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Question

Three concentric spherical shells have radii a, b, and c(a < b < c) and have surface charge densities σ, σ andσ respectively. If VA, VB and VC denote the potentials of the three shells, then, for c = a + b, we have :

A
VC = VB = VA
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B
VC = VAVB
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C
VC = VBVA
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D
VCVBVA
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Solution

The correct option is B VC = VAVB
It is clear from figure that
Va=σaε0σbε0+σcε0=σε0(ab+c)c=a+b
As c=a+b
VA=σε0(2a)
VB=σε0[a2bb+c]=σε0[a2bb+a+b]
VB=σε0[a2b+a]=σaε0(a+b)b=σ0acε0b
VC=σε0[a2ba2c+c]=σaε0[a2b2+c2c]=σε0[(a+b)(ab)+(a+b)2c]
VC=σε0[(a+b)c(ab+a+b)]=σ2aε0
we found that, VC = VAVB
1032141_71332_ans_72dc4174f25d4bc8baacb7e0b238a08d.PNG

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