Question

Three concentric metallic spherical shells of radii $R,2R,3R$ are given $Q_1,Q_2,Q_3$ respectively. It is found that the surface charge densities on the outer surfaces of shells are equal. Then, the ratio of the charges given to the shells $Q_1:Q_2:Q_3$ is

• A. $1:8:18$
• B. $1:3:5$
• C. $3:4:5$
• D. $1:4:9$

Answer 1

Answer: (B)

Due to induction, net charge on outer surfaces of spheres will be as
$\sigma =\frac{Q_1}{4\pi R_{}^2}=\frac{Q_1+Q_2}{4\pi {\left(2R\right)}^2}=\frac{Q_1+Q_2+Q_3}{4\pi {\left(3R\right)}^2}$
$\Rightarrow Q_1=\frac{Q_1+Q_2}{4}=\frac{Q_1+Q_2+Q_3}{9}$
On solving, we get
$Q_2=3Q_1$ and $Q_3=5Q_1$
Therefore, $Q_1:Q_2:Q_3=1:3:5$