HW 7 Phys5405 f04 due Nov. 4, 20041) Using onlyFμν, andijkl, showE·BandB2-E2/c2are Lorentz invariants. The secondtensor is the completely antisymmetric tensor of rank 4 with the same properties as that ofrank 3ijkthat we have studied.2a) Show that the 4-vector potentialAμis not unique, by showing the 4-vector potential,Aμ=Aμ+∂Ψ∂rμ, gives the sameFμν.2b) What equation does Ψ have to satisfy in order that you can work with anAμthat sat-isfies,∇ ·A= 0 or∇ ·A+∂Φ/∂t= 0, even if the givenAμdoesn’t have these properties.3)This problem is like JDJ 12-6. You can forget about part a because in the last homeworkyou showed you can find a frame whereEandBare parallel. Thus assume you transferredto this frame just show that part b) holds in this frame. If you want to get JDJ’s solution youshould work in cgs units as he does. ThereF=q(E+v×B/c). What are the appropriateintegration constants corressponding to JDJ’s solution?
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