Two insulated charged copper spheres $A$ and $B$ have their centres separated by a distance of $50 \;cm$. the charge on each is $6.5 \times 10^{-7}\; C?$ Suppose the spheres $A$ and $B$ have identical sizes.A third sphere of the same size but uncharged is brought in contact with the first, then brought in contact with the second, and finally removed from both. What is the new force of repulsion between $A$ and $B?$
Two insulated charged copper spheres $A$ and $B$ have their centres separated by a distance of $50 \;cm$. the charge on each is $6.5 \times 10^{-7}\; C?$ Suppose the spheres $A$ and $B$ have identical sizes.A third sphere of the same size but uncharged is brought in contact with the first, then brought in contact with the second, and finally removed from both. What is the new force of repulsion between $A$ and $B?$
Distance between the spheres, $A$ and $B, r=0.5\,m$
Initially, the charge on each sphere, $q=6.5 \times 10^{-7} \,C$
When sphere $A$ is touched with an uncharged sphere $C, q / 2$ amount of charge from $A$ will transfer to sphere $C$. Hence, charge on each of the spheres, $A$ and $C ,$ is $q / 2 .$
When sphere $C$ with charge $q / 2$ is brought in contact with sphere $B$ with charge $q$, total charges on the system will divide into two equal halves given as,
$\frac{1}{2}\left(q+\frac{q}{2}\right)=\frac{3 q}{4}$
Hence, charge on each of the spheres, $C$ and $B ,$ is $\frac{3 q}{4}$ Force of repulsion between sphere A having charge $q / 2$ and sphere $B$ having charge $\frac{3 q}{4}$ is $F=\frac{1}{4 \pi \varepsilon_{0}} \cdot \frac{q_{A} q_{B}}{r^{2}}=\frac{1}{4 \pi \varepsilon_{0}} \cdot \frac{\frac{q}{2} \times \frac{3 q}{4}}{r^{2}}$
$=\frac{1}{4 \pi \varepsilon_{0}} \cdot \frac{3 q^{2}}{8 r^{2}}=\frac{9 \times 10^{9} \times 3 \times\left(6.5 \times 10^{-7}\right)^{2}}{8 \times(0.5)^{2}}$$=5.703 \times 10^{-3}\, N$
Therefore, the force of attraction between the two spheres is $5.703 \times 10^{-3} \;N$.
Similar Questions
As shown in the figure. a configuration of two equal point charges $\left( q _0=+2 \mu C \right)$ is placed on an inclined plane. Mass of each point charge is $20\,g$. Assume that there is no friction between charge and plane. For the system of two point charges to be in equilibrium (at rest) the height $h = x \times 10^{-3}\,m$ The value of $x$ is $..........$.(Take $\left.\frac{1}{4 \pi \varepsilon_0}=9 \times 10^9\,Nm ^2 C ^{-2}, g=10\,ms ^{-1}\right)$
As shown in the figure. a configuration of two equal point charges $\left( q _0=+2 \mu C \right)$ is placed on an inclined plane. Mass of each point charge is $20\,g$. Assume that there is no friction between charge and plane. For the system of two point charges to be in equilibrium (at rest) the height $h = x \times 10^{-3}\,m$ The value of $x$ is $..........$.(Take $\left.\frac{1}{4 \pi \varepsilon_0}=9 \times 10^9\,Nm ^2 C ^{-2}, g=10\,ms ^{-1}\right)$
- [JEE MAIN 2023]
Two charged spheres separated at a distance $d$ exert a force $F$ on each other. If they are immersed in a liquid of dielectric constant $2$, then what is the force (if all conditions are same)
Two charged spheres separated at a distance $d$ exert a force $F$ on each other. If they are immersed in a liquid of dielectric constant $2$, then what is the force (if all conditions are same)
- [AIIMS 1997]
The electric field between the two spheres of a charged spherical condenser
The electric field between the two spheres of a charged spherical condenser
The electrostatic force on a small sphere of charge $0.4 \;\mu\, C$ due to another small sphere of charge $-0.8 \;\mu \,C$ in air is $0.2\; N .$
$(a)$ What is the distance between the two spheres?
$(b)$ What is the force on the second sphere due to the first?
The electrostatic force on a small sphere of charge $0.4 \;\mu\, C$ due to another small sphere of charge $-0.8 \;\mu \,C$ in air is $0.2\; N .$
$(a)$ What is the distance between the two spheres?
$(b)$ What is the force on the second sphere due to the first?
Two identical tennis balls each having mass $m$ and charge $q$ are suspended from a fixed point by threads of length $l$. What is the equilibrium separation when each thread makes a small angle $\theta$ with the vertical?
Two identical tennis balls each having mass $m$ and charge $q$ are suspended from a fixed point by threads of length $l$. What is the equilibrium separation when each thread makes a small angle $\theta$ with the vertical?
- [JEE MAIN 2021]