Eight identical spherical drops, each having a potential of 9 V are combined together to form a single large drop. The potential of this large drop will be:
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 36 V
When the drops merge, charge is conserved and the volume is conserved. The potential of a charged sphere of radius \( r \) is \( V = kq/r \).
\( \displaystyle Q = 8q \)
\( \displaystyle \frac{4}{3}\pi R^{3} = 8 \times \frac{4}{3}\pi r^{3} \;\Rightarrow\; R = 2r \)
\( \displaystyle V' = \frac{kQ}{R} = \frac{k(8q)}{2r} = 4\,\frac{kq}{r} = 4 \times 9\,\mathrm{V} = 36\,\mathrm{V} \)