Question

$n$ charged drops, each of radius $r$ and charge $q$, coalesce to form a big drop of radius $R$ and charge $Q$. If $V$ is the electric potential and $E$ is the electric field at the surface of a drop, then :

• A. $E_{big}=n^{2/3}{E}_{small}$
• B. $V_{big}=n^{1/3}{V}_{small}$
• C. $E_{small}=n^{2/3}{E}_{big}$
• D. $V_{big}=n^{2/3}{V}_{small}$

Answer 1

Answer: (D)

$V_{big}=n^{2/3}{V}_{small}$

total charge and charge density remain same

$Q=nq$

$\rho Vo{l}_1=n\rho Vo{l}_2$

$\frac{4\pi R^3}{3}=n\frac{4\pi r^3}{3}$

$R=n^{1/3}r$

$E_{small}=\frac{kq}{r^2},E_{big}=\frac{kQ}{R^2}$

$E_{big}=\frac{knq}{n^{2/3}{r}^2}=\left(n^{1/3}\right)\frac{kq}{r^2}=n^{1/3}{E}_{small}$

$V_{small}=\frac{kq}{r},V_{big}=\frac{kQ}{R}$

$V_{big}=\frac{knq}{n^{1/3}r}=\left(n^{2/3}\right)\frac{kq}{r}=n^{2/3}{V}_{small}$