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Electric Potential Due to a Solid Sphere of Charge

Two concentri...

Question

Two concentric spheres of radii $R_{1}$ and $R_{2} > R_{2} > R_{1}$ carry charges $Q_{1}$ and $Q_{2}$ respectively. The potential at a point in between the two spheres and at a distance $r$ from the centre will be

A

k (\frac{Q_{1}}{R_{1}} + \frac{Q_{2}}{R_{2}})

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B

k (\frac{Q_{1} + Q_{2}}{r})

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C

k (\frac{Q_{1}}{r} + \frac{Q_{2}}{R_{2}})

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D

k (\frac{Q_{1}}{R_{1}} + \frac{Q_{2}}{r})

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Solution

The correct option is C $k (\frac{Q_{1}}{r} + \frac{Q_{2}}{R_{2}})$
The potential at every point inside the hollow sphere $Q_{2}$ is constant and is equal to the on its surface. The potential due to $Q_{1}$ outside its surface at $P$ is at a distance $r$ .
The potential at $P$ is given by
$V = \frac{1}{4 π ϵ_{0}} [\frac{Q_{1}}{r} + \frac{Q_{2}}{R_{2}}]$
$= k [\frac{Q_{1}}{r} + \frac{Q_{2}}{R_{2}}] [w h e r e k = \frac{1}{4 π ϵ_{0}}]$ .

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