Question

Sixty four spherical drops each of radius 2 cm
and carrying 5C charge combine to form a
bigger drop. Its capacity is​

Answer 1

Answer ⇒ Capacitance = 14.22 × 10⁻¹¹ F.

Explanation ⇒

Charge on one drop = 5 C.

Radius of one small drop = 2 cm.

Charge on bigger drop = 64 × 5 C.

Now, Using the formula,

Potential of big sphere = $n^{\frac{2}{3} }$ Potential on small sphere.

∴ Potential on small sphere = kQ/r

= 9 × 10⁹ × 5/0.02

= 22.5  × 10¹¹ V.

Now, Using the formula,

 Capacitance = Total charge/Total potential.

∴ Capacitance = 64 × 5/(22.5 × 10¹¹)

Thus, Capacitance = 14.22 × 10⁻¹¹ F.

Hope it helps.

Answer 2

Explanation ⇒

Charge on one drop = 5 C.

Radius of one small drop = 2 cm.

Charge on bigger drop = 64 × 5 C.

Now, Using the formula,

Potential of big sphere = Potential on small sphere.

∴ Potential on small sphere = kQ/r

= 9 × 10⁹ × 5/0.02

= 22.5  × 10¹¹ V.

Now, Using the formula,

 Capacitance = Total charge/Total potential.

∴ Capacitance = 64 × 5/(22.5 × 10¹¹)

Thus, Capacitance = 14.22 × 10⁻¹¹ F.