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hw7_p5405_f07 - F μν show E B and B 2-E 2/c 2 are...

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HW 7 Phys5405 f07 due 11/1/07 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 = ω 0 e z and thereafter there is no external force. Find a value for the current. 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 ). 2) Using only
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Unformatted text preview: F μν , show E · B and B 2-E 2 /c 2 are Lorentz invariants. 3) Suppose E · B = 0 and you can transfer to O’ where only B = 0. What velocity will effect this transformation? What is the magnitude of E ? If B = B e z , E = 5 e x KV/m, and B is half its maximum allowed value, what is the velocity that effects the transformation? 4)This problem is like JDJ 12-7 b (1st part). Assume the particle enters the field at x=y=z=0. Where does it leave the field 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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