A point charge +Q is located at out side point, at a distance of r from the centre of an uncharged conducting sphere of radius R. Find the electric field and electric potential at the centre of the sphere due to induced charges on the sphere ?

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$\frac{1}{4 π \in_{0}} \frac{Q}{r^{2}}$ and zero

zero and $\frac{1}{4 {πϵ}_{0}} \frac{Q}{R}$

$\frac{1}{4 {πϵ}_{0}} \frac{Q}{R^{2}} and \frac{1}{4 {πϵ}_{0}} \frac{Q}{R}$

$\frac{1}{4 {πϵ}_{0}} \frac{Q}{R^{2}}$ and zero

answer is D.

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Detailed Solution

Induced charge is on the surface of conducting sphere so $E = \frac{1}{4 {πε}_{0}} \frac{Q}{r^{2}}$ Induced negative and positive charges are equal and equidistant from center , So due to induced charges potential at center $V_{Centre} = 0$

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