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Question

The figure shows two conducting concentric sperical shells of radii R and 2R.
The inner shell has a charge +Q and the outer one is neutral.

(A) Energy stored in region given by R < r < 2R P) Q232πϵoR
(B) Energy stored in region given by 2R<r<
Q) Q216πϵoR
(C) Energy stored in region given by 2R < r < 4R R) Q28πϵoR
(D) Heat generated when switch S is closed S) zero
T) None

A
A Q, B Q, C P, D Q,
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B
A R, B Q, C S, D S,
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C
A R, B R, C P, D Q,
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D
A Q, B R, C S, D S,
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Solution

The correct option is A A Q, B Q, C P, D Q,
Energy stored in region is
du = 12ϵoE2×4πr2dr
where E = Q4πϵor2
=du=12ϵo(Q4πϵor2)2×4πr2dr
=Q28πϵor2r1r2dr=Q28πϵo[1r11r2]

Varying r1 & r2 energies for different regions can be found.

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