Q. Two spheres $A$ and $B$ of radius $'a^{'}$ and $'b'$ respectively are at same electric potential. The ratio of the surface charge densities of $A$ and $B$ is
A) $\frac{a}{b}$
B) $\frac{b}{a}$
C) $\frac{a^{2}}{b^{2}}$
D) $\frac{b^{2}}{a^{2}}$
Explanation
(b) Given electric potential of spheres are same $i.e$
$V_{A} = V_{B}$
$\Rightarrow \frac{1}{4\pi\varepsilon_{0}}.\frac{Q_{1}}{a} = \frac{1}{4\pi\varepsilon_{0}}.\frac{Q_{2}}{b} \Rightarrow \frac{Q_{1}}{Q_{2}} = \frac{a}{b}$ …(i)
As surface charge density $\sigma = \frac{Q}{4\pi r^{2}}$
$\Rightarrow \frac{\sigma_{1}}{\sigma_{2}} = \frac{Q_{1}}{Q_{2}} \times \frac{b^{2}}{a^{2}} = \frac{a}{b} \times \frac{b^{2}}{a^{2}} = \frac{b}{a}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.