(A) The potential energy of the charge $q$ at the center of the ring is $U_i = \frac{kQq}{R}$.When the charge is at infinity,the potential energy is $

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(A) The potential energy of the charge $q$ at the center of the ring is $U_i = \frac{kQq}{R}$.When the charge is at infinity,the potential energy is $U_f = 0$.By the law of conservation of mechanical energy,the initial potential energy is converted into the final kinetic energy of the charge.$U_i + K_i = U_f + K_f$$\frac{kQq}{R} + 0 = 0 + \frac{1}{2}mv^2$$\frac{1}{2}mv^2 = \frac{kQq}{R}$$v^2 = \frac{2kQq}{mR}$$v = \sqrt{\frac{2kQq}{mR}}$

Class 12 Physics Electric Potential and Capacitance Electric potential

Easy

$A$ point charge $q$ of mass $m$ is placed at the center of a ring of radius $R$ carrying a charge $Q$. When it is slightly displaced,the point charge accelerates to infinity along the $x$-axis. The ultimate speed of the point charge is .......

A
$\sqrt{\frac{2kQq}{mR}}$
B
$\sqrt{\frac{kQq}{mR}}$
C
$\sqrt{\frac{kQq}{2mR}}$
D
$0$

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Class 12 Questions

Class 12

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Electric Potential and Capacitance

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Electric potential

At the centre of a half ring of radius $R=10 \ cm$ and linear charge density $\lambda = 4 \ nC \ m^{-1}$,the potential is $x \pi \ V$. The value of $x$ is . . . . .

DifficultJEE MAIN 2024

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If an electron moves from rest from a point at which potential is $50\, V$ to another point at which potential is $70\, V$,then its kinetic energy in the final state will be:

Easy

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$A$ charged spherical conductor has radius '$r$'. The potential difference between its surface and a point at a distance '$3r$' from the center is '$V$'. The electric intensity at a distance '$3r$' from the center of the conductor is:

MediumMHT CET 2021

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$A$ solid sphere of radius $R$ is charged uniformly. At what distance from its surface is the electrostatic potential half of the potential at the centre?

Difficult

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Three particles,each having a charge of $10\,\mu C$,are placed at the corners of an equilateral triangle of side $10\,cm$. The electrostatic potential energy of the system is.....$J$ (Given $\frac{1}{4\pi\varepsilon_0} = 9 \times 10^9\,N\cdot m^2/C^2$).

Medium

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$A$ point charge $q$ of mass $m$ is placed at the center of a ring of radius $R$ carrying a charge $Q$. When it is slightly displaced,the point charge accelerates to infinity along the $x$-axis. The ultimate speed of the point charge is .......

Similar Questions

At the centre of a half ring of radius $R=10 \ cm$ and linear charge density $\lambda = 4 \ nC \ m^{-1}$,the potential is $x \pi \ V$. The value of $x$ is . . . . .

If an electron moves from rest from a point at which potential is $50\, V$ to another point at which potential is $70\, V$,then its kinetic energy in the final state will be:

$A$ charged spherical conductor has radius '$r$'. The potential difference between its surface and a point at a distance '$3r$' from the center is '$V$'. The electric intensity at a distance '$3r$' from the center of the conductor is:

$A$ solid sphere of radius $R$ is charged uniformly. At what distance from its surface is the electrostatic potential half of the potential at the centre?

Three particles,each having a charge of $10\,\mu C$,are placed at the corners of an equilateral triangle of side $10\,cm$. The electrostatic potential energy of the system is.....$J$ (Given $\frac{1}{4\pi\varepsilon_0} = 9 \times 10^9\,N\cdot m^2/C^2$).

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