Physics 308: Equations and Principles, Spring 2000
Daniel W. Koon, St. Lawrence University

Chapters are from Purcell's Electricity and Magnetism
 Chapter 1: Coulomb: Electric field: Potential energy: Flux & Gauss: F = Charge distributions:       spherical       line charge       surface charge Energy density:
NOTE: For CGS units, set k=1. For MKS, 4p k=1/eo.

You should memorize:
The MKS, CGS units of charge, force, energy, etc.
The expressions for force, electric field for collections of discrete charges
You should be able to:
Calculate force, e-field, potential energy, and energy density for collections of point charges
Apply Gauss' Law to calculate E for simple symmetries (point, plane, line, spherically symmetric charge density)
Integrate spherically symmetric charge densities to get E or stored energy
Identify the appropriate Gaussian surfaces for simple symmetries

Chapter 2:
Nabla ("Del" operator):
Divergence:
Curl:
Laplacian:
Gauss' Law (differential form):
Curl of :
Electric potential
'The circle':
Energy density: u=½r f

You should memorize:
 The equations for div, grad, curl, Laplacian       All six equations from "the wheel" The equations for F, E, PE, and V       What the divergence and curl of the electric field equal
You should know:
The similarities and differences between F, E, PE, and V
You should know how to:
Convert between E, r, and F, including being able to do the appropriate path, polar, and spherical integrations
Apply Gauss' and Stokes' Theorems, using the appropriate integrations

 Chapter 3: Perfect conductors: E = 0 inside f=constant on surface E|| = 0 at surface E^ = 4p[ k]s at surface Boundary value problems:       Uniqueness       Method of images       Conformal mapping       Spherical or cylindrical harmonics       Relaxation, overrelaxation Capacitance: C=Q/V       of isolated sphere:       of isolated disc:       of parallel plates:       of parallel capacitors:       of series capacitors: Energy storage: U=½QV=½CV2=
You should memorize:
The definition of capacitance and its units
The expressions for capacitance of series and parallel capacitors
Any one of the three expressions for the energy stored in a capacitor
You should know:
The qualitative properties of a Faraday cage, the rules about an electric field in a conductor
You should be able to:
Solve boundary value problems (BVPs) using the method of images, relaxation
Calculate the capacitance of simple symmetric systems, including parallel plates, isolated sphere, coaxial cable, and nested spheres.

 Chapter 4: Current: Current density: Continuity: Ohm: V = IR               Conductance: s = nem = Resistivity: r = = 1/ s Kirchhoff: ,       Equivalent resistances: Rs = R1 + R2 + ...       Power dissipation R: P = VI = I2R =V2/R Thevenin: e Th = Vopen       RTh = e Th/Ishort Charging RC circuit: Q=Q0(1-e-t/RC) Discharging RC circuit: Q=Q0e-t/RC
You should memorize:
The continuity equation (Eq. 9)
Ohm's Law in microscopic form (Both eqs.)
The formulae for series and parallel resistors
Both of Kirchhoff's Laws
The time constant of an RC circuit
You should know:
What causes electrical resistance
How resistivity varies with temperature for metals and for semiconductors, and why
You should be able to:
Simplify complex resistor networks
Solve complex networks of resistors and batteries
Apply Thévenin's theorem
Convert between resistance and resistivity for a wire
Devise the equations for Q, I, VR, and VC in an RC circuit

 Chapter 5: Lorentz force: Charge is relativistically invariant. in different frames: E'|| = E|| Accelerating charges ® electromagnetic waves is a consequence of relativity.
You should know:
That charge is both conserved and invariant in all inertial reference frames
How magnetic fields, electrostatics, and special relativity are interrelated
You should be able to:
Apply the equations for a relativistic electric field (Sections 5 & 6)
Apply the equation for the perpendicular component of 'magnetic' force (Eq. 24)

 Chapter 6: Magnetic field: and Biot & Savart: Ampere: Vector potential: Field due to . . .       long wire:       single coil: on axis                   at center       solenoid: Hall effect: , RH=
You should memorize:
CGS and MKS expressions for force on a charge
The curl of the magnetic field
Ampere's law
You should know:
the right-hand rules for field and force
You should be able to:
Calculate the total B-field due to more than one long wire, using the appropriate right-hand rules
Calculate the B-field near a cylindrically symmetric current density
You should keep for future reference:
The formulae for B near a long wire, coil, solenoid

Comparison of electrostatic and magnetostatic fields:

 Electrostatics -- Magnetostatics -- Source of field Coulomb: Biot & Savart: Force = q Lorentz: CGS Units of field statvolt/cm = dyne/esu = esu/cm/cm Gauss = same as units of How to calculate: Gauss' Law: Ampere's Law: (local form) Gauss' Law (local form): Ampere's Law (local form): Potential Since , there is a scalar       potential, , such that Since , there is a vector       potential, , such that "Sandwich" DE = 4p[k]s = 4p[k] Q/A DB=4pJ/c =4pI/lc
 Chapter 7 Motional emf: bar: e= Motional emf: loop: e= Faraday:     Flux form:e =       Differential form: Eddy currents, eddy fields, Meissner effect Flux through a coil:     NBAcosf Self Inductance: L = -e11/ LR circuit: t = L/R Energy storage: u =
You should memorize:
Both forms (flux and differential) of Faraday's law
The expression for the flux through a coil
The expression for the emf across an inductor
The expression for the time constant in an LR circuit
You should know:
What eddy currents are, where they come from, and some examples of them
You should be able to:
Calculate all the voltages and currents in an LR circuit
Compare the energy stored by an inductor to the energy density in its magnetic field
You should keep for future reference:
The motional emf of a moving bar or loop
The energy stored in an inductor
The energy stored in a magnetic field

 Chapter 8: Resonant circuit: XC = XL,           Z = R at resonance Quality factor:   Q = RCw = w L/R Complex analysis: I = Re(Ioeiwt) Admittance: Y = I/V Reactance: X = Im [V/I] Impedance: Z = V/I Z   of resistor: R       of inductor: iwL       of capacitor: Power dissipation:       instantaneous: P = VI       average, for resistor: P = VrmsIrms       average, in general: P = Vrm sIrm scosf

You should memorize:
The impedance for R, L, and C
You should know:
The condition for resonance (ZC=ZL)
You should be able to:
Calculate the impedance of any combination of R, L, and C
Calculate the power dissipated in any circuit containing R, L, and C
You should keep for future reference:
The expression for the quality factor, Q
 Chapter 9: Gauss: Faraday: Gauss for magnetic field: Ampere/Maxwell: Electromagnetic waves in free space: v=c and E0 = B0 energy density: = Poynting:
You should memorize:
The CGS relation between B0 and E0
The velocity of an electromagnetic wave
You should be able to:
Show whether a given expression for E or B, or both, is consistent with Maxwell's equations
Solve for E(x,y,z,t), given B, or vice versa
You should keep for future reference:
Maxwell's equations (so far)
The expressions for energy density and for the magnitude of the Poynting vector (in MKS)

 Chapter 10: Capacitors: C = Energy density: u = Multipole expansion: Point electric dipole: Electric field due to dipole:                   Dipole in -field:             Polarization: Displacement vector:                         Boundary conditions: continuous Maxwell update: Electromagnetic waves: Rayleigh scattering: µ w 4
Note: e o = 1 for CGS, 4p k = 1/e o for MKS.
You should memorize:
The definition of the electric dipole
The equations for energy and torque of a dipole in a field
The capacitance of a capacitor with a dielectric between its plates
You should know:
What causes Rayleigh scattering, and its properties
What Fresnel's equations are, and how they relate to E&M
You should be able to:
Calculate the dipole moment of a collection of discrete charges
Calculate U, t, and F of a dipole in a field
You should keep for future reference:
The definitions of the vectors D, P, and related quantitites
The updated Maxwell's equations

 Chapter 11: Diamagnets, Paramagnets, Ferromagnets Absence of magnetic monopoles Point magnetic dipole: Magnetic field due to dipole:       Dipole in -field: Magnetic field ()magnetization () Magnetic induction:             Boundary conditions: perp and par are continuous Maxwell's equations in materials: m o=1 in CGS Electromagnetic waves:
You should know:
What the three major categories of materials are (in terms of magnetic response), and the properties of each
You should be able to:
Calculate magnetic [dipole] moment
Calculate U, t, and F of a magnetic dipole in a magnetic field
Describe magnetism in a material both microscopically and macroscopically
You should keep for future reference:
The final version of Maxwell's equations (See below)

MAXWELL'S EQUATIONS, final version:
 Equation: CGS MKS Electric: divergence Electric: curl Magnetic: divergence Magnetic: curl

COMPARISON BETWEEN:
Polarization and magnetization     /     Electric dipoles and magnetic dipoles     /     Chapter 10 and Chapter 11
 Electric Magnetic Dipoles E-field E-field Energy Torque Force Internal field Free charges and currents

CONVERSIONS:
Charge: 1 esu = 1/3´ 10-9C
Voltage: 1 statvolt = 300V
Capacitance: 1 cm = 1.11pF
Current: 1 esu/s = 1/3 ´ 10-9A
Resistance: 1 s/cm = 9´ 1011W
Inductance: 1 s2/cm = 9´ 1011H
Magnetic field: (B): 1 G = 10-4T