Three concentric metal shells A , B and C of respective radii a , b and c ( a

Question

Three concentric metal shells A , B and C of respective radii a , b and c ( a < b < c ) have surface charge densities + σ , - σ and + σ respectively. The potential of shell B is:

TestHub · Accepted Answer

Net potential at B is due to the superposition of potential due to all shells,

$\lor_{B} = \lor_{B (I)} + \lor_{B (I I)} + \lor_{B (I I I)}$

$= \frac{K 4 π a^{2} σ}{b} + \frac{K 4 π b^{2} (- σ)}{b} + \frac{K 4 π c^{2} (σ)}{c}$

Required potential of b

$= \frac{σ a^{2}}{ε_{0} b} - \frac{σ b^{2}}{ε_{0} b} + \frac{σ c^{2}}{ε_{0} c}$

$= \frac{σ}{ε_{0}} (\frac{{a^{2} - b}^{2}}{b} + c)$

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