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