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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
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B
2(Qq)4πϵ0R
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C
2Q+q4πϵ0R
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D
2Q4πϵ0R
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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)

849626_596406_ans_53ee92629bfb491bb4d4ac0105bc9715.jpg

Physics
NCERT
Standard XII

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