JEE Main · 2020 · 03 Sep 2020 · Shift 1 · Electrostatics

Two isolated conducting spheres

S_{1}

and

S_{2}

of radius

\frac{2}{3} R

and

\frac{1}{3} R

have

12 μ C

and -3

μ 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:

(A) $+ 4.5 μ C$ and $- 4.5 μ C$
(B) $4.5 μ C$ on both
(C) $6 μ C$ and $3 μ C$ ✓ Correct
(D) $3 μ C$ and $6 μ C$

Answer: (C)

Solution

Joined by a wire, the spheres share charge until they reach a common potential; since the capacitance of an isolated sphere is proportional to its radius, the final charges are in the ratio of the radii,

\frac{2}{3} R : \frac{1}{3} R = 2 : 1

. The total charge is conserved,

12 + (- 3) = 9 μ

C, so it divides as

q_{1} = \frac{2}{3} \times 9 = 6 μ

C and

q_{2} = \frac{1}{3} \times 9 = 3 μ

JEE Main · 2020 · 03 Sep 2020 · Shift 1 · Single correct option

Practise more: all JEE Main PYQs on Electrostatics →

JEE Main · 2020 · 03 Sep 2020 · Shift 1 · Electrostatics

Solution

More JEE Main questions on Electrostatics