Two concentric conducting spherical shells have radii a and b (a < b). The inner shell has charge +q and the outer shell is grounded (V = 0). What is the electric potential V(r) of the inner shell relative to infinity?
Answer and explanation
Correct answer: C. k_e q (1/a - 1/b)
- Step 1: Since the outer shell at r = b is grounded, its potential is V(b) = 0.
- Step 2: In the region a < r < b, the electric field is E(r) = k_e * q / r^2.
- Step 3: The potential difference between a and b is V(a) - V(b) = - int_b^a E(r) dr = k_e q (1/a - 1/b).
- Step 4: Since V(b) = 0, V(a) = k_e q (1/a - 1/b).
Answer
k_e q (1/a - 1/b).
Why not the others: k_e q / a ignores the grounding of the outer shell; k_e q / b is the potential of an isolated shell of radius b; the plus sign in 1/a + 1/b is an integration sign error.
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