A spherical drop of liquid carrying charge Q | vedclass

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

Question

(B) Given,charge of each small spherical drop $= Q$ and potential at its surface $= V_0$. Let $r$ be the radius of each small drop. The potential is g

Vedclass · Accepted Answer

$4^{1/3} V_0$

Vedclass · Answer

(B) Given,charge of each small spherical drop $= Q$ and potential at its surface $= V_0$. Let $r$ be the radius of each small drop. The potential is given by $V_0 = \frac{1}{4 \pi \varepsilon_0} \frac{Q}{r}$.When two such drops combine to form a single large drop of radius $R$,the volume is conserved: $\frac{4}{3} \pi R^3 = 2 	imes \frac{4}{3} \pi r^3$,which gives $R^3 = 2r^3$ or $R = 2^{1/3} r$.The total charge on the new large drop is $Q' = Q + Q = 2Q$.The potential at the surface of the new drop is $V' = \frac{1}{4 \pi \varepsilon_0} \frac{Q'}{R} = \frac{1}{4 \pi \varepsilon_0} \frac{2Q}{2^{1/3} r}$.Substituting $V_0 = \frac{1}{4 \pi \varepsilon_0} \frac{Q}{r}$,we get $V' = V_0 	imes \frac{2}{2^{1/3}} = V_0 	imes 2^{1 - 1/3} = V_0 	imes 2^{2/3} = V_0 	imes (2^2)^{1/3} = 4^{1/3} V_0$.

$A$ spherical drop of liquid carrying charge $Q$ has potential $V_0$ at its surface. If two drops of same charge and radius combine to form a single spherical drop,then the potential at the surface of the new drop is (Assume $V=0$ at infinity.)

Similar Questions

Two positive charges $Q$ and $4Q$ are placed at points $A$ and $B$ respectively, where $B$ is at a distance $d$ units to the right of $A$. The total electric potential due to these charges is minimum at point $P$ on the line segment joining $A$ and $B$. What is the distance of $P$ from $A$?

The potential at a distance $R/2$ from the centre of a conducting sphere of radius $R$ will be

Consider a sphere of radius $R$ having charge $q$ uniformly distributed inside it. At what minimum distance from its surface is the electric potential half of the electric potential at its centre?

If identical charges $(-q)$ are placed at each corner of a cube of side $b$,then the electric potential energy of charge $(+q)$ which is placed at the center of the cube will be:

What is the electric potential at the center $O$ of a circle of radius $0.4 \ m$ with the charges arranged as shown in the figure?

Vedclass Test Series

Exam Paper Generator

Online Exam Module