Question

Two spherical conductors of radii $4m$ and $5m$ are charged to the same potential. If ${\sigma }_1$ and ${\sigma }_2$ be the respective values of the surface density of charge on the two conductors, then the ratio $\frac{{\sigma }_1}{{\sigma }_2}$is

• A. $\frac{4}{5}$
• B. $\frac{5}{4}$
• C. $\frac{16}{25}$
• D. $\frac{25}{16}$

Answer 1

The correct option is B $\frac{5}{4}$

here, $V_1=V_2$
or $\frac{k{q}_1}{r_1}=\frac{k{q}_2}{r_2}$

or $\frac{q_1}{q_2}=\frac{r_1}{r_2}............\left(1\right)$

now, ${\sigma }_1=\frac{q_1}{4\pi r_1^2}$ and ${\sigma }_2=\frac{q_2}{4\pi r_2^2}$

thus, $\frac{{\sigma }_1}{{\sigma }_2}=\frac{q_1}{q_2}.\frac{r_2^2}{r_1^2}=\frac{r_1}{r_2}.\frac{r_2^2}{r_1^2}=\frac{r_2}{r_1}=\frac{5}{4}$