Two uniformly charged spherical drops at potential V coalesce to form a larger drop.If capacity of each smaller drop is C then find capacity and potential of larger drop.

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Solution

Dear student

$L e t r, q a n d v b e t h e r a d i u s, c h a r g e a n d p o t e t i a l o f a s m a l l d r o p . T h e t o t a l c h a r g e o n t h e b i g g e r d r o p i s t h e s u m o f a l l c h a r g e o n s m a l l d r o p s s Q = N q T h e v o l u m e o f N s m a l l d r o p s = N \times \frac{4}{3} π r^{3} a n d f o r t h e b i g g e r d r o p = \frac{4}{3} π R^{3} h e n c e \frac{4}{3} π R^{3} = N \times \frac{4}{3} π r^{3} R = N^{1 / 3} r s o t h e p o t e n t i a l o n b i g g e r d r o p V = \frac{1}{4 π ε_{o}} \frac{Q}{R} = \frac{1}{4 π ε_{o}} \frac{N q}{N^{1 / 3} r} = N^{2 / 3} \times \frac{1}{4 π ε_{o}} \frac{q}{r} V = N^{2 / 3} \times v a n d t h e c a p a c i \tan c e C = 4 π ε_{o} R C = 4 π ε_{o} N^{1 / 3} r = N^{1 / 3} (4 π ε_{o} r) C = N^{1 / 3} c$
Here in question, N= 2, putting it in equation
New C= 2^1/3C
New V=2^2/3V

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