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Question

A thin spherical conduction shell of radius R has a charge q. another charge Q is placed atthe centre of the shell. The electrostatic potential at a point P at a distance R$$/2$$ from thecentre 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)4πε02R
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Solution

The correct option is B $$\displaystyle \dfrac{2\mathrm{Q}}{4\pi\epsilon_{0}\mathrm{R}}+\dfrac{\mathrm{q}}{4\pi\varepsilon_{0}\mathrm{R}}$$
Here the point is inside the shell. 
so, the potential at P $$=$$ potential due to charge Q$$+$$ potential at surface of shell
or $$V_P=\dfrac{Q}{4\pi\epsilon_0(R/2)}+\dfrac{q}{4\pi\epsilon_0 R}$$

Physics
NCERT
Standard XII

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