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Unformatted text preview: Formulae Maxwell’s Equations (SI units) ∇ · D = ρ free ∇ · B = 0 ∇ × E = ∂ B ∂t ∇ × H = J free + ∂ D ∂t D = E + P H = B μ M Multipole Moments p k = Z d 3 rr k ρ ( r ) Q km = Z d 3 r (3 r k r m δ km r 2 ) ρ ( r ) m k = 1 2 Z d 3 r [ r × J ( r )] k Laplacian in Cylindrical Coordinates ∇ 2 = 1 ρ ∂ ∂ρ ρ ∂ ∂ρ + 1 ρ 2 ∂ 2 ∂ϕ 2 + ∂ 2 ∂z 2 Laplacian in Spherical Coordinates ∇ 2 = 1 r 2 ∂ ∂r r 2 ∂ ∂r + 1 r 2 sin θ ∂ ∂θ sin θ ∂ ∂θ + 1 r 2 sin 2 θ ∂ 2 ∂ϕ 2 Legendre polynomials and Spherical Harmonics Rodrigues : P l ( x ) = 1 2 l l ! d l dx l ( x 2 1) l Orthogonality : Z 1 1 dxP l ( x ) P l ( x ) = 2 2 l + 1 δ ll P m l = ( ) m 2 l l ! (1 x 2 ) m/ 2 d l + m dx l + m ( x 2 1) l Y lm ( θ, ϕ ) = r 2 l + 1 4 π s ( l m )! ( l + m )! P m l (cos θ ) e imϕ Energy and Momentum Densities (Linear materials: D = E , B = μ H ) u = 1 2 ( E · D + H · B ) , g = D × B Energy Flux and Stress Tensor (Linear materials: D...
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This note was uploaded on 09/25/2011 for the course PHY 6346 taught by Professor Staff during the Spring '08 term at University of Florida.
 Spring '08
 Staff

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