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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
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Total charge=64*C=64C
Now,4/3πr³=64*4/3πR³
r=4R
C’=4π£R
C’=4π£(4R)
C’=4C (Answer)