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. $\frac{{{b}^{2}}}{{{a}^{2}}}$

Answer 1

Answer: (A)

$\frac{b}{a}$

Answer 2

Given electric potential of spheres are same ie,
${{V}_{A}}={{V}_{B}}$ $\frac{1}{4\pi {{\varepsilon }_{0}}}.\frac{{{Q}_{1}}}{a}=\frac{1}{4\pi {{\varepsilon }_{0}}}.\frac{{{Q}_{2}}}{b}$
$\frac{{{Q}_{1}}}{{{Q}_{2}}}=\frac{a}{b}$ ..(i)
Surface charge density $\sigma =\frac{Q}{4\pi {{r}^{2}}}$
$\Rightarrow$ $\frac{{{\sigma }_{1}}}{{{\sigma }_{2}}}=\frac{{{Q}_{1}}}{{{Q}_{2}}}\times \frac{{{b}^{2}}}{{{a}^{2}}}$
$=\frac{a}{b}\times \frac{{{b}^{2}}}{{{a}^{2}}}$ $=\frac{b}{a}$