PHYS 435 :: Physics Illinois :: University of Illinois at UrbanaChampaign
Course Description
This course presents a systematic development of electrodynamics, including Maxwell's equations, electrostatics and magnetostatics, boundary value problems, fields in matter, and electromagnetic waves. The second semester (PHYS 436) covers electromagnetic waves, potentials and gauge invariance, and relativistic electrodynamics.
Prerequisite: MATH 285; credit or concurrent enrollment in PHYS 325.
Note: Math 241 (vector calculus) is much more important in E&M than in mechanics.
Course Topics
Selected Griffiths problems in parentheses.
 Electric field:
 Divergence → charge density. Gauss' law.
 Curl = 0 (static) → Electric potential.
 Electrostatic energy
 You should know how to:
calculate the charge density. (2.9)
apply Gauss’ law. (2.16)
calculate potential differences (e.g., do line integrals). (2.21)
calculate fluxes (surface integrals). (2.10)
calculate the field energy. (2.36)
 Conductors:
 Equipotential surfaces.
 Induced charge.
 Capacitors
 Method of images
 You should know how to:
calculate capacitance. (2.43, 2.44)
use images to solve (simple) problems. (3.7)
 Laplace's equation:
 Separation of variables
 Boundary conditions: V or E at a surface.
 Multipole expansion
 Cartesian, cylindrical, spherical coordinates
 You should know how to:
solve in various coordinate systems (3.45)
apply boundary conditions (3.43)
solve problems with electric (and magnetic) dipoles (3.33)

Electric fields in matter:
 Polarization
 E, D, and P
 Linear dielectrics
 Boundary conditions
 Field energy
 You should know how to:
calculate bound charges (4.10)
calculate the force and torque on a dipole (4.6, 4.9)
apply the boundary conditions (4.16, 4.18 4.22)
calculate the field energy and forces (4.26, section 4.4.4)
 Magnetic fields:
 Lorentz force
 BiotSavart and Ampere’s laws
 Vector potential
 You should know how to:
calculate forces on moving charges and current carrying wires (5.425.44)
calculate the field produced by a current (5.9)
calculate the vector potential, given the current (5.23, 5.24)
 Magnetic fields in matter:
 Magnetization
 B, H, and M
 Bound currents
 Boundary conditions
 You should know how to:
calculate forces on magnetic dipoles (and current loops) (6.1, 6.3)
calculate the bound currents and field of a magnetized object (6.76.9)
apply boundary conditions (6.17, 6.18)
 Time dependence:
 Ohm's law
 Electromotive force, motional emf, Faraday's law
 Inductance and magnetic energy
 Maxwell’s equations in vacuum and in matter
 You should know how to:
solve RC, LC, and RLC circuits (7.2, 7.3, 7.31)
calculate inductance and field energy (7.28, 7.32)
calculate induced currents (7.24)