Q 12-02-157JEE MainJEE Main 2020 (3 Sep, Shift 1)Easy
Two isolated conducting spheres $S_1$ and $S_2$ of radius $\dfrac23R$ and $\dfrac13R$ have $12\ \mu\text{C}$ and $-3\ \mu\text{C}$ charges, respectively, and are at a large distance from each other. They are now connected by a conducting wire. A long time after this is done the charges on $S_1$ and $S_2$ are respectively:
Answer: (D) $6\ \mu\text{C}$ and $3\ \mu\text{C}$
Total charge $= 12 - 3 = 9\ \mu\text{C}$. At equal potential $\dfrac{kq_1}{r_1} = \dfrac{kq_2}{r_2}$, so the charge divides in the ratio of the radii, $2 : 1$.
$q_1 = 6\ \mu\text{C}$, $q_2 = 3\ \mu\text{C}$.
Solution by Sreeraj P, M.Sc Physics