Twenty-seven drops of water of the same size | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(A) Let the radius of each small drop be $r$ and the charge on each be $q$.The potential of a small drop is $v = \frac{kq}{r}$.When $n = 27$ drops uni

Vedclass · Accepted Answer

$9$

Vedclass · Answer

(A) Let the radius of each small drop be $r$ and the charge on each be $q$.The potential of a small drop is $v = \frac{kq}{r}$.When $n = 27$ drops unite to form a big drop of radius $R$,the volume remains conserved:$\frac{4}{3} \pi R^3 = n \cdot \frac{4}{3} \pi r^3 \implies R^3 = n r^3 \implies R = n^{1/3} r$.For $n = 27$,$R = (27)^{1/3} r = 3r$.The total charge on the big drop is $Q = nq = 27q$.The potential of the big drop is $V = \frac{kQ}{R} = \frac{k(nq)}{n^{1/3}r} = n^{2/3} \left( \frac{kq}{r} \right) = n^{2/3} v$.Substituting $n = 27$,we get $V = (27)^{2/3} v = (3^3)^{2/3} v = 3^2 v = 9v$.Thus,the potential increases by a factor of $9$.

Twenty-seven drops of water of the same size are equally and similarly charged. They are then united to form a bigger drop. By what factor will the electrical potential change?

Similar Questions

Do free electrons travel to a region of higher potential or lower potential?

Write an expression for the potential at a point outside a uniformly charged spherical shell,on the surface,and inside the shell.

$A$ uniform electric field exists in the positive $x$-direction. Let $A$ be the origin. Point $B$ is at $x = +1 \ cm$ on the $x$-axis and point $C$ is at $y = +1 \ cm$ on the $y$-axis. Which of the following relations is correct regarding the potentials at $A, B,$ and $C$?

If a unit positive charge is shifted from a region of low potential to a region of high potential,then the electric potential energy of the system

As shown in the figure,positive and negative charges of $1\ \mu C$ are placed at two points. Find the potential difference between $A$ and $B$ in $volt$.

Vedclass Test Series

Exam Paper Generator

Online Exam Module