Question

Two isolated metallic spheres of radii 2 cm and 4 cm are given equal charge, then the ratio of charge density on the surfaces of the spheres will be:

• A. $1:2$
• B. $4:1$
• C. $1:4$
• D. $2:1$

Answer 1

Answer: (B)

$4:1$

The spheres are conducting (metallic)

Due to repulsion between charger, all charges accumulate at the surface of the spheres.

We define surface charge Density $\left(\sigma \right)$ as :

$\sigma =\frac{Q}{A}=\frac{Q}{4\pi R^2}$ [A : surface area]

So, for equal $Q,\sigma \alpha \frac{1}{R^2}$

Thus, ratio of surface charge densities between them :

$\frac{{\sigma }_1}{{\sigma }_2}={\left(\frac{R_2}{R_1}\right)}^2$

From question, $R_1=2cm,R_2=4cm$

$\Rightarrow \frac{{\sigma }_1}{{\sigma }_2}={\left(\frac{4}{2}\right)}^2=4$