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homework_3_solution - 1 T = F J c M =(x T x T = T T x T x T...

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μ T μ ν = 1 c F νλ J λ λ M μ νλ = λ ( x μ T νλ x ν T μ λ ) = δ μ λ T νλ δ ν λ T μ λ + x μ λ T νλ x ν λ T μ λ = x μ λ T νλ x ν λ T μ λ = 1 c ( x ν F μ α J α x μ F νρ J ρ ) = 1 c ( x μ J α F αν x ν J α F α μ ) M μ νλ λ M μ νλ = 0 j ν 0 ˆ d 3 xj 0 = ˆ d 3 x i j i = ˆ d S · j = 0
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Q 0 = ˆ d 3 xj 0 M μ νλ Q μ ν M = ˆ d 3 xM μ ν 0 T μ ν T μ ν = E 1 c S x 1 c S y 1 c S z 1 c S x σ xx σ xy σ xz 1 c S y σ yx σ yy σ yz 1 c S z σ zx σ zy σ zz E = 1 8 π ( | E | 2 + | B | 2 ) S = c 4 π E × B M ij 0 = x i T j 0 x j T i 0 = 1 c ( x i S j S i x j ) = 1 c ijk ( x × S ) k Q ij M = ˆ d 3 x 1 c ijk ( x × S ) k M i 00 = x i T 00 x 0 T i 0 = x i E x 0 1 c S i = ( x E t c S ) i Q i 0 M = ˆ d 3 x ( x E t c S ) i
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x = 0 x = 0 E = 4 πσ e x (0 < x < a ) ϕ ( x ) = 4 πσ x (0 < x < a ) 2 πσ e x f = 2 πσ 2 e x T ij = 1 8 π | E | 2 0 0 0 1 8 π | E | 2 0 0 0 1 8 π | E | 2 =
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