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Q.

A point charge Q is placed inside a conducting spherical shell of inner radius 3R and outer radius 5R at a distance R from the centre of the shell. The electric potential at the centre of the shell will be.

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a

$\frac{1}{4 {πε}_{0}} . \frac{7 Q}{9 R}$

b

$\frac{1}{4 {πε}_{0}} . \frac{5 Q}{6 R}$

c

$\frac{1}{4 {πε}_{0}} . \frac{13 Q}{15 R}$

d

$\frac{1}{4 {πε}_{0}} . \frac{Q}{R}$

answer is C.

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Detailed Solution

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$\begin{array}{rcl} V_{net} & = & \frac{Q}{4 {πε}_{0}} [\frac{1}{r} - \frac{1}{a} + \frac{1}{b}] \\ V_{net} & = & \frac{Q}{4 {πε}_{0}} [\frac{1}{R} - \frac{1}{3 R} + \frac{1}{5 R}] \\ V_{net} & = & \frac{1}{4 {πε}_{0}} [\frac{13 Q}{15 R}] \end{array}$

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A point charge Q is placed inside a conducting spherical shell of inner radius 3R and outer radius 5R at a distance R from the centre of the shell. The electric potential at the centre of the shell will be.