Question

A spherical conducting shell of inner radius $r_1$ and outer radius $r_2$ has a charge Q. A charge $-q$ is placed at the center of the shell. The surface of the shell will be

• A. $\frac{q}{4\pi r_1^2}$ and $\frac{Q}{4\pi r_2^2}$
• B. $\frac{-q}{4\pi r_1^2}$ and $\frac{Q+q}{4\pi r_2^2}$
• C. $\frac{q}{4\pi r_1^2}$ and $\frac{Q-q}{4\pi r_2^2}$
• D. $0$ and
  

Answer 1

The correct option is B $\frac{-q}{4\pi r_1^2}$ and $\frac{Q+q}{4\pi r_2^2}$

$+Q$ charge is on the outer surface of the shell .

Charge $q$ is placed at the centre, it introduce a charge $-q$ on the inner surface and charge $+q$ on the outer surface of shell-

$inner=\frac{-q}{4\pi r_1^2}$

$TotalCh\arg e=Q+q$

$Outer=\frac{Q+q}{4\pi r_2^2}$

Applying gauss’s law-

$\varphi \overline{E}.d\overline{s}=\frac{Q+q}{{\epsilon }_0}$

$\overline{E}=\frac{Q+q}{4\pi r_2^2}{f}_0$