Two identical metallic spheres A and B when p | vedclass

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

Question

(B) Let the initial charges on spheres $A$ and $B$ be $q_A = q_B = q$. The initial force is $F = \frac{Kq^2}{r^2}$.When sphere $C$ (initially uncharge

Vedclass · Accepted Answer

$3F / 4$

Vedclass · Answer

(B) Let the initial charges on spheres $A$ and $B$ be $q_A = q_B = q$. The initial force is $F = \frac{Kq^2}{r^2}$.When sphere $C$ (initially uncharged) is placed in contact with $A$,the charge redistributes equally: $q_A' = q_C' = \frac{q}{2}$.Now,sphere $C$ is placed in contact with $B$. The total charge is $q + \frac{q}{2} = \frac{3q}{2}$. Upon separation,each gets $q_B' = q_C'' = \frac{3q/2}{2} = \frac{3q}{4}$.Now,$A$ has charge $\frac{q}{2}$ and $B$ has charge $\frac{3q}{4}$. Sphere $C$ is placed at the midpoint (distance $r/2$ from both).The force on $C$ due to $A$ is $F_1 = \frac{K(q/2)(3q/4)}{(r/2)^2} = \frac{3Kq^2/8}{r^2/4} = \frac{3Kq^2}{2r^2} = \frac{3F}{2}$ (towards $A$).The force on $C$ due to $B$ is $F_2 = \frac{K(3q/4)(3q/4)}{(r/2)^2} = \frac{9Kq^2/16}{r^2/4} = \frac{9Kq^2}{4r^2} = \frac{9F}{4}$ (towards $A$).The net force on $C$ is $F_{net} = F_2 - F_1 = \frac{9F}{4} - \frac{3F}{2} = \frac{9F - 6F}{4} = \frac{3F}{4}$.

Similar Questions

Four identical point masses,each of mass $m$ and carrying charge $+q$,are placed at the corners of a square of side $a$ on a frictionless horizontal surface. If the particles are released simultaneously,the kinetic energy of the system when they are infinitely far apart is

The electric field is in the direction of the $x$-axis. The work done to move a charge of $0.2 \ C$ by a distance of $2 \ m$ at an angle of $60^\circ$ with the $x$-axis is $4 \ J$. What is the value of the electric field $E$ in $N/C$?

$A$ uniformly charged thin spherical shell of radius $R$ carries a uniform surface charge density of $\sigma$ per unit area. It is made of two hemispherical shells, held together by pressing them with force $F$ (see figure). $F$ is proportional to

Vedclass Test Series

Exam Paper Generator

Online Exam Module