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Suppose that a parallel-plate capacitor has circular plates with radius R = 30 mm and a plate separation of 7.5 mm. Suppose also that a sinusoidal potential difference with a maximum value of 150 V and a frequency of 60 Hz is applied across the plates; that is
. (a) Find
, the maximum value of the induced magnetic field that occurs at r = R. (b) Plot
Find the electric field outside a uniformly charged hollow cylindrical shell with radius R and charge density , an infinitesimal distance away from it. Do this in the following way. (a) Slice the shell into parallel infinite rods, and integrate the field contributions from all the rods. You should obtain the incorrect result of . (b) Why isn’t the result correct? Explain how to modify it to obtain the correct result of . Hint: You could very well have performed the above integral in an effort to obtain the electric field an infinitesimal distance inside the cylinder, where we know the field is zero. Does the above integration provide a good description of what’s going on for points on the shell that are very close to the point in question?