Two conducting spheres of radii 5 cm and 10 cm are given a charge of 15 µC each. If the two spheres are now joined by a conducting wire, the charge on the smaller sphere will be:

10 µC

The correct answer is Option (2) → 10 µC

$r_1 = 5,\ r_2 = 10$

$\text{Total charge} = 15 + 15 = 30 \ \mu C$

$\text{On connecting: potentials equal}$

$\frac{q_1}{r_1} = \frac{q_2}{r_2}$

$\frac{q_1}{5} = \frac{q_2}{10} \Rightarrow q_2 = 2q_1$

$q_1 + q_2 = 30$

$q_1 + 2q_1 = 30 \Rightarrow 3q_1 = 30$

$q_1 = 10 \ \mu C$

The charge on the smaller sphere is $10 \ \mu C$.