Question

Two conducting spheres $A$ and $B$ of radius $a$ and $b$ respectively are at the same potential. The ratio of the surface charge densities of $A$ and $B$ is

• A. $\frac{b}{a}$
• B. $\frac{a}{b}$
• C. $\frac{a^2}{b^2}$
• D. $\frac{b^2}{a^2}$
• E. $\frac{(a+b)}{(ab)}$

Answer 1

Answer: (A)

Given electric potential of spheres are same ie,
$V_A=V_B$ $\frac{1}{4\pi {\epsilon }_0}.\frac{Q_1}{a}=\frac{1}{4\pi {\epsilon }_0}.\frac{Q_2}{b}$
$\frac{Q_1}{Q_2}=\frac{a}{b}$ ..(i)
Surface charge density $\sigma =\frac{Q}{4\pi r^2}$
$\Rightarrow$ $\frac{{\sigma }_1}{{\sigma }_2}=\frac{Q_1}{Q_2}\times \frac{b^2}{a^2}$
$=\frac{a}{b}\times \frac{b^2}{a^2}$ $=\frac{b}{a}$