Question

A conducting sphere of radius 10 cm is charged to $10\mu C$. Another uncharged sphere of radius 20 cm is allowed to touch it for some time. After that if the spheres are separated then surface density of charges, on the spheres will be in the ratio of:

• A. 1:3
• B. 3:1
• C. 2:1
• D. 1:1

Answer 1

The correct option is C 2:1

After redistribution, new charges on sphere are
$Q_1=\left(\frac{10}{10+20}\right)\times 10=\frac{10}{3}\mu C$
and $Q_2=\left(\frac{20}{10+20}\right)\times 10=\frac{20}{3}\mu C$
Ratio of charge densities

$\frac{{\sigma }_1}{{\sigma }_2}=\frac{Q_1}{Q_2}\times \frac{r_2^2}{r_1^2}=\left(\frac{\frac{10}{3}}{\frac{20}{3}}\right)\times {\left(\frac{20}{10}\right)}^2=\frac{2}{1}$