Question

# A thin spherical conducting shell has radius $$R$$ and charge $$q$$. Another charge $$Q$$ is placed at the centre of the shell. The electric potential at a point $$P$$ at a distance $$0.5d$$ from the centre of the shell is :

A
2(q+Q)4πϵ0R
B
2(Qq)4πϵ0R
C
2Q+q4πϵ0R
D
2Q4πϵ0R

Solution

## The correct option is C $$\dfrac{2Q+q}{4\pi\epsilon_0R}$$$$r=\dfrac{R}{2}$$Potential at any point inside a shell is given by $$\dfrac{q}{4\pi\epsilon_o R}$$$$V=V_{charge Q}+V_{shell}$$$$\implies V=\dfrac{1}{4\pi\epsilon_o}\left(\dfrac{Q}{r}+\dfrac{q}{R}\right)$$$$\implies V=\dfrac{1}{4\pi\epsilon_o}\left(\dfrac{2Q}{R}+\dfrac{q}{R}\right)$$$$\implies V=\dfrac{2Q+q}{4\pi\epsilon_o R}$$Answer-(C)PhysicsNCERTStandard XII

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