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homework_3 - ELECTRODYNAMICS PROBLEM SET 3 due February 16...

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Unformatted text preview: ELECTRODYNAMICS PROBLEM SET 3 due February 16 th , before class Problem 1.: Angular momentum One point that was not emphasized enough in class is that conservation laws are a consequence of symmetries of Nature. For instance, translation symmetry leads to the conservation of momentum and energy, gauge invariance leads to conservation of charge, ... Rotation invariance, being a symmetry of the electromagnetic action, should lead to the existence of a conserved quantity: angular momentum. a) Show that the angular momentum tensor M μνλ = x μ T νλ- x ν T μλ satisfy ∂ λ M μνλ = 1 /c ( x μ J α F αν- x ν J α F αμ ). b) Write down the conserved charge in terms of the Poynting vector. Problem 2.: Stress-tensor in action Consider two parallel, infinite charged planes with (surface) charge density equal to σ and- σ . a) Calculate the electric field generated by them. b) Calculate the potential generated by them....
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