.50eV?
b) What is the momentum of an electron in that state? (Hint: Its KE is equal to the magnitude of its total energy)
c) What wavelength of photon is produced when an electron falls from the state calculated in part (a) to the next lower state?
deBroglie
18. The 'wavelength' of a marathon runner is
a) smaller than the nucleus
b) smaller than the atom but larger than the nucleus
c) comparable to the size of the runner
d) there is no such thing

19. An 80kg student has grown concerned about being diffracted while passing through a 75cm wide doorway. Assuming that significant diffraction occurs when the width of the diffraction aperture is less than 10 times the wavelength of the wave being diffracted,
(a) Determine the maximum speed at which the student can pass through the doorway in order to be significantly diffracted.
(b) With that speed, how many years will it take the student to pass through the doorway if it is 15cm thick?

20. a) Calculate the wavelength of a photon that has the same momentum as a proton moving at 2.33% of the speed of light
b) What is the energy of the photon in MeV?
c) What is the kinetic energy of the proton in MeV?
Heisenberg
21. If your mass is about 1032 times greater than that of an electron in the ground state of hydrogen, and the uncertainty of the x-component of your momentum is the same as for the electron, then what is the minimum uncertainty in your position, approximately?

22. A hydrogen atom emits a photon as its electron falls from a state practically at En=0 to the second lowest energy level.
a) What is the wavelength of the photon?
b) What is the radius of the final energy state?
c) If the photon is confined to that atom, then
Dx=2r. What is the uncertainty in the photon's momentum?
d) Given that photons obey deBroglie's equation, compare p to
Dp.

23. Consider the tenth lowest energy level of a hydrogen atom.
a) Calculate the uncertainty in position, if we equate it with twice the radius of the electron's orbit.
b) Calculate the uncertainty in the horizontal component of momentum, if we equate this with twice the
magnitude of the momentum, and the kinetic energy equals 1.36meV.

24. One of the most important questions about the atom is why the energy levels of the electron are quantized. For each part, give the name of the physicist who suggested the following reasons for energy quantization:
________because angular momentum is conserved?
________because the electron sets up 'standing wave patterns'?
________because we don't know the direction of the electron's momentum?

25. An electron in the ground state of a hydrogen atom is confined so that its position is uncertain by 0.5A.
a) What is the uncertainty in its velocity?
b) What is the fractional uncertainty in its velocity if it has a nonrelativistic kinetic energy of 13.6eV?

26. Application of the Uncertainty Principle to the ground state electron in hydrogen gives a minimum uncertainty in its position of about what?

27. We wish to put a dust particle of 1
mg mass into a quantum state such that its quantum uncertainty in position equals its size of 0.1mm.
a) What is the corresponding minimum uncertainty in its momentum?
b) If the kinetic energy of the particle is 10-17J, what is the fractional uncertainty in its momentum?

28. a) What is the lowest energy for a photon in the Balmer series?
b) What is the momentum of this photon?
c) If we don't know which way the photon is moving,
Dpx=p. What is the smallest uncertainty we can ever have of its position?

29. A 400ng sample of americium is confined to the insides of a smoke detector. It has been measured using advanced laser Doppler technology to be moving at less than lnm/s.
a) Does lnm/s give us the upper or lower limit for the americium sample's wavelength?
b) What is that limit? (the wavelength)
c) What is the smallest possible uncertainty in the americium's position?

30. Consider Bohr's model of the hydrogen atom. Consider the third electron energy level. Its kinetic
energy equals the magnitude of the total energy of that state, which is nonrelativistic.
a) Calculate the momentum of the electron in this state.
b) Calculate the uncertainty in the momentum, assuming the same Dpx=1.41p we used in class for the ground state.
c) Calculate the uncertainty in position, using
Dx =1.41r, where r is the radius of the electron's orbit.
d) Are the results of (b) and (c) consistent with the laws of quantum mechanics? Why or why not?

31. Consider a simple sugar molecule, C6H12O6, in which the hydrogen is 1H, the carbon is 12C, and the oxygen is 16O. Let's estimate the size as about 0.5nm, and assume that its position can be located to within 1% of that size.
a) What is the quantum uncertainty in the molecule's speed?
b) If we set the minimum momentum equal to
Dp, then what is the wavelength of this particle?

32. a) If the position of a chlorine ion in a membrane is measured to an accuracy of 0.63 microns, what is its minimum uncertainty in velocity, given its mass is 5.86´ 10-26kg?
b) If the ion has this velocity, what is its kinetic energy in eV?
Nucleus
33. In Rutherford's scattering experiments, alpha particles are fired at a "fixed" nucleus. If that nucleus is
, how energetic must the alphas be to just barely reach the surface?

34. 126C has a mass of exactly 12u. If it can be formed by combining two 63Li atoms of mass of 6.015121u, is energy released or absorbed by the reaction?

35. The half-life of 14C is 5730yr. Carbon dating using this half-life was used by scientists to judge the age of the Shroud of Turin, a cloth believed by some to have been manufactured about 2000 yr ago, but shown by carbon dating to be only about 670yr old.
a) The radioactivity of the sample of the Shroud used for carbon dating would be what fraction of its original activity if it were 670 years o1d?
b) What would be the age of the Shroud if the activity were 79% of its original value?

36. TRUE/FALSE
-- We can measure the radii of nuclei by letting alpha particles approach them and determining when the distribution of scattered alpha particles cannot be explained by electric forces alone.
-- If an electron is not moving, then it is everywhere.
-- DeBroglie's equation can be used to explain the quanfizafion of electron states in hydrogen.
-- Bohr's Postulates can be used to explain the spectra of all of the elements.
-- Cathode rays are not waves.

37. A tritium nucleus (31H ) is fused to a deuterium nucleus (21H) to form (42He) and a neutron.
a) If the mass of the tritium nucleus is 3.01605u, what is its binding energy?
b) If the mass of the deuterium nucleus is 2.0140u, and the mass of the helium nucleus is 4.00260u, is energy released or absorbed in the reaction? How much?

38. The radius of a certain nucleus is as many fm as the radius of a hydrogen atom in its third lowest energy state is in Angstrom. What can we say about the nucleus?

39. The ratio of the radius of the largest naturally-occurring nucleus to the smallest is about
a) 1                b) 6                c) 92                d) 238

40. What is the approximate mass density of the nucleus of 23892U in MKS units?

41. The volume of a hydrogen atom is larger than the volume of a hydrogen nucleus by how many orders of magnitude? (Answer 'two' if it is larger by 100, 'ten' if larger by 10x, etc. I'll give you credit if you are within three orders of magnitude.)

42. 12656Te has a mass of 125.903314u. If it can be formed by combining two 6326Fe atoms of mass of 62.94075u, is energy released or absorbed by the reaction?

43. A 'neutron star' can be thought of as a gigantic nucleus. If a particular neutron star has a mass of 1033kg, how large is it?

44. An atom of radon 222 (22286Rn) decays by alpha emission into polonium.
a) What are the atomic number and atomic mass of polonium?
b) If the radon atom has a mass of 222.017570u, and the alpha particle has a mass of 4.00260u, and the alpha particle has an energy of 5.59MeV, then what is the mass of the polonium atom?

45. From the chart of isotopes given below,
a) Calculate the mass defect of 19F.
b) Calculate the binding energy of 19F.
c) Is energy released or absorbed in the reaction 8Be--> 4He+ 4He? How much?

46. The half-life of 14C is 5730yr.
a) The bones of one of your ancestors of 23 generations ago (Assume about 27yr per generation.) woud be how much less radioactive now than when she was alive? (assuming that 14C is the only source of radioactivity)
b) How long would it take 14g of radioactive carbon to decay (statistically) to a dozen remaining atoms?

47. a) 400ng of americium has been sitting on a lab bench for a week without moving any more than 0.lmm. What is the minimum uncertainty in its position at any point in time?
b) If it had moved 0.lmm in one week, what would its wavelength be?

48. The isotope 218O has a mass of 21.008730u. 219F has a mass of 20.999948u. Both decay by beta emission.
a) What is the binding energy of the oxygen isotope?
If a 21O isotope decayed by beta emission to 21F,
b) would it be
b+ or b-?
c) how much energy would be given off or absorbed? (Which?)

49. Consider the reaction: 2H+ 3H --> 4He + X
a) What is the unknown reaction product, X?
b) How much energy is given off absorbed in this reaction? Is it given off or absorbed?
c) What is the binding energy of 4He?

50. The mass of the
atom is 239.05216u.
a) What is its mass defect?
b) What is its binding energy?
c) How much energy is released if it fissions into
(163.93920u), (63.92796u), and a bunch of neutrons (1.008665u)?
The mass of a hydrogen atom is 1.007825u.

51. Consider the reaction 4He + n ---> 2H + X
a) What is the particle X?
b) Is energy absorbed or emitted in this reaction? How much?
c) What is the binding energy of 4He?

Subnuclear particles
52. a) Given the tables of quarks and hadrons below, find the binding energy of the proton (uud).
b) Give a reason why the reaction n-->p+e cannot occur.
c) Calculate the energy given off by the reaction K- +p-->Z+
p.

53. Consider the reaction: K- + p -->
S+ +p-
a) Verify three absolute conservation laws for this reaction. (Obviously, we don't have enough information to prove for example, momentum conservation.)
b) How much energy is given off or absorbed in this reaction? Is it given off or absorbed?
c) Calculate the binding energy of the K- particle, given its mass in the table below. (In the actual exam, it would actually be there.)

54. A theorist has assigned the up and down quarks each a mass of 335MeV/c2, and the strange quark a mass of 340MeV/c2.
a) Calculate the binding energy of a 938.3MeV/c2 proton (uud), assuming these quark mass values.
b) Calculate the mass defect of a 494MeV/c2 kaon-plus (u, s-bar).

55. The half-life of a neutron (outside of the nucleus) is 10.6min, after which it decays by beta emission to become a proton.
a) What kind of beta emission is it, positive or negative?
b) How long would one need to wait after entering a room full of Avogadro's number of loose neutrons before there was approximately only one left?


56. The Sun has an inner temperature of about 108K. Its surface temperature is such that its radiant output is in the visible -- let's say 550nm.
a) What is the Sun's surface temperature?
b) The Earth's surface temperature averages about 300K. A global change of about 10K would probably be disastrous to life as we know it. If this change in temperature is due to a decrease in the sunlight hitting the Earth, what percentage decrease would have to occur to see this large a global cooling?

57. When x-rays pass through a one-atomic-layer thick gold foil, the holes between atoms behave like interference slits.
a) If the atoms are 5×10-10m apart, what wavelength x-ray will cause the first interference maximum to occur at 100?
b) How many interference maxima will occur between -90o and 90o?

58. An electron can travel in a straight line in
a) a uniform E-field perpendicular to the electron's path.
b) an E-field and B-field both parallel to the electron's motion
c) E-field and B-fields perpendicular to each other and the electron's motion
d) a uniform B-field perpendicular to the electron's path

59. TRUE / FALSE
_____ Lasers are more efficient at converting energy into light than most light sources.
_____ The energy of  an electron's orbit decreases as "n" increases.
_____ "The whole is greater than the sume of the parts", as far as the mass of nuclei and the masses of neutrons and protons is concerned.
_____ The density of mass in a nucleus is roughly the same for 1H as it is for 238U.
_____ Cathode rays are not particles.

60. In Chapters 25-31 we have sometimes had to abandon the laws of classical physics to explain observed phenomena, as happened with Relativity.  Cite an instance where the laws of modern physics contradict those of classical physics, and explain why the laws of classical physics are violated.

61. The kinetic energy of a molecule of air at standard temperature and pressure is about 1/40eV.  This is certainly not enough to ionize a hydrogen atom in its ground state, but it will ionize a more energetic hydrogen atom.
a) What is the quantum number, n, of the lowest-lying energy state of hydrogen that can be ionized by 1/40eV?
b) What is the radius of a hydrogen atom in the state described in (a)?
c) What is the wavelength of a photon produced when an electron falls from the state given in (a) to the next lower energy state?

62. The proton, m=1.66×10-27 kg, is about 1 fm =10-15m large.
a) If 1 fm represents the uncertainty of the proton's position, then what is the minimum uncertainty in its momentum?
b) Find the wavelength of a proton traveling at 1% of the speed of light. (Assume classical dynamics.)
c) Compare the momentum of such a proton with the uncertainty calculate in (a).

63. When 235U fissions into two nuclei, it releases about 200 MeV.
a) How many kg of mass is converted into energy?
b) Since such a small fraction of the mass is converted into energy, almost all of the mass is converted into waste.  How many kilograms of waste is produced in creating 200 MeV?
c) How many kg of waste would be produced in creating 1020J of energy, approximately one year's world energy needs?

64. Answer 10 of the following True/False questions:
a. _____ Electrons are composed of three smaller particles called quarks.
b. _____ The proton is the electron's antiparticle and vice versa.
c. _____ Electrons are, as near as can be determined, pointlike particles having no size.
d. _____ The purpose of the helium in a HeNe laser is to "optically pump" the neon atoms.
e. _____ A photon incident on an atom in the active medium of a laser can result in two photons leaving the atom.
f. _____ The coherence of laser light depends on the nature of the "stimulated emission."
g. _____ The number of hydrogen atoms that could be squeezed onto the 0.3mm square head of a pin is about 1011, within a factor of ten.
h. _____ The 4000th excited hydrogen state has a radius smaller than 1 mm.
i. _____ The energy of the 200th level of hydrogen is E200= -0.068 eV.
j. _____ For Bragg scattering from a given crystal, decreasing the wavelength of incoming radiation will decrease the scattering angle.
k. _____ The path of a cathode ray can be bent by a magnetic field.
l. _____ Two carbon nuclei (Z=6), if fused together, would give off energy.

65. The isotope 218O has a mass of 21.008730u. 219F has a mass of 20.999948u. Both decay by beta emission.
a) What is the binding energy of the oxygen isotope?
If a 21O isotope decayed by beta emission to 21F,
b) would it be beta+ or beta-?
c) how much energy would be given off or absorbed? (Which?)

66. A neutron star is a stellar object which consists of a gigantic nucleus composed of neutrons only.  Consider such a star which has a radius equal to the Sun's:  r = 7.0 × 108m.
a)  What is the atomic mass, A, of this "nucleus"?
b)  What is its mass?
c)  What is its mass density in kg/m3?

67. Among the more toxic products of the incident at Chernobyl (1985?) are the following:
90Sr (Z=38)  half-life = 28.8 year................ 109Cd (Z=48)  half-life = 453 days ..................131I  (Z=53)  half-life = 8 days
For each radioactive species, calculate the ratio of its radioactivity today to its radioactivity when originally released. (Round to the nearest year.)

68. The density of gold is 19.3 g/cm3; its atomic mass is 197.0g.
a) How many atoms of gold are there in a cubic centimeter?
b) What is the distance between gold atoms?
c) If the distance between atoms were doubled and the mass of each atom were doubled, how would the density change?

69. A theorist has assigned the up and down quarks each a mass of 335MeV/c2, and the strange quark a mass of 340 MeV/c2.
a) Calculate the binding energy of a 938.3 MeV/c2 proton (uud), assuming these quark mass values.

b) Calculate the mass defect of a 494 MeV/c2 kaon-plus (An up quark and an 'anti-up' ).

70. The half-life of a neutron (outside of the nucleus) is 10.6min, after which it decays by beta emission to become a proton.
a) What kind of beta emission is it: positive or negative?
b) How long would one need to wait after entering a room full of Avogadro's number of loose neutrons before there was approximately only one left?
c) Give one reason why the reaction n ---> p + beta is not allowed.

71. Consider the reaction: 2H + 3H ---> 4He + X
a) What is the unknown reaction product, X?
b) How much energy is given off or absorbed in this reaction? Is it given off or absorbed?
c) What is the binding energy of 4He?

72. Consider Bohr's model of the hydrogen atom. Consider the third electron energy level. Its kinetic energy equals the magnitude of the total energy of that state, which is nonrelativistic.
a) Calculate the momentum of the electron in this state.
b) Calculate the uncertainty in the momentum, assuming the same Delta px=1.41p we used in class for the ground state.
c) Calculate the uncertainty in position, using Delta x =1.41r, where r is the radius of the electron's orbit.
d) Are the results of (b) and (c) consistent with the laws of quantum mechanics? Why or why not?

73. Consider the reaction: K - + p ---> Sigma+ +pi-
a) Verify three absolute conservation laws for this reaction. (Obviously, we don't have enough information to prove for example, momentum conservation.)
b) How much energy is given off or absorbed in this reaction? Is it given off or absorbed?
c) Calculate the binding energy of the K - particle, given its mass in the table below. (In the actual exam, the table would actually be there.)

74. A 400ng sample of americium is confined to the insides of a smoke detector. It has been measured using advanced laser Doppler technology to be moving at less than 1nm/s.
a) Does 1nm/s give us the upper or lower limit for the americium sample's wavelength?
b) What is that limit? (the wavelength)
c) What is the smallest possible uncertainty in the americium's position?

Lasers
75. What are the photon energies of the output of the following:
a) CO2 laser (10.6micron)...........................b) Nd:YAG laser (1.06micron)
c) AlGaAs diode laser at 800nm...............d Er:ZBLAN fiber laser at  550nm

76. What range of wavelengths could one get out of a hydrogen-atom laser, if such a thing exists, and if any of the states could be the final state?

77. An upconversion fiber laser has a laser cavity which consists of a long optical fiber, doped with some optically active material. Consider a 2m-long fiber laser, which is pumped with 980nm laser light and which lases at 550nm. The index of refraction of the glass fiber is 1.500.
a) How many half-wavelengths of the 'pump' light fit inside the length of the fiber?
b) How many half-wavelengths of the laser light fit inside the length of the fiber?

78. A diode laser has a laser cavity of 0.1mm length and emits 635nm light. Assume the index of refraction to be 1.40.
a) How many half-wavelengths fit inside the laser cavity?
b) By what fraction would the wavelength change if there was one fewer half-wavelength? Would it increase or decrease?
c) By how many Hertz will the frequency of the emitted light change? This is called the 'mode spacing' of the laser.

79. A hypothetical laser emits light of wavelength of exactly 450nm, as measured in a vacuum.
a) This corresponds to an electron transition of how much energy?
b) If the optical resonator of the laser has a length of exactly 10cm and the index of refraction of exactly 1.8, then how many half-wavelengths, N, fit in the resonator?
c) What is the smallest amount by which the resonator could be lengthened and still allow the same exact wavelength to lase?