Question

8 identical droplets are charged to potential v each. if they coalesce to form single drop, then its potential will be?
(1) V
(2) 2V
(3) 4V
(4) V/2​

Answer 1

Hi mate yr answer is 3) 4V .. mark answer as brainlist.....

Answer 2

Answer:

The potential on bigger drop is 4V.

(3) is correct.

Explanation:

Let r,q and v be the radius ,charge and potential of a small drop.

The total charge on the bigger drop is the sum of all charge on small drops.

Q = 8q

The volume of bigger drop is

$V =\dfrac{4}{3}\pi R^3$

The volume of small drops are

$V =8\times\dfrac{4}{3}\pi r^3$

The volume of bigger drop = the volume of small drop

$\dfrac{4}{3}\pi R^3=8\times\dfrac{4}{3}\pi r^3$

$R=8^{\frac{1}{3}}r$

$R=2r$

The potential on small drop is

$V = \dfrac{1}{4\pi\epsilon_{0}}\times\dfrac{q}{r}$

The potential on bigger drop is

$V' = \dfrac{1}{4\pi\epsilon_{0}}\times\dfrac{Q}{R}$

$V' =\dfrac{1}{4\pi\epsilon_{0}}\times\dfrac{8q}{2r}$

$V' = 4\times\dfrac{1}{4\pi\epsilon_{0}}\times\dfrac{q}{r}$

$V' =4V$

Hence, The potential on bigger drop is 4V.