## Phys 3330 Electricity and Magnetism II Spring 2019

#### Introduction

This, the second semester of the PHYS 3320/3330 Electricity and Magnetism sequence, is primarily concerned with the methods of solving Maxwell's Equations
• divD = ρ
• divB = 0
• curlE = - ∂B/∂t
• curlH = J + ∂D/∂t
There are two cases to consider
• Electrostatic and magnetostatic solutions; time independent equations, for which the electric and magnetic fields are independent of one another and can be solved separately
• Electromagnetism; time dependent equations, for which the electric and magnetic fields are inherently linked, in which case Maxwell's equations must be solved as a set of simultaneous equations
We shall make some simplifying assumptions in order to extract solutions
• that the free charge and current densities (ρ and J) are both zero
• that the natural of materials is restricted to those which are linear, isotropic, and homogeneous. Solutions in which the material is non-linear (e.g. frequency doubling crystals) or anisotropic (birefringence) are covered in the class PHYS 4900 Modern Optics and Lasers.

#### Required mathematics

Solutions of Maxwell's Equations relies on knowledge of the appropriate mathematics, all of which we covered in PHYS 3010 Mathematical Physics I. I will review as appropriate, but it is also to your advantage to review the following ahead of time
• for static solutions
• partial differential equations, especially the method of separation of variable
• Special functions, especially the Legendre equation and Legendre polynomials
• for time dependent solutions
• vector calculus
• complex numbers, and the representation of a wave in complex form.
• relativity
• matrices, and matrix multiplication

### Class Material

• Review of E&M I
• Maxwell's Equations
• in a vacuum
• in a material
• in a LIH material
• Boundary conditions
• Continuity equation
• Poynting vector
• Time independent solutions
• Laplace's equation
• Separation of variables
• Cartesian coordinates
• Cylindrical polar coordinates
• Spherical polar coordinates
• Complex functions
• Time dependent solutions
• Electromagnetic Waves
• Derivation of wave equation
• Real solution of 1-variable wave equation - plane waves
• Solution of 1-variable wave equation - spherical waves
• 3-variable wave equation - plane waves
• Complex notation for waves
• complex solution of wave equation - plane waves in three variables
• Energy carried by waves - Poynting vector
• Plane waves at boundaries
• refection and transmission conditions
• Radiation from oscillating dipole
• Relativistic E&M

### Test Schedule

Test dates are to be determined according to the rate of coverage of material. Each test, except the first, will consist of an in class portion worth 30% of the points for that test, and a take home portion worth the remaining portion. The take home portions will be due at the beginning of the following class, and must be your individual effort. Collaboration is permitted on homework assignments.

Test # Topics Points Points Points
in class
take home
total
1
Review of E&M I
10

10
2
Time independent solutions
Answers
6
14
20
3
Time dependent solutions
6
14
20
Final
Comprehensive
6
14
20

Assignments

30

Total

100