Question

8 identical droplets are charged to potential v each. If they coalesce to form single drop , then it's potential will be ?

Answer 1

Let radius of droplet is r and radius of drop is R.

a/c to question, 8 droplets coalesce to form a single drop.

volume of drop = 8 × volume of droplet

or, 4/3 πR³ = 8 × 4/3 πr³

or, R³ = 8r³

or, R = 2r .........(1)

capacitance of each droplet, C = $4\pi\epsilon_0r$

so, charge on each droplet , q = Cv

= $4\pi\epsilon_0rv$

net charge on 8 droplets , Q = 8q = $32\pi\epsilon_0rv$

now capacitance of drop, C' = $4\pi\epsilon_0R$

= $4\pi\epsilon_0(2r)$[From equation (1) ]

=$8\pi\epsilon_0r$

Let the potential on drop is V

so, Q = C'V [ charge on drop is same as charge on 8 droplets ]

or, $32\pi\epsilon_0rv=8\pi\epsilon_0rV$

or, V = 4v

hence, potential of drop will be 4v