hw8_p5405_f05 - HW 8 Phys5405 f05 due 10/27/05 1) A...

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HW 8 Phys5405 f05 due 10/27/05 1) A homopolar generator of electric current consists of a solid, cylindrical 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 e z and thereafter there is no external force. Find a value for the current as a function of ω (t). Does the current flow fron R i to R o or visa versa? Show that the disk will slow down and find an expression for ω ( t ). 2a) 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 .
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hw8_p5405_f05 - HW 8 Phys5405 f05 due 10/27/05 1) A...

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