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: (a) (σ)/(ε₀)[(b²-c²)/(c)+a] (b) (σ)/(ε₀)[(a²-b²)/(a)+c] (c) (σ)/(ε₀)[(a²-b²)/(b)+c] (d) (σ)/(ε₀)[(b²-c²)/(b)+a]

Answer: (c). Charges: qA = 4π a²σ, qB = -4π b²σ, qC = 4π c²σ. VB = (1)/(4πε₀)((qA + qB)/(b) + qC/c) VB = (σ)/(ε₀)[(a² - b²)/(b) + c] So the answer is (c).

Three concentric metal shells A, B and C of respective radii a, b and… | JEE Main 2018

Q98JEE Main 2018Medium

Electric Potential & Equipotentials

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

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Answer: (c)

Charges: $q_A = 4\pi a^2\sigma$ , $q_B = -4\pi b^2\sigma$ , $q_C = 4\pi c^2\sigma$ .
$V_B = \frac{1}{4\pi\varepsilon_0}\left(\frac{q_A + q_B}{b} + \frac{q_C}{c}\right)$
$V_B = \frac{\sigma}{\varepsilon_0}\left[\frac{a^2 - b^2}{b} + c\right]$
So the answer is (c).

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