# PHYS 435 :: Physics Illinois :: University of Illinois at Urbana-Champaign

## 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.

1. 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)
2. 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)
3. 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)
4. 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)
5. Magnetic fields:
• Lorentz force
• Biot-Savart and Ampere’s laws
• Vector potential
• You should know how to:
calculate forces on moving charges and current carrying wires (5.42-5.44)
calculate the field produced by a current (5.9)
calculate the vector potential, given the current (5.23, 5.24)
6. 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 (6.7-6.9)
apply boundary conditions (6.17, 6.18)
7. 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)