Assume two parallel conducting plates perpendicular to the z axis of Cartesian system. They are separated by “d”. The coordinate center is at the center of the plate system. Each plate is large with and edge length of L. The upper plate has a surface charge density of – sigma and the lower has + sigma. Between the plates oriented along the x axis there is a constant magnetic field B0. Use Faraday’s law to confirm the motion of the plates as B0 goes to zero and show that the net momentum they receive is that of the fields’ initial momentum. Imagine that instead of B0 going to zero, this time we discharge the plate with a narrow conducting rod on the z axis between the plates. In this case, the electric field goes to zero. What happens to plates and how does the field momentum get transferred to them? Show the mathematical details of the momentum transfer.
Assume two parallel conducting plates perpendicular to the z axis of Cartesian system. They are separated by “d”. The coordinate center is at the center of the plate system. Each plate is large with and edge length of L. The upper plate has a surface charge density of – sigma and the lower has + sigma. Between the plates oriented along the x axis there is a constant magnetic field B0.
Use Faraday’s law to confirm the motion of the plates as B0 goes to zero and show that the net momentum they receive is that of the fields’ initial momentum.
Imagine that instead of B0 going to zero, this time we discharge the plate with a narrow conducting rod on the z axis between the plates. In this case, the electric field goes to zero. What happens to plates and how does the field momentum get transferred to them? Show the mathematical details of the momentum transfer.
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