hw7_p5405_f02 - E and B are parallel. Thus assume you...

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HW 7 Phys5405 f02 due 11/12/02 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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Unformatted text preview: E and B are parallel. Thus assume you transferred to this frame just show that part b) holds in this frame. If you want to get JDJs solution you should work in cgs units as he does. There F = q ( E + v B /c ). What are the appropriate integration constants corressponding to JDJs solution? 5)This problem is like JDJ 12-7 b (1st part). Assume the particle enters the eld at x=y=z=0. Where does it leave the eld and What are the momentum components as-suming initially P = P e x . Compare the answers for positrons and protons if P = 300 MeV/c, a = 0.5 m, and B = 1 T? For what values of P would protons not get to x > a? 1...
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