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Three concentric metallic spherical shells A, B and C have radii a, b and c respectively (a < b < c) and carry surface charge densities +sigma, -sigma and +sigma respectively. Find the electric potential at shell B.
- (sigma/eps0)[(a² - b²)/b + c]
- (sigma/eps0)[(b² - c²)/b + a]
- (sigma/eps0)[(b² - c²)/c + a]
- (sigma/eps0)[(a² - b²)/a + c]
Correct answer: (sigma/eps0)[(a² - b²)/b + c]
Solution
Charges: Q_A = sigma*4*pi*a², Q_B = -sigma*4*pi*b², Q_C = sigma*4*pi*c². At point B (r = b): shell A is inside B so contributes kQ_A/b; shell B contributes kQ_B/b (at its own surface); shell C is outside B so contributes kQ_C/c. V_B = k[Q_A/b + Q_B/b + Q_C/c] = (sigma/eps0)[a²/b - b²/b + c²/c] = (sigma/eps0)[(a² - b²)/b + c].
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