Two identical conducting spheres carry identi | vedclass

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

Question

(D) Initial condition: Two spheres $A$ and $B$ each have charge $q$ and are separated by distance $r$. The initial force is $F = \frac{k q^2}{r^2}$.St

Vedclass · Accepted Answer

$\frac{3F}{8}$

Vedclass · Answer

(D) Initial condition: Two spheres $A$ and $B$ each have charge $q$ and are separated by distance $r$. The initial force is $F = \frac{k q^2}{r^2}$.Step $1$: When the uncharged sphere $C$ is touched to sphere $A$,the total charge $q + 0 = q$ is shared equally between them because they are identical. Thus,the charge on $A$ becomes $q_A = \frac{q}{2}$ and the charge on $C$ becomes $q_C = \frac{q}{2}$.Step $2$: Now,sphere $C$ (with charge $\frac{q}{2}$) is touched to sphere $B$ (with charge $q$). The total charge is $q + \frac{q}{2} = \frac{3q}{2}$. Since the spheres are identical,this charge is shared equally between $B$ and $C$. Therefore,the new charge on $B$ is $q_B = \frac{1}{2} 	imes \frac{3q}{2} = \frac{3q}{4}$.Step $3$: The final force $F^{\prime}$ between sphere $A$ (charge $\frac{q}{2}$) and sphere $B$ (charge $\frac{3q}{4}$) at the same distance $r$ is:$F^{\prime} = \frac{k q_A q_B}{r^2} = \frac{k (q/2) (3q/4)}{r^2} = \frac{3}{8} \frac{k q^2}{r^2}$.Since $F = \frac{k q^2}{r^2}$,we have $F^{\prime} = \frac{3}{8} F$.

Similar Questions

The dimensional formula of $k$ (Coulomb's constant) is . . . . . . .
(Take $I$ as the dimension of current.)

Four point charges $q_{A}=2\; \mu C, q_{B}=-5\; \mu C, q_{C}=2\; \mu C,$ and $q_{D}=-5\; \mu C$ are located at the corners of a square $ABCD$ of side $10\; cm$. What is the force on a charge of $1\; \mu C$ placed at the centre of the square (in $; N$)?

$A$ point charge $A$ of $+10 \mu C$ and another point charge $B$ of $+20 \mu C$ are kept $1 \ m$ apart in free space. The electrostatic force on $A$ due to $B$ is $F_1$ and the electrostatic force on $B$ due to $A$ is $F_2$. Then:

There are two charges $+1 \ \mu C$ and $+5 \ \mu C$. The ratio of the forces acting on them will be

Vedclass Test Series

Exam Paper Generator

Online Exam Module