2B29 Electromagnetic Theory Course summary (UCL)

Start of Course

2B29

1. Revise 1B26, especially electrically polarised media and displacement, leading to

D(r ) ≡ (ε 0 Ε(r ) + P(r ))

2. Study magnetic materials, based on magnetic effects of

 B(r )  dipole loop currents; leading to H(r ) ≡  − M (r )  ; µ0   para- dia- and ferromagnetism.

3. Understand simple electromagnets, stored energy in fields, forces generated by magnets.

4. Find inadequacy of Ampere Law. Add displacement current Spring 2004. 2B29 Summary

Centre of Course - Maxwell’s Equations ∂D   Ampere Law (+Maxwell) H l J S . d . d = + v∫P ∫S  f ∂t  ∂D P

∇×H = J f +

∂t

2B29

0 No v∫ B.dS =Monopoles S

∇.B = 0

dΦC Faraday Law (+Lenz) ∂B vC∫ E.dl =−S∫ ∂t .dS =− dt C ∂B v∫ D.dS = ∫ ρ f dτ = ∑ qi

∇×E =−

Integral and Differential forms linked by

S

∂t

τ

τ

∇.D = ρ f

Gauss Law

∫ (∇ × A).dS = v∫ A.dl

SC

Spring 2004. 2B29 Summary

C

Stokes Theorem

∫ ∇ ⋅ A d τ = v∫ A ⋅ nˆ d S = v∫ A ⋅ d S

V

S

Gauss Theorem

S

Waves in good conductors - skin depth Waveguides

Special Wave Equations and dispersion relations

Energy transfer rate J.E +Energy Densities Ue, Um

2B29

Poynting Vector; Energy Flow Radiation Pressure

Maxwell’s Equations

Waves in Plasma

Wave Equation.

Solution simplifies to unbounded plane wave

E(r, t ) = E0 e

Waves from a Hertzian dipole Spring 2004. 2B29 Summary

i ( k.r −ωt +φ )

Waves at dielectric boundary: * reflection * Snell’s law * Fresnell relations * Total reflection. * Brewster angle * Polarisation