Eight charged water drops, each with a radius of 1 mm and a charge of 10-10 C, coalesce to form a single drop. The potential of the big drop is

Question

Eight charged water drops, each with a radius of 1 mm and a charge of 10-10 C, coalesce to form a single drop. The potential of the big drop is (A) 3.6 V (B) 36 V (C) 360 V (D) 3600 V

Tardigrade Admin · Accepted Answer

Volume is conserved. ∴ (4/3) π r3=8 × (4/3) π r3 or R3=23 r3 or R=2 r V=(1/4 π ε0) (8 q/2 r) =(4 × 9 × 109 × 10-10/1 × 10-3) volt =3600 volt

Q. Eight charged water drops, each with a radius of $1 mm$ and a charge of $1 0^{- 10} C$ , coalesce to form a single drop. The potential of the big drop is

3.6 V

36 V

360 V

3600 V

Volume is conserved.
$∴ \frac{4}{3} π r^{3} = 8 \times \frac{4}{3} π r^{3}$
or $R^{3} = 2^{3} r^{3}$ or $R = 2 r$
$V = \frac{1}{4 π ε _{0}} \frac{8 q}{2 r}$
$= \frac{4 \times 9 \times 1 0 ^{9} \times 1 0 ^{- 10}}{1 \times 1 0 ^{- 3}}$ volt
$= 3600$ volt

Q. Eight charged water drops, each with a radius of 1mm and a charge of 10−10C, coalesce to form a single drop. The potential of the big drop is