These lecture notes are for the advanced undergraduate course PHY331 and for the graduate course PHY530. In PHY331 only parts of the first 13 modules are used and some of the simpler exercises. In PHY530 parts of most earlier modules serve as review materials. More modules are covered and the focus is on more advanced applications/exercises.

Additional modules are planned for the graduate course PHY630.

A different set of lecture notes and slides for a one-semester introductory course on electricity and magnetism (PHY204) is available elsewhere:

http://www.phys.uri.edu/gerhard/PHY204/lecslif14.html

- Coulomb force between point charges
- Coulomb force mediated by electric field
- Charge densities
- Electric potential
- Gauss's law for the electric field

- Electric flux
- Electrostatic field at surfaces and interfaces
- Electrostatic field determined via Gauss's law
- Electrostatic energy
- Multipole expansion

Exercises:

- Electrostatic field of two point charges [lex39]

- Electric field of a charged rod I [lex1]

- Electric field of a charged ring I [lex2]

- Electric field of a charged spherical shell [lex3]

- Electric field of a charged ring II [lex4]

- Electric field of a charged rod II [lex5]

- Electric field of a charged rod III [lex6]

- Electric field of V-shaped line charge [lex7]

- Electric field of parabolic line charge [lex8]

- Electric potential of charged rod [lex42]

- From electric potential to electric field and
back [lex40]

- Electric flux through cube and net charge
inside [lex41]

- Electric dipole field [lex9]

- Electric field of uniformly charged concentric
spheres [lex46]

- Electric field of uniformly charged coaxial
cylinders [lex47]

- ...

- Electrical insulators and conductors
- Electrostatic properties of conductors
- Specifications of conductors at equilibrium
- Electric field at the surface of a conductor
- Electrostatic pressure
- Existence and uniqueness of electrostatic equilibrium
- Boundary value problem
- Electric field in empty cavity
- Capacitor
- Method of images for induced charges
- Solutions in search of a problem
- Applications with planar, spherical, or
cylindrical symmetry

Exercises:

- Parallel-plate capacitor [lex10]

- Cylindrical capacitor [lex11]

- Spherical capacitor [lex12]

- Point charge near plane conducting surface [lex13]

- Electric dipole near plane conducting surface
I [lex14]

- Electric dipole near plane conducting surface
II [lex15]

- Point charge near perpendicular plane
conducting surfaces [lex16]

- Line charge near plane conducting surface [lex18]

- Conducting hyperbolic trough [lex43]

- Conducting sphere in uniform electric field [lex17]
- Conducting cylinder in uniform electric field
[lex19]

- ...

- Uniqueness theorem for Laplace equation
- Separable solutions in Cartesian coordinates
- Separable solutions in spherical coordinates
- Separable solutions in cylindrical coordinates

- Solutions from conjugate functions
- Application to charged plane surface
- Application to charged cylindrical surface

Exercises:

- Square pipe made of conducting walls at
different potential [lex20]

- Conducting rectangular pipe with end-plate
potential [lex21]

- Conducting hemispherical shells at different
electric potential [lex22]

- Oppositely charged hemispherical shells [lex23]

- Series expansion of off-center Coulomb
potential [lex24]

- Conducting half-cylindrical shells at
different electric potential [lex25]

- Conducting plates intersecting at right angle
[lex26]

- Electric potential and field at edge of large
conducting plate [lex27]

- Fringe electric potential and field of
parallel plates [lex28]

- ...

- Induced electric dipole moments
- Polar molecules
- Polarization and bound charge
- Displacement field
- Boundary conditions involving dielectrics
- Linear dielectrics
- Poisson equation for uniform linear dielectric
- Clausius-Mossotti model
- Energy density in dielectric
- Capacitance with dielectric
- Impact of dielectric added to capacitor

Exercises:

- Uniformly polarized dielectric sphere [lex29]

- Dielectric sphere polarized by uniform
electric field [lex30]

- Lateral force on dielectric slab between
parallel plates [lex31]

- Point charge near plane surface of dielectric
I [lex32]

- Capacitor with stacked dielectrics I [lex44]

- Capacitor with stacked dielectrics II [lex45]
- Point charge near plane surface of dielectric
II [lex48]

- Insertion of conducting slab between capacitor
plates I [lex53]

- Insertion of conducting slab between capacitor
plates II [lex54]

- ...

- Electric current density
- Electric current
- Charge conservation
- Ohm's law
- Device with capacitance and resistance
- Electric field driving steady current
- Classical model of conductivity

- Power dissipation in resistive materials
- Electric current in vacuum tube
- Resistor circuits in steady state
- Capacitor circuits at equilibrium
- RC circuits

Exercises:

- Charge accumulated in conductor with steady
current [lex33]

- Capacitor circuit I [lex34]

- Resistor circuit I [lex35]
- Resistor circuit II [lex49]

- Capacitor circuit II [lex55]

- Capacitor circuit III [lex56]
- RC circuit I at equilibrium [lex57]

- RC circuit I with currents flowing [lex58]

- RC circuit I: transfer of energy between
devices [lex61]

- ...

- Lorentz force
- Magnetic force on a charged particle
- Magnetic force on current-carrying conductor
- Biot-Savart law
- Magnetic flux
- Gauss's law for the magnetic field
- Ampère's law restricted to steady states
- Steady-state magnetism and electrostatics
- Consistency of the Biot-Savart law with Ampère's law
- Vector potential
- Magnetic dipole moment
- Torque and force on magnetic dipole
- Principle of relativity

Exercises:

- Magnetic dipole field [lex36]

- Motion in crossed electric and magnetic fields
[lex50]

- Magnetic field of straight current segment I [lex51]

- Magnetic field of straight current segment II [lex52]
- Magnetic field of a circular current I [lex59]

- Magnetic field of a square-shaped wire [lex60]
- Velocity selector [lex62]

- Magnetic moment of rotating charged disk [lex63]

- Magnetic moment of rotating charged spherical
shell [lex64]

- Magnetic field along the axis of a solenoid [lex65]

- Mass spectrometer [lex71]
- Magnetic moment of rotating charged solid
sphere [lex78]

- ...

- Magnetic dipole moments of elementary particles
- Electric and magnetic dipoles -- commonalites
and differences

- Magnetization and bound currents
- Magnetic field H and magnetic induction B
- Scalar magnetic potential

- Boundary conditions

- Diamagnetism
- Paramagnetism

- Ferromagnetism

Exercises:

- Current-carrying magnetic slab [lex66]

- Vector potential of uniformly magnetized
sphere [lex67]

- Magnetic field of uniformly magnetized sphere
[lex68]

- Magnetic material between coaxial cylinders
with current [lex69]

- Magnetized material with cavities of different shapes [lex70]
- Solid sphere placed in a uniform magnetic
field [lex72]

- Magnetic shielding inside a magnetizable
spherical shell [lex73]

- ...

- Faraday's law of electromagnetic induction
- Motional EMF
- Consistency of motional EMF with Faraday's law

- Faraday disk generator
- Eddy currents and magnetic attenuation
- Alternating current generator
- Cyclotron
- Betatron
- Inductance

- Self-induction
- Energy stored in inductor

- Mutual induction
- Magnetic field energy density

- RL circuits
- Electromagnetic oscillator (LC circuit)
- LC circuit with two modes

Exercises:

- Energy dissipation in Faraday disk generator [lex74]

- Faraday wheel I [lex75]

- Free fall attenuated by eddy current [lex76]

- Inductance of a toroid [lex77]
- RL circuit I [lex79]

- RL circuit turning into LC circuit [lex80]

- Motional EMF I [lex81]

- Mutual inductance of solenoid and ring [lex86]

- RC circuit turning into LC circuit [lex87]

- Circuit breaker contest [lex88]

- ...

- Maxwell's equations in vacuum
- Scalar potential and vector potential
- Gauge invariance
- Maxwell's equations in matter
- Path from restricted scenarios toward generality
- Poynting theorem
- Electromagnetic waves in vacuum
- General plane-wave solution
- Energy and momentum densities

- Spherical wave solution

Exercises:

- Conduction current versus displacement current
[lex82]

- Maxwell's equations for scalar and vector
potentials [lex83]

- Vector and scalar potentials of spherical wave
[lex84]

- Electric and magnetic fields of spherical wave [lex85]
- Energy delivery into current-carrying wire [lex89]

- ...

- Postulates of special relativity

- Spacetime coordinate transformations
- Flash of light expanding
- Paradigm shift
- Einstein's signature clock

- Time dilation
- Length contraction
- Addition of velocities
- Doppler effect for sound
- Doppler effect for light

- Spacetime

- Events and world lines

- Kinematics
- Energy and momentum

- Dynamics
- Lorentz force and electromagnetic field tensor
- Lorentz transformation of electromagnetic field tensor
- Continuity equation
- Maxwell's equations
- 4-vector potential
- Summary list of Lorentz transformations
- Electromagnetic wave observed in moving frames
- Energy-momentum flux tensor

Exercises:

- Exchange of light signals [lex90]

- Velocity addition rule from principle of relativity [lex91]
- Internal clock of pions [lex92]

- Jet propulsion [lex93]

- Photon absorption and photon emission [lex94]
- Fields and forces between capacitor plates at rest and in motion [lex95]
- Electric and magnetic fields of point charge
in uniform motion [lex96]

- ...

- Electromagnetic wave in dielectric
- Reflection and refraction at plane dielectric interface
- Total internal reflection
- Normal-incidence reflectivity
- Nonreflecting surface via dielectric coating
- Reflectivity for incidence at an angle
- Reflection and refraction of TE plane wave

- Reflection and refraction of TM plane wave
- Brewster angle
- Energy conservation

- Electromagnetic waves in a conductor
- Reflection from conductor
- Dispersion
- Dispersion in a dielectric
- Dispersion in a plasma

Exercises:

- Anti-reflection coating [lex97]

- Fresnel equation for TE wave [lex98]

- Fresnel equation for TM wave [lex99]

- Electromagnetic wave in a conductor [lex100]

- Reflection of electromagnetic wave from a
conductor [lex101]

- Driven harmonic oscillator: steady-state
solution [lex102]

- Dispersion and absorption in a dielectric [lex103]

- ...

- Electromagnetic wave between parallel conducting plates
- Transverse electric and magnetic (TEM) wave
- Transverse electric (TE) wave
- Energy transport in TE wave
- Geometrical interpretation of phase/group
velocities

- Transverse magnetic (TM) wave
- Energy transport in TM wave

- Rectangular wave guide
- TE modes in rectangular wave guide
- TM modes in rectangular wave guide

- Wave guide with cross section of arbitrary shape
- TE modes in wave guides of arbitrary cross
section

- TM modes in wave guides of arbitrary cross section
- Conditions for TEM modes in wave guides of
arbitrary cross section

- TEM mode in coaxial cable

Exercises:

- TE mode in rectangular wave guide [lex104]

- Surface charge and current in rectangular wave
guide I [lex105]

- Surface charge and current in rectangular wave
guide II [lex106]

- Helmholtz equation for wave guide I: TE modes
[lex107]

- Helmholtz potential for wave guide II: TM
modes [lex108]

- TEM mode in coaxial cable I: electric and
magnetic fields [lex109]

- TEM mode in coaxial cable II: impedance [lex110]

- ...

- Retarded potentials
- Radiation from electric dipole
- Hertzian dipole (special case)
- Radiation from magnetic dipole
- Electric dipole radiation at arbitrary distance
- Half-wave linear antenna
- Radiation from an accelerated charged particle
- Light scattering from bound charged particle

Exercises:

- Green's function of $\backslash nabla^2+k^2$ [lex111] $$
- Planar surface current abruptly established [lex112]

- Electric dipole moment from charge density or
current density [lex113]

- Magnetic radiation field of electric dipole [lex114]

- Electric radiation field of electric dipole [lex115]
- Poynting vector and radiation power of
electric dipole [lex116]

- Antenna resistance of Hertzian dipole [lex117]

- Radiation fields an Poynting vector for
half-wave linear antenna [lex118]

- Larmor formula for radiation of accelerated
charged particle [lex119]

- ...

- Angular momentum of electrons
- Two-electron wave function
- Atomic electrons in a magnetic field
- Diamagnetism
- Paramagnetism
- Fine structure
- Hund's rule
- Russell-Saunders coupling
- Landé g-factor
- Nuclear spins
- Hyperfine structure

Exercises:

- Diamagnetic response of electron in circular
orbit [lex121]

- Dynamic response of electric and magnetic
moment to torque [lex122]

- Hyperfine-coupling Hamiltonian [lex123]

- ...

- Vector addition

- Dot product of vectors
- Cross product of vectors

- Identities involving products of vectors

- Differential operators
- Identities involving differential operators

- Integral theorems (Gauss's theorem and Stokes' theorem)
- Integration by parts

- Curvilinear coordinates
- Summary table for Cartesian coordinates
- Summary table for cylindrical coordinates
- Summary table for spherical coordinates
- Helmholtz theorem
- Dirac delta function

- Further mathematical identities
- ...

Exercises:

- Meaning of orthogonality

- Fourier series
- Fourier integral

- Legendre polynomials
- ...

- Complex algebra
- Complex derivative
- ...

- Atomic polarizabilities
- Dielectric properties of insulators
- Resistivity of conducting materials
- Magnetic susceptibilities of some elements and compounds
- Spectrum of electromagnetic waves
- ...

Some Relevant Textbooks and Monographs:

- R. H. Good:
*Classical Electromagnetism*. Saunders, 1999. - D. J. Griffiths:
*Introduction to Electrodynamics*. Prentice Hall, 1999. - J. D. Jackson: Classical
*Electrodynamics*(3rd Ed.) Wiley, New York 1999. - G. L. Pollack and D. R. Stump:
*Electromagnetism*. Addison Wesley, San Francisco 2002. - J. R. Reitz, F. J. Milford, and R. W. Christy:
*Foundations of Electromagnetic Theory*. Addison Wesley, 1993 - S. Blundell: Magnetism in Condensed Matter.
Oxford University Press 2011.

- ...

Last updated 01/08/22