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Electric Potential at a Point in Space Due to a Point Charge Q

The potential...

Question

The potential at P due to induced charge is

A

K q (\frac{1}{r_{1}} - \frac{1}{r_{2}})

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B

K q (\frac{1}{r_{1}} + \frac{1}{r_{2}})

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C

K q (- \frac{1}{r_{1}} + \frac{1}{r_{2}})

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D

\frac{K q}{r_{1}}

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Solution

The correct option is D $\frac{K q}{r_{1}}$
$q$ inside cavity will induce -q on the inner walls of cavity and +q at the outer surface of sphere.
At point P, the potential due to charge distribution will be such that whole charge is concentrated as a point charge at centre of sphere i.e. q.
Thus, $V_{P} = \frac{1}{4 π ϵ_{0}} \frac{q}{r_{1}} = \frac{K q}{r_{1}}$

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