27: Problem 27.38

INTRO:
A hollow metal sphere has inner radius a and outer radius b. The hollow sphere has charge +2Q. A point charge +Q sits at the center of the hollow sphere.

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PART A:
Determine the magnitude of the electric field in the region r≤a. Give your answer as a multiple of Q/ε₀.
You need only input the coefficient that would multiplied to the expression at right of the answer box to give the answer.

SOLUTION:
A_sphere = 4πr²

Φ_E = ∫E⋅dA = q/ε₀
E = q/(A⋅ε₀) = q/(4πr²ε₀)

for r≤a, q_in = +Q
E = 1/(4πr²)⋅Q/ε₀

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PART B:
Determine the magnitude of the electric field in the region a<r<b. Give your answer as a multiple of Q/ε₀.
You need only input the coefficient that would multiplied to the expression at right of the answer box to give the answer.

SOLUTION:
for a<r<b, q_in = +Q -Q = 0
E = 0⋅Q/ε₀

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PART C:

Determine the magnitude of the electric field in the region r≥b. Give your answer as a multiple of Q/ε₀.

You need only input the coefficient that would multiplied to the expression at right of the answer box to give the answer.

SOLUTION:

for r≥b, q_in = 2Q +Q = 3Q
E = 3/(4πr²)⋅Q/ε₀

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PART D:

How much charge is on the inside surface of the hollow sphere? Give your answer as a multiple of Q.
You need only input the coefficient that would multiplied to the expression at right of the answer box to give the answer.

SOLUTION:

q = -1⋅Q

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PART E:

How much charge is on the exterior surface? Give your answer as a multiple of Q.
You need only input the coefficient that would multiplied to the expression at right of the answer box to give the answer.

SOLUTION:

q = 3⋅Q

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