27: Problem 27.46

INTRO:
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 +2Q.


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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.
Express your answer in terms of some or all of the variables a, b, c, r, and the constant π.

SOLUTION:
A_sphere = 4πr²

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

for r≤a, q_in = -Q
E = -r/(4πa³)⋅Q/ε₀ r^

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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.
Express your answer in terms of some or all of the variables a, b, c, r, and the constant π.

SOLUTION:
<< explanation to be added >>
E = -1/(4πr²)⋅Q/ε₀ r^

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PART C:

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

Express your answer in terms of some or all of the variables a, b, c, r, and the constant π.

SOLUTION:

<< explanation to be added >>

0

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PART D:

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

Express your answer in terms of some or all of the variables a, b, c, r, and the constant π.

SOLUTION:

<< explanation to be added >>

E = 1/(4πr²)⋅Q/ε₀ r^

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