A parallel-plate capacitor consists two circular plates of radius R, separated b

Question

A parallel-plate capacitor consists two circular plates of radius R, separated by a distance d R (see figure below). The capacitor is charged by a constant current I, carried by thin wires that connect to the centre of the plates. Assume that the current flows out over the plates in such a way that the surface charge is uniform, at any time, and is zero at t = 0s. Neglecting boundary effects, find the electric field (direction and magnitude) between the plates, at any time t. Find the displacement current I_d through a circle of radius s R (see figure) in the plane midway between the plates. Using the circle of part (ii) as your "Amperian loop", and the flat surface that spans it, find the magnetic field (direction and magnitude) at a distance s

Explanation / Answer

i) electric field = eo * [(pi * R2)/s] * dI/di

Direction = upwards

ii) displacement current , Id = (eo * s) * R/t

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