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Electric Potential Due to Shell

Spherical cav...

Question

Spherical cavity of spherical conductor has point $A$ inside conductor at distance $r$ from charge $Q$ & point $B$ is also inside conductor at distance $2 r$ from charge $Q$ , then

A

V_{A} : V_{B} = 2 : 1

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B

V_{A} : V_{B} = 1 : 2

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C

V_{A} : V_{B} = 4 : 1

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D

V_{A} : V_{B} = 1 : 1

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Solution

The correct option is D $V_{A} : V_{B} = 1 : 1$
$E$ inside conductor $= 0$ (in static condition)
$Δ V = E . Δ r = 0 (Δ r) = 0$
$V_{A} = V_{B}$

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