Q. 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 ($\sigma_1/\sigma_2$) is:
A) $\frac{R_2}{R_1}$
B) $\sqrt{\frac{R_1}{R_2}}$
C) $\frac{R_1^2}{R_2^2}$
D) $\frac{R_1}{R_2}$
Explanation
[Solution] Connected spheres are at equal potential: $Q_1/R_1 = Q_2/R_2$, so $\sigma \propto Q/R^2 \propto 1/R$ and $\sigma_1/\sigma_2 = R_2/R_1$. Answer (1).
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.