31_Oct_08 - Electricity and Magnetism I (P331) M. R....

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Electricity and Magnetism I (P331) M. R. Shepherd October 31, 2008 The moving capacitor Today in lecture we worked out both the magnetic and electric pressures on the plate of a capacitor due to the other plate. At the end of class I tried to qualitatively draw a connection to relativity. If we had just a little more time I would have made this connection a little more quantitative. Let’s finish off the problem. We showed that the magnetic pressure due to the upper plate on the lower plate is repulsive and has a magnitude ± ± ± ± F A ± ± ± ± = μ 0 σ 2 v 2 2 , (1) here σ is the charged density and v is the velocity of the plates. At the same time the electric pressure due to the lower plate on the upper plate is attractive and has a a magnitude ± ± ± ± F A ± ± ± ± = σ 2 2 ± 0 . (2) Let’s assume that the plates have equal but opposite charges ± q . Then, we can write the net upward force on the lower plate as F = q 2 2 ± 0 - q 2 v 2 μ 0 2 = q 2 2 ± 0 ( 1 - v 2 μ 0 ± 0 ) . (3) Now, suppose that we have two observers. One observer is standing on the upper plate as the plates
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This note was uploaded on 01/20/2012 for the course PHYSICS 331 taught by Professor Staff during the Fall '09 term at Indiana.

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