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Question

A thin spherical conducting shell of radius $$R$$ has a charge $$q$$. Another charge $$Q$$ is placed at the centre of the shell. The electrostatic potential at a point P at a distance $$R/2$$ from the centre of the shell is :


A
2Q4πε0R
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B
2Q4πε0R2q4πε0R
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C
2Q4πε0R+q4πε0R
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D
(q+Q)24πεoR
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Solution

The correct option is A $$\dfrac{2Q}{4\pi\varepsilon _{0}R}+\dfrac{q}{4\pi\varepsilon _{0}R}$$
At P, potential due to shell :
$$V_1 = \dfrac {q}{4 \pi \epsilon_0 R}$$
At P , potential due to Q :
$$V_2 = \dfrac {Q}{4 \pi \epsilon_0 \dfrac {R}{2}}$$
$$\therefore$$  Net potential at P
$$V = V_1 + V_2$$
$$= \dfrac {q}{4 \pi \epsilon_0 R} + \dfrac {2Q}{4 \pi \epsilon_0 R}$$
157472_76623_ans.JPG

Physics
NCERT
Standard XII

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