Question

The potential of a large liquid drop when eight liquid drops are combined is 20 V. Then, the potential of each single drop was:

• A. 10 V
• B. 7.5 V
• C. 5 V
• D. 2.5 V

Hint:

When combining drops, the potential scales with the radius, and charge conservation must be considered.

Answer 1

The Correct Option is C

Step 1: {Volume and charge conservation}
\[ 8 \times \frac{4}{3}\pi r^3 = \frac{4}{3}\pi R^3 \Rightarrow R = 2r \] \[ 8q = Q \] Step 2: {Relating potentials}
\[ V' = \frac{kq}{r}, \quad V = \frac{kQ}{R} = \frac{k \times 8q}{2r} = 4 \frac{kq}{r} = 4V' \] \[ 20 = 4V' \Rightarrow V' = 5 \, {V} \] Thus, the potential of each single drop was 5 V.