Question

Two charged spherical conductors of radius $R_1$ and $R_2$ are connected by a wire. Then the ratio of surface charge densities of the spheres $\left({\sigma }_1/{\sigma }_2\right)$ is

• A. $\frac{R_1}{R_2}$
• B. $\frac{R_2}{R_1}$
• C. $\sqrt{\left(\frac{R_1}{R_2}\right)}$
• D. $\frac{R_1^2}{R_2^2}$

Answer 1

Answer: (B)

$\frac{Q_1}{4\pi {\epsilon }_0{R}_1}=\frac{Q_2}{4\pi {\epsilon }_0{R}_2}=V$
$\therefore \frac{Q_1}{Q_2}=\frac{R_1}{R_2}$
$\therefore \frac{{\sigma }_1}{{\sigma }_2}=\frac{Q_1/4\pi R_1^2}{Q_2/4\pi R_2^2}$
$=\frac{Q_1}{Q_2}{\left(\frac{R_2}{R_1}\right)}^2=\left(\frac{R_1}{R_2}\right){\left(\frac{R_2}{R_1}\right)}^2$
$\Rightarrow \frac{{\sigma }_1}{{\sigma }_2}=\frac{R_2}{R_1}$