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. $\frac{2Q}{4\pi {\epsilon }_{0}R}$
• B. $\frac{2Q}{4\pi {ϵ}_{0}R}-\frac{2q}{4\pi {\epsilon }_{0}R}$
• C. $\frac{2Q}{4\pi {ϵ}_{0}R}+\frac{q}{4\pi {\epsilon }_{0}R}$
• D. $\frac{(q+Q)}{4\pi {\epsilon }_0}\frac{2}{R}$

Answer 1

Answer: (C)

$\frac{2Q}{4\pi {ϵ}_{0}R}+\frac{q}{4\pi {\epsilon }_{0}R}$

Here the point is inside the shell.
so, the potential at P $=$ potential due to charge Q$+$ potential at surface of shell
or $V_P=\frac{Q}{4\pi {ϵ}_0\left(R/2\right)}+\frac{q}{4\pi {ϵ}_{0}R}$