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Question:

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

σϵ₀[b²−c²/b+a]

σϵ₀[b²−c²/c+a]

σϵ₀[a²−b²/b+c]

σϵ₀[a²−b²/a+c]

Solution:

Vouter = KQ/r where r is the distance of the point from the center of the shell
Vinside = KQ/R where R is the radius of the shell
VB = KqA/b - KqB/b + KqC/c
VB = 1/4πε₀[(σ4πa²/b) - (σ4πb²/b) + (σ4πc²/c)]
VB = σε₀[a²/b - b/b + c/b]
VB = σε₀[a²/b - 1 + c/b]
VB = σε₀[(a² - b + c)/b]