Test Index

Electrostatics Part 3

Section: Physics

Question : 20 of 80

Marks: +1, -0

Solution:

Concept:

When identical charged bubbles coalesce, total charge and total volume are conserved.

Explanation:

Let each small bubble have radius

r

and charge

q

Its surface potential is

V_1 = \frac{1}{4\pi\epsilon_0} \frac{q}{r}

Three bubbles coalesce into one big bubble of radius

R

and total charge

Q = 3q

Conserving volume:

3 \times \frac{4}{3}\pi r^3 = \frac{4}{3}\pi R^3 \implies 3r^3 = R^3 \implies R = 3^{1/3}r

Potential of big bubble:

V_2 = \frac{1}{4\pi\epsilon_0} \frac{Q}{R} = \frac{1}{4\pi\epsilon_0} \frac{3q}{3^{1/3}r} = 3^{2/3} \cdot \frac{1}{4\pi\epsilon_0} \frac{q}{r} = 3^{2/3} V_1

Thus ratio

V_1 : V_2 = 1 : 3^{2/3}

Answer:

Option A:

1:3^{\frac{2}{3}}

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