Acidified water from certain reservoir kept at a potential V falls...

Acidified water from certain reservoir kept at a potential

V

falls in the form of small droplets each of radius

r

through a hole into a hollow conducting sphere of radius

a

. The sphere is insulated and is initially at zero potential. If the drops continue to fall until the sphere is half full, the potential acquired by the sphere is

Options

A $\frac{a^2 V}{2 r^2}$
B $\sqrt{\frac{a}{r}} \frac{V}{2}$
C $\frac{a^3 V}{2 r^3}$
D $\frac{a V}{r}$

Correct answer

A. $\frac{a^2 V}{2 r^2}$

Step-by-step solution

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