A point charge q is placed inside a conducting spherical shell of inner radius 2R and outer radius 3R at a distance of R from the centre of the shell. The electric potential at the centre of shell will be $\frac{1}{4 π ϵ_{0}}$ times.

$\frac{q}{2 R}$

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$\frac{4 q}{3 R}$

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$\frac{5 q}{6 R}$

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$\frac{2 q}{3 R}$

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Solution

The correct option is C
$\frac{5 q}{6 R}$

Induced charges will be $- q$ and $+ q$ as shown in figure.

Potential at center will be $V_{0} = \frac{1}{4 π ϵ_{0}} [\frac{q}{R} - \frac{q}{2 R} + \frac{q}{3 R}]$

$= \frac{1}{4 π ϵ_{0}} (\frac{5 q}{6 R})$

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A point charge q is placed inside a conducting spherical shell of inner radius 2R and outer radius 3R at a distance of R from the centre of the shell. The electric potential at the centre of shell will be 14πϵ0 times.

The correct option is C 5q6R Induced charges will be −q and +q as shown in figure. Potential at center will be V0=14πϵ0[qR−q2R+q3R] =14πϵ0(5q6R)

A point charge q is placed inside a conducting spherical shell of inner radius 2R and outer radius 3R at a distance of R from the centre of the shell. The electric potential at the centre of shell will be $\frac{1}{4 π ϵ_{0}}$ times.

The correct option is C
$\frac{5 q}{6 R}$

Induced charges will be $- q$ and $+ q$ as shown in figure.

Potential at center will be $V_{0} = \frac{1}{4 π ϵ_{0}} [\frac{q}{R} - \frac{q}{2 R} + \frac{q}{3 R}]$

$= \frac{1}{4 π ϵ_{0}} (\frac{5 q}{6 R})$