Question

- 125 drops of water each of radius 2 mm and
carrying charge of 1 nC are made to form a bigger
drop. Find the capacitance and potential of the
bigger drop.
[Ans. 1.1 pF, 113.6 V]​

Answer 1

Explanation ⇒ For small drop,

v = kq/r

∴ v = 9 × 10⁹ × 10⁻⁹/(2 ×  10⁻³)

v = 4.5 × 10³ V

For bigger drop,

V = knq/R

Now, Volume of final sphere = n × Volume of small sphere

∴ R³ = n × r³

∴ R = n¹⁾³ × r

∴ V = kn²⁾³ × q/R

∴ V = 9 × 10⁹ × 5² × 10⁻⁹/2 × 10⁻³

V = 122.5 V.

For Capacitance,

C = Q/V

C = 125 × 10⁻⁹/122.5

∴ C = 1.02 nF

[Answer given in question are wrong.]

Hope it helps.

Answer 2

Explanation ⇒ For small drop,

v = kq/r

∴ v = 9 × 10⁹ × 10⁻⁹/(2 ×  10⁻³)

v = 4.5 × 10³ V

For bigger drop,

V = knq/R

Now, Volume of final sphere = n × Volume of small sphere

∴ R³ = n × r³

∴ R = n¹⁾³ × r

∴ V = kn²⁾³ × q/R

∴ V = 9 × 10⁹ × 5² × 10⁻⁹/2 × 10⁻³

V = 122.5 V.

For Capacitance,

C = Q/V

C = 125 × 10⁻⁹/122.5

∴ C = 1.02 nF