Question

Two charged spheres of radii $R_1 \, and \, R_2$ have equal surface charge density. The ratio of their potential is

• A. $R_1/ R_2$
• B. $R_2/ R_1$
• C. $(R_1/ R_2)^2$
• D. $(R_2/ R_1)^2$

Answer 1

Answer: (A)

$R_1/ R_2$

Answer 2

Surface charge densities are given as
$\sigma=\frac{Q}{A}=\frac{Q}{4 \pi R^{2}}$
$Q_{1}=Q_{2}=Q$
As $\sigma_{1}=\sigma_{2}$
$\Rightarrow \frac{Q_{1}}{4 \pi \varepsilon_{0} R_{1}^{2}}=\frac{Q_{2}}{4 \pi \varepsilon_{0} R_{2}^{2}}$
$\frac{ V _{1}}{ V _{2}}=\frac{ R _{1}}{ R _{2}}$