Two identical thin rings each of radius $R$ meters are coaxially placed at a distance $R$ meters apart. If $Q_1$ coulomb and $Q_2$ coulomb are respectively the charges uniformly spread on the two rings, the work done in moving a charge $q$ from the centre of one ring to that of other is
Two identical thin rings each of radius $R$ meters are coaxially placed at a distance $R$ meters apart. If $Q_1$ coulomb and $Q_2$ coulomb are respectively the charges uniformly spread on the two rings, the work done in moving a charge $q$ from the centre of one ring to that of other is
- A
Zero
- B
$\frac{{q({Q_1} - {Q_2})(\sqrt 2 - 1)}}{{\sqrt 2 .4\pi {\varepsilon _0}R}}$
- C
$\frac{{q\sqrt 2 ({Q_1} + {Q_2})}}{{4\pi {\varepsilon _0}R}}$
- D
$\frac{{q({Q_1} + {Q_2})(\sqrt 2 + 1)}}{{\sqrt 2 .4\pi {\varepsilon _0}R}}$
Similar Questions
A proton and an anti-proton come close to each other in vacuum such that the distance between them is $10 \,cm$. Consider the potential energy to be zero at infinity. The velocity at this distance will be ........... $\,m / s$
A proton and an anti-proton come close to each other in vacuum such that the distance between them is $10 \,cm$. Consider the potential energy to be zero at infinity. The velocity at this distance will be ........... $\,m / s$
- [KVPY 2020]
A particle of mass $100\, gm$ and charge $2\, \mu C$ is released from a distance of $50\, cm$ from a fixed charge of $5\, \mu C$. Find the speed of the particle when its distance from the fixed charge becomes $3\, m$. Neglect any other force........$m/s$
A particle of mass $100\, gm$ and charge $2\, \mu C$ is released from a distance of $50\, cm$ from a fixed charge of $5\, \mu C$. Find the speed of the particle when its distance from the fixed charge becomes $3\, m$. Neglect any other force........$m/s$
A point charge $q$ of mass $m$ is suspended vertically by a string of length $l$. A point dipole of dipole moment $\overrightarrow{ p }$ is now brought towards $q$ from infinity so that the charge moves away. The final equilibrium position of the system including the direction of the dipole, the angles and distances is shown in the figure below. If the work done in bringing the dipole to this position is $N \times( mgh )$, where $g$ is the acceleration due to gravity, then the value of $N$ is. . . . . . (Note that for three coplanar forces keeping a point mass in equilibrium, $\frac{F}{\sin \theta}$ is the same for all forces, where $F$ is any one of the forces and $\theta$ is the angle between the other two forces)
A point charge $q$ of mass $m$ is suspended vertically by a string of length $l$. A point dipole of dipole moment $\overrightarrow{ p }$ is now brought towards $q$ from infinity so that the charge moves away. The final equilibrium position of the system including the direction of the dipole, the angles and distances is shown in the figure below. If the work done in bringing the dipole to this position is $N \times( mgh )$, where $g$ is the acceleration due to gravity, then the value of $N$ is. . . . . . (Note that for three coplanar forces keeping a point mass in equilibrium, $\frac{F}{\sin \theta}$ is the same for all forces, where $F$ is any one of the forces and $\theta$ is the angle between the other two forces)
- [IIT 2020]
A conducting sphere of radius a has charge $Q$ on it. It is enclosed by a neutral conducting concentric spherical shell having inner radius $2a$ and outer radius $3a.$ Find electrostatic energy of system.
A conducting sphere of radius a has charge $Q$ on it. It is enclosed by a neutral conducting concentric spherical shell having inner radius $2a$ and outer radius $3a.$ Find electrostatic energy of system.
$n$ the rectangle, shown below, the two corners have charges ${q_1} = - 5\,\mu C$ and ${q_2} = + 2.0\,\mu C$. The work done in moving a charge $ + 3.0\,\mu C$ from $B$ to $A$ is.........$J$ $(1/4\pi {\varepsilon _0} = {10^{10}}\,N{\rm{ - }}{m^2}/{C^2})$
$n$ the rectangle, shown below, the two corners have charges ${q_1} = - 5\,\mu C$ and ${q_2} = + 2.0\,\mu C$. The work done in moving a charge $ + 3.0\,\mu C$ from $B$ to $A$ is.........$J$ $(1/4\pi {\varepsilon _0} = {10^{10}}\,N{\rm{ - }}{m^2}/{C^2})$