The figure below shows a cylindrical capacitor; it consists of a solid metal rod

Question

The figure below shows a cylindrical capacitor; it consists of a solid metal rod of radius r_1 surrounded by a metal cylinder with inner radius r_2 and outer radius r_3. Suppose the capacitor has length L (with L very large). Also suppose a charge +Q is placed on the inner rod and a charge -Q is placed on the outer cylinder. Find the electric field inside the rod (i.e., for r r > r_1). (Use the following as necessary: k where Find the electric field outside the capacitor (r > r_3). (Use the following as necessary: k where k

Explanation / Answer

We can use Gauss Law to solve this basically Gauss law states the Flux = q enclosed /o

Since the inner rod is a conductor, al of the charge resides on the outer surface of the inner rod.

Therefore for r<r1 the field E = 0 since there is no charge enclosed.

For the region r1<r<r2 , the net charge is Q...So we have E*A = Q/o...
So E = Q/(2orL)


For r>r3 the net charge enclosed is 0 so E = 0

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