Question

twenty seven drops of same sizes are charged at 220V each. They coalesce to form a bigger drop. Calculate the potential of the bigger drop.

Answer 1

let r and R be radius of small and large drips respectively.

And v be the potential of small drip,

$v=220V$

Q and q be the charge on each small sphere and bigger sphere. and since charge is constant.

$Q=27q \to(1)$

From the constant volume of the drops,assuming drops are spherical applying volume equation,

$\frac{4}{3} \pi R^3=27\times\frac{4}{3} \pi r^3\\ R^3=(3r)^3\\ R=3r \to(2)$

Potential of bigger drop

$V_1=\frac{Q}{C}=\frac{27q}{3(4\pi\epsilon_ 0r)}=9[\frac{q}{4\pi \epsilon_0r}]\\ V_1=9\times220\\ V_1=1980V$