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Unformatted text preview: Formulae Maxwells Equations (SI units) D = free B = 0 E = B t H = J free + D t D = E + P H = B  M Multipole Moments p k = Z d 3 rr k ( r ) Q km = Z d 3 r (3 r k r m km r 2 ) ( r ) m k = 1 2 Z d 3 r [ r J ( r )] k Laplacian in Cylindrical Coordinates 2 = 1 + 1 2 2 2 + 2 z 2 Laplacian in Spherical Coordinates 2 = 1 r 2 r r 2 r + 1 r 2 sin sin + 1 r 2 sin 2 2 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 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 ( , ) = r 2 l + 1 4 s ( l m )! ( l + m )! P m l (cos ) e im Energy and Momentum Densities (Linear materials: D = E , B = H ) u = 1 2 ( E D + H B ) , g = D B Energy Flux and Stress Tensor (Linear materials: D...
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 Spring '08
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