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Question

A point charge q is kept at a distance of 2R from centre of an uncharged spherical shell of radius R. The potential at centre of the shell due to charges induced on shell is


A
q4πE0R
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B
q4πE02R
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C
q4πE0R
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D
Zero
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Solution

The correct option is C $$\dfrac{-q}{4 \pi E_0R}$$
Charge $$=q$$
distance $$=2R$$
radius $$=R$$
$$V=$$ Potential at centre of the shell due to charge induced on shell.
As the electric field inside a conductor is zero. The electrostatic potential is constant it. The potential at centre will be the potential of entire conductor. The entire charge of conductor is on surface $$N$$.
Now, $$V=\dfrac { -1 }{ 4\pi { \epsilon  }_{ 0 } } \dfrac { q }{ R } $$
The $$(-Ve)$$ sign due to spherical shell of centre (inside).

Physics
NCERT
Standard XII

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