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Electric Potential Due to Shell

Question

A hollow conducting spherical shell of radius $R$ is charged with $Q$ coulomb. The amount of work done for moving any charge $q$ from the centre to the surface of the shell will be
Zero
$\frac{q Q}{4 π ϵ_{0} R}$
$\frac{2 Q q}{π ϵ_{0} R}$
$\frac{Q q}{π ϵ_{0} R}$

A

\frac{Q q}{π ϵ_{0} R}

B

Zero

C

\frac{q Q}{4 π ϵ_{0} R}

D

\frac{2 Q q}{π ϵ_{0} R}

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Solution

Verified by Toppr

Potential inside the hollow conducting sphere is same as potential at the surface of sphere
i.e. $\frac{Q}{4 π ϵ_{0} R}$
Difference in potential between the surface and center $Δ V = 0$
Thus work done, $W = q Δ V = 0$
So, no work done is done in moving a charge on a equipotential region.

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