hw6_p5405_f03

# hw6_p5405_f03 - R i to R o or visa versa? Show that the...

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HW 6 Phys5405 f03 due Oct. 23, 2003 1) A homopolar generator of electric current consists of a solid, cylindical metal disk of moment of inertia I, inner radius R i , and outer radius R o that is free to rotate without friction about an insulating cylindrical axle of radius R i . The axle is directed along the z axis and there is everywhere a constant magnetic ﬁeld B = B 0 e z . Via brush contacts a load resistance R at point a is connected to the disk at R i and at point b on the other side of the resistance to the disk at R o . The disk is started with angular velocity ω 0 and thereafter there is no external force. Find a value for the current. Does the current ﬂow fron
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Unformatted text preview: R i to R o or visa versa? Show that the disk will slow down and ﬁnd an expression for ω ( t ). 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 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 μ that satisﬁes, ∇ · A = 0 or ∇ · A + 1 c 2 ∂ Φ ∂t = 0, even if A μ doesn’t have these properties. 4)JDJ 11-15 1...
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## This note was uploaded on 12/24/2011 for the course PHYS 5406 taught by Professor Blecher during the Spring '10 term at Virginia Tech.

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