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

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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 move by. That observer is at rest with respect to the plates. The other observer is at rest in the lab watching
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