 AbrahamLorentz formula – physical basis
 Accelerating an atomic electron with a changing magnetic field
 Alfven’s theorem
 Alternating current
 Ampère’s law for steady currents
 Ampère’s law and the steady current assumption
 Ampère’s law: slab of current
 Ampère’s law: surface of integration
 Angular momentum in electromagnetic fields
 Angular momentum of a charge and magnetic monopole
 Angular momentum in a magnetized sphere
 Angular momentum conservation: example with a solenoid
 Auxiliary magnetic field H
 Average field over a sphere
 Average magnetic field within a sphere
 Average of product of two waves
 Balancing magnetic force with gravity
 BiotSavart law – current loops
 BiotSavart law: a couple more examples
 BiotSavart law: force on other currents
 A bizarre example of Faraday’s law
 Bound charges in a dielectric
 Boundary between magnetic materials
 Capacitance
 Changing a particle’s speed in a cyclotron
 Charging and discharging a capacitor: applying Ohm’s law
 Charging and discharging a capacitor: general case
 ClausiusMossotti formula – examples
 Coaxial cable with dielectric
 Coaxial cable with varying current
 Coaxial solenoids
 Coaxial wave guides: TEM mode
 Conducting sphere halfembedded in dielectric plane
 Conservation of energy in a capacitor
 Copper pipes in a conducting medium
 Coulomb’s law
 Coulomb’s law – deviation
 Coulomb and Lorentz gauges
 Curl & potential in electrostatics
 Curl & Stokes’s theorem
 Current between two plates with a spherical perturbation
 Current loop in a magnetic field
 Currents in magnetic fields
 Currents and relativity
 Cycloid motion in crossed electric and magnetic fields
 Decay time for free charge in a conductor
 Detecting magnetic monopoles
 Diamagnetism
 Dielectric constant
 Dielectric cube: bound charges
 Dielectric cylinder in uniform electric field
 Dielectric examples
 Dielectric shell surrounding conducting sphere
 Dielectric sphere in uniform electric field
 Dielectric sphere with free charge
 Dipole in dielectric sphere
 Dipoledipole interactions
 Dipoledipole forces and torques
 Dipole force and energy
 Dipole between two angled conducting planes
 Dipoles
 Dirac delta function and divergence theorem
 Displacement current in a capacitor
 Displacement current in an infinite wire
 Displacement current is very small
 Divergence of magnetic field: magnetic monopoles
 Divergenceless vector field as a curl
 Dropping loops through magnetic fields
 Duality transformation for magnetic and electric charge
 Electric dipole timevarying potentials; Lorentz gauge condition
 Electric dipole radiation from an arbitrary source
 Electric displacement
 Electric displacement: boundary conditions
 Electric field & potential – more examples
 Electric field of a dipole
 Electric field outside an infinite wire
 Electric field within a cavity inside a dielectric
 Electric and magnetic fields: cycloid motion
 Electric and magnetic forces in two charged wires
 Electric potential
 Electric potential – examples
 Electric potential from charges – Examples 1
 Electric potential from charges – Examples 2
 Electric potential from a steady current
 Electric quadrupole radiation
 Electromagnetic field tensor: change in kinetic energy
 Electromagnetic field tensor: conservation of mass
 Electromagnetic waves in vacuum
 Electromagnetic waves: energy, momentum and light pressure
 Electromagnetic waves in matter: normal reflection and transmission
 Electromagnetic waves in matter: reflection and transmission coefficients
 Electromagnetic waves in conductors: phases and amplitudes
 Electromagnetic waves in conductors: energy density and intensity
 Electromagnetism in Gaussian (CGS) units
 Electromotive force
 The electron as electromagnetic energy and angular momentum
 Electron charge to mass ratio
 Electron speed in a copper wire
 Electrostatic boundary conditions
 Electrostatic boundary conditions – examples
 Electrostatic pressure
 Electrostatics – conductors
 Electrostatics – linear charge distributions
 Electrostatics – point charges
 Electrostatics – surface charges
 Emf near an infinite wire
 Emf in a spinning spherical shell
 Energy in a dielectric
 Energy of conducting sphere in a dielectric shell
 Energy flow in timedependent fields
 Energy of magnetic dipole in magnetic field
 Energy in a magnetic field
 Energy in a toroidal solenoid
 Energy transfer in a solenoid
 Faraday field and magnetic vector potential
 Faraday’s law
 Faraday’s law, Ampère’s law and the quasistatic approximation
 Faraday’s law and the BiotSavart law
 Faraday’s law: cutting a currentcarrying wire
 Faraday’s law: wire loop encircling a solenoid
 Fermat’s principle of least time and Snell’s law
 Floating a magnet above a superconductor
 Force between current loops: Newton’s third law
 Field of a polarized cylinder
 Field of a polarized object
 Field of a polarized object – examples
 Fields and radiated power from an oscillating electric dipole
 Fields of an oscillating magnetic dipole
 Fields of a moving magnetic monopole
 Fields of a moving point charge
 Fields of a point charge moving in one dimension
 Fields of a point charge moving in a circle
 Fields due to a moving linear charge
 Fields and radiation from a timedependent sheet of current
 Force on a dielectric
 Force on a dielectric sphere due to a charged wire
 Force between two sheets of current
 Force between two magnetic dipoles
 Force on a magnetic dipole
 Force on a magnetic dipole – a better derivation
 Force on a magnetic dipole in a slab of current
 Force of point charge in a hyperbolic trajectory on a fixed point charge
 Force and momentum with two moving point charges
 Fourier transform of superposition of plane waves
 Frequency dependence of electric permittivity
 Fresnel equations for perpendicular polarization
 Gauge transformations in electrodynamics
 Gauss’s Law
 Gauss’s Law – examples
 Gauss’s law for a relativistic point charge
 Green’s reciprocity theorem
 Group velocity of electromagnetic waves in a dispersive medium
 Gyromagnetic ratio
 Hall effect
 Helmholtz coil
 Inductance of a coaxial cable
 Induction between a wire and a torus
 Jefimenko’s equation for timedependent electric field
 Jefimenko’s equation for timedependent magnetic field
 Laplace’s equation – average values of solutions
 Laplace & Poisson equations – uniqueness of solutions
 Laplace’s equation – charged disk
 Laplace’s equation – charged line segment
 Laplace’s equation – charged sphere
 Laplace’s equation – conducting sphere and shell of charge
 Laplace’s equation – cylindrical coordinates
 Laplace’s equation – cylindrical shell
 Laplace’s equation – cylindrical shell with opposing charges
 Laplace’s equation – Fourier series examples 1
 Laplace’s equation – Fourier series examples 2
 Laplace’s equation – Fourier series examples 3 – three dimensions
 Laplace’s equation – Fourier series examples 4
 Laplace’s equation – infinite pipe
 Laplace’s equation – separation of variables
 Laplace’s equation – spherical coordinates
 Laplace’s equation in spherical coordinates: examples 1
 Laplace’s equation in spherical coordinates: surface charge
 LC circuit – the oscillator
 Liénard’s generalization of the Larmor formula for an accelerating charge
 LR circuit
 Lenz’s law
 LiénardWiechert potentials for a moving point charge
 LiénardWiechert potentials for a charge moving with constant velocity
 LiénardWiechert potential for a charge moving on a hyperbolic trajectory
 Lorentz gauge is always possible
 Magnet falling through a metal pipe
 Magnetic dipole
 Magnetic dipole: average field over a sphere
 Magnetic dipole embedded in sphere
 Magnetic dipole in a constant field
 Magnetic dipole field of a finite solenoid
 Magnetic dipole moment of a current loop
 Magnetic dipole moment of spinning disk
 Magnetic dipole moment of spinning spherical shell
 Magnetic dipole moment for volume current
 Magnetic dipoles versus monopoles; an experiment
 Magnetic field of current loop – off axis field
 Magnetic field of rotating sphere of charge
 Magnetic field of a semicircular current loop
 Magnetic field of a solenoid
 Magnetic field of a sphere in a uniform field
 Magnetic fields of spinning disk and sphere
 Magnetic field of square current loop
 Magnetic field: uniqueness conditions
 Magnetic field within a cavity
 Magnetic field within a currentcarrying wire
 Magnetic flux
 Magnetic force of attraction between hemispheres
 Magnetic monopole: force on a charge
 Magnetic monopole force law
 Magnetic permeability
 Magnetic scalar potential
 Magnetic scalar potential: dipole and rotating sphere
 Magnetic toy
 Magnetic vector potential
 Magnetic vector potential: div, curl and Laplacian
 Magnetic vector potential of constant field
 Magnetic potential and field of a rotating sphere of charge
 Magnetic vector potential as the curl of another function
 Magnetic vector potential and current
 Magnetic vector potential of an infinite wire
 Magnetic vector potential from magnetic field
 Magnetic vector potential: sheet of current
 Magnetization: bound currents
 Magnetization: microscopic versus macroscopic
 Magnetostatics – the Lorentz force law
 Magnetostatic boundary conditions
 Magnetostatic boundary conditions: a couple of examples
 Magnetostatic boundary conditions; Laplace’s equation
 Magnetostatic formulas from electrostatic formulas
 Maxwell’s correction to Ampère’s law
 Maxwell’s equations and an expanding shell of charge
 Maxwell’s equations with varying charge but constant current
 Maxwell’s equations in matter
 Maxwell’s equations in matter: boundary conditions
 Maxwell’s equations in terms of potentials
 Maxwell stress tensor
 Maxwell stress tensor: force between two charges
 Maxwell stress tensor and electromagnetic waves
 Method of images
 Method of images – moving charge and plane
 Method of images – point charge and sphere
 Method of images – point charge and two planes
 Method of images – sphere in uniform field
 Method of images: two conducting planes
 Microwave shielding for perfect transmission
 Momentum in a capacitor
 Momentum in electromagnetic fields
 Momentum in a magnetized and polarized sphere
 Momentum of a point charge outside a solenoid
 Motional emf
 Multipole expansion in electrostatics
 Multipole expansion of linear charge
 Mutual inductance
 Mutual inductance between two magnetic dipoles
 Mutual inductance between two loops
 Mutual inductance: calculation from the integral
 Ohm’s law, conductivity and resistivity
 Ohm’s law with variable conductivity
 Optical properties of diamond
 Perpetual motion in an electric circuit?
 Phase velocity and group velocity in a wave packet
 Physical basis of the radiation reaction force
 Point charge and neutral atom
 Point charge embedded in dielectric plane
 Point charge in dielectric sphere
 Point charge in hyperbolic motion: visible and invisible points
 Point charge moving at constant velocity satisfies Lorentz gauge
 Polarizability of hydrogen
 Polarizability of hydrogen – quantum version
 Polarizability – linear charge distribution
 Potential of two charged wires
 Potential of two copper pipes
 Potentials for an electromagnetic wave
 Potentials for a point charge
 Power due to point charge moving with constant velocity
 Power radiated by radiation reaction force
 Power radiated by a spinning ring of charge
 Poynting’s theorem
 Poynting’s theorem and conservation of energy
 Quadrupole moment
 Radially symmetric magnetic field
 Radiation damping
 Radiation resistance
 Radiation resistance of an oscillating magnetic dipole
 Radiation from a charge falling under gravity
 Radiation from a charge in hyperbolic motion
 Radiation from a charge on a spring
 Radiation from a point charge; the Larmor formula
 Radiation from a point charge near a conducting plane
 Radiation from a radio station
 Radiation from a rotating dipole
 Radiation from a magnetic dipole composed of monopoles
 Radiation from the magnetic dipoles of Earth and pulsars
 Radiation from a current loop with timevarying current
 Radiation reaction: the AbrahamLorentz force
 Radiation reaction: a few examples
 Radiation reaction with a deltafunction external force
 Radiation reaction: energy conservation with a constant external force
 Radiative decay of the Bohr hydrogen atom
 Rectangular resonant cavity
 Rectangular wave guides: transverse electric waves
 Rectangular wave guides: TE modes and the cutoff frequency
 Rectangular wave guide: transverse magnetic modes
 Reflection at a conducting surface: the physics of mirrors
 Refraction and dispersion coefficients
 Relation between polarizability and susceptibility
 Relations among charge, current, potentials and fields
 Relativistic electromagnetic force
 Relativistic invariants involving electromagnetic fields
 Relativistic transformation of electromagnetic waves; the Doppler effect
 Relativistic transformation of force, electric and magnetic fields
 Relativistic transformation of electric and magnetic fields: an example
 Resistance in a conical capacitor
 Resonances in a dispersive medium
 Retarded potentials
 Retarded potentials in an infinite straight wire
 Retarded potential of a wire loop
 Retarded potentials for a sinusoidal current loop
 Selfinductance
 Selfinductance of a long rectangle
 Skin depth of electromagnetic waves in conductors
 Skin depth of water and metals
 Solenoid with arbitrary crosssection
 Solenoid field from BiotSavart law
 Spherical electromagnetic wave
 Superconducting loop in a magnetic field
 Surface and volume current in a wire
 Surface and volume current density 2
 Surface current induced by a magnet floating over a superconductor
 Susceptibility of a polar dielectric
 Symmetry of a rank 2 tensor is preserved under Lorentz transformation
 Synchrotron radiation
 ThompsonLampard theorem
 Three laws of geometrical optics
 Toroidal solenoid with a gap
 Torque on a magnetic dipole
 Torque on a magnetic moment; general current distribution
 Total internal reflection
 Transformers
 Transforming the electric field in relativity
 Transmission coefficient for a wave passing through 3 media
 Transmission coefficients from water through glass into air
 Transmission lines
 Tunnelling through a potential barrier with the radiation reaction force
 Two charged wires and a cylinder
 Uniform charge, polarization & magnetization
 Uniqueness of potential in dielectrics
 Vacuum diode
 Vector area
 Volume current density and dipole moment
 Waves: boundary conditions
 Waves: boundary condition with a massive knot
 Waves: polarization
 Wave equation: derivation and examples
 Wave equation: sinusoidal waves and complex notation
 Wave equation: solution by separation of variables
 Wave equation: wave speed and standing waves
 Waves in a viscous fluid
 Wave guides: derivation of the wave equation
 Wave guide: energy flows at the group velocity
 Work and energy – continuous charge
 Work and energy – point charges

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