JEE Main · 2022 · 25 Jun 2022 · Shift 2 · Electrostatics

27 identical drops are charged at 22 V each. They combine to form a bigger drop. The potential of the bigger drop will be

____

Answer: 198

Solution

When

n

identical drops combine, the total charge becomes

n q

and the volume is conserved:

n \cdot \frac{4}{3} π r^{3} = \frac{4}{3} π (r^{'})^{3}

r^{'} = n^{1/3} r

The potential of a charged sphere is

V = \frac{k q}{r}

. For the combined drop:

V^{'} = \frac{k ( n q )}{n ^{1/3} r} = n^{2/3} \cdot \frac{k q}{r} = n^{2/3} V

With

n = 27

and

V = 22 V

V^{'} = 2 7^{2/3} \times 22 = 9 \times 22 = 198 V

JEE Main · 2022 · 25 Jun 2022 · Shift 2 · Integer answer