Question
Physics Question on electrostatic potential and capacitance
27 small drops each having charge q and radius r coalesce to from big drop. How many times charge and capacitance will become?
A
44647
B
27, 3
C
27, 27
D
44623
Answer
27, 3
Explanation
Solution
Let R and r be the radii of bigger and each smaller drop
respectively. In coalescing into a single drop, charge remains
conserved.
Charge on bigger drop
\hspace30mm = 27 x charge on smaller drop
ie, \hspace15mm q' = 27 q
Now, before and after coalescing, volume remains same.
\hspace30mm \frac{4}{3} \pi R^3 = 27 \times \frac{4}{3} \pi r^3
\therefore \hspace30mm R = 3r
Hence, capacitance of bigger drop
\hspace30mm C' = 4 \pi \varepsilon_0 R
\hspace30mm = 4 \pi \varepsilon_0 (2r)
\hspace30mm = 3 (4 \pi \varepsilon_0 r)
\hspace30mm = 3C