Problem 35P

The preceding problem was an artificial model for the charging capacitor, designed to avoid complications associated with the current spreading out over the surface of the plates. For a more realistic model, imagine thin wires that connect to the centers of the plates (Fig. 7.46a). Again, the current I is constant, the radius of the capacitor is a, and the separation of the plates is w ≪ a. Assume that the current flows out over the plates in such a way that the surface charge is uniform, at any given time, and is zero at t = 0.

(a) Find the electric field between the plates, as a function of t.

(b) Find the displacement current through a circle of radius s in the plane midway between the plates. Using this circle as your “Amperian loop,” and the flat surface that spans it, find the magnetic field at a distance s from the axis.

(c) Repeat part (b), but this time use the cylindrical surface in Fig. 7.46(b), which is open at the right end and extends to the left through the plate and terminates outside the capacitor. Notice that the displacement current through this surface is zero, and there are two contributions to Ienc

Solution 35P

Step 1 of 5:

In this question, we have a charging model of an artificial capacitor

In part a, we need to find electric field between the plates, as function of time

In part b, we need to find the displacement current through a circle of radius in the plane midway the plates, considering the circle as Amperian loop we need to find the magnetic field at a distance from the axis

In part c, we need to repeat steps of part (b) but using a cylindrical surface, which is open at the right end and extends to the left through the plate and terminates outside the capacitor

We also need to check that there are two contributions to enclosed current