hw6_p5405_f01 - HW 6 Phys5405 f01 due Nov. 29, 2001 1)...

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HW 6 Phys5405 f01 due Nov. 29, 2001 1) Suppose E · B = 0 and you can transfor to O’ where only B 0 = 0. What velocity will ef- fect this transformation? What is the magnitude of E 0 ? Suppose in this problem B = B 0 e z , E = 5 e x KV/m, and B 0 is half its maximum allowed value for this case? 2) Using only F μν , show E · B and B 2 - E 2 /c 2 are Lorentz invariants. 3) Show that the 4-vector potential A μ is not unique, by showing the 4-vector potential, A 0 μ = A μ + Ψ ∂r μ , gives the same F μν . What equation does Ψ have to satisfy in order that you can work with an A 0 μ that satisfies, ∇ · A 0 = 0 or ∇ · A 0 + Φ 0 /∂t = 0, even if A μ doesn’t have these properties. 4)This problem is like JDJ 12-6. You can forget about part a because in the last homework you showed you can find a frame where
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