64 identical spheres of charge q and capacitance C each are combined to form a large sphere. The charge and capacitance of the large sphere is

Options

(a) 64q, C
(b) 16q, 4C
(c) 64q, 4C
(d) 16q, 64C

Correct Answer:

64q, 4C

Explanation:

64 drops have formed a single drop of radius R.

Volume of big drop = Volume of small drop

.·. (4/3) πR³ = 64 × (4/3) πr³ ⇒ R = 4r —–(1)

So, the total current is Q(total) = 64q

As, C’ = Q / V and V = (1/4πε₀) (Q/R)

C’ = 4πε₀R ——–(2)

Substituting Eqn (1) in Eqn (2), we get

C’ = 4πε₀ × 4r = 4C