A uniformly charged ball of radius a and charge ? Q is at the center of a hollow

Question

A uniformly charged ball of radius a and charge ?Q is at the center of a hollow metal shell with inner radius b and outer radius c. The hollow sphere has net charge +4Q.

Part A

Determine the electric field strength in the region r?a.

ANSWER:

Determine the electric field strength in the region .

Part B

Determine the electric field strength in the region a<r<b.

ANSWER:

Determine the electric field strength in the region .

Part C

Determine the electric field strength in the region b?r?c.

ANSWER:

Determine the electric field strength in the region .

Part D

Determine the electric field strength in the region c<r.

ANSWER:

Determine the electric field strength in the region .

Explanation / Answer

Using Gauss's Law we have E*A = q enclosed /?o

In the first q enclosed = -q...and A = 4?r^2...So E = 1/(4??o)r^2*-q = - 1/(4??o)*q/r^2...#1


in the next q enclosed = -q+2q = q...So E = 1/(4??o)*q/r^2...#3

In the last the answer is zero because the field inside a conductor is zero

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