question_answer

A thin spherical conducting shell of radius R has a charge q. Another charge 0 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 [AIEEE 2003]

A) \[\frac{2Q}{4\pi {{\varepsilon }_{0}}R}\]

B) \[\frac{2Q}{4\pi {{\varepsilon }_{0}}R}-\frac{2q}{4\pi {{\varepsilon }_{0}}R}\]

C) \[\frac{2Q}{4\pi {{\varepsilon }_{0}}R}+\frac{q}{4\pi {{\varepsilon }_{0}}R}\]

D) \[\frac{(q+Q)}{4\pi {{\varepsilon }_{0}}R}\frac{2}{R}\]

Correct Answer: C

Solution :

[c] At P, potential due to shell

\[{{V}_{1}}=\frac{q}{4\pi \,{{\varepsilon }_{0}}R}\]

At P, due to charge

\[{{V}_{2}}=\frac{Q}{4\pi {{\varepsilon }_{0}}\frac{R}{2}}\]

\[=\frac{2Q}{4\pi {{\varepsilon }_{0}}R}\]

\[\therefore \] Net potential at P,

\[V={{V}_{1}}+{{V}_{2}}=\frac{q}{4\pi {{\varepsilon }_{0}}R}+\frac{2Q}{4\pi {{\varepsilon }_{0}}R}\]

(\[\because \] v is scalar quantity)