Question

'\(n\)' small spherical drops of the same size which are charged to 'V' volt each coalesce to form a single big drop. The potential of a big drop is

• A. \(nV\)
• B. \(\frac{V}{n}\)
• C. \((n^{\frac{1}{3}})V\)
• D. \((n^{\frac{2}{3}})V\)

Hint:

Charge adds up and the radius scales as n^(1/3).

Answer 1

The Correct Option is D

Step 1: Two Effects:
Potential is charge over radius. Charge grows by a factor $n$, and radius grows by $n^{1/3}$.

Step 2: Combine:
The factor for the potential is $\dfrac{n}{n^{1/3}}=n^{2/3}$.

Step 3: Answer:
$V'=n^{2/3}V$. Option (D).

Final Answer:
Option (D). \[ \boxed{\text{(D) } n^{2/3}V} \]