Question

Small rain drops of the same size are charged to potential $V$ volt each. If $n$ such drops coalesce to form a single drop, then the potential of the bigger drop is

• A. $n^{1/3}V$
• B. $n^{2/3}V$
• C. $nV$
• D. $n^{3/2}V$

Hint:

Potential of a charged drop is proportional to $n^{2/3}$ when $n$ drops coalesce.

Answer 1

The Correct Option is B

Step 1: Understanding the Concept:
Volume conservation: $R = n^{1/3}r$. Charge conservation: $Q = nq$.
Step 2: Detailed Explanation:
Potential of smaller drop: $V = \frac{q}{4\pi\epsilon_0 r}$. Potential of bigger drop: $V' = \frac{Q}{4\pi\epsilon_0 R} = \frac{nq}{4\pi\epsilon_0 n^{1/3}r} = n^{2/3} \frac{q}{4\pi\epsilon_0 r} = n^{2/3}V$.
Step 3: Final Answer:
The potential is $n^{2/3}V$.