(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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Electric Potential and Capacitance

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Electric potential

An electric dipole is placed as shown in the figure. The electric potential (in $10^2 \ V$) at point $P$ due to the dipole is ($\epsilon_0 =$ permittivity of free space and $\frac{1}{4 \pi \epsilon_0} = K$):

MediumNEET 2023

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As shown in the figure,positive and negative charges of $1\ \mu C$ are placed at two points. Find the potential difference between $A$ and $B$ in $volt$.

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$A$ charge of total amount $Q$ is distributed over two concentric hollow spheres of radii $r$ and $R$ $(R > r)$ such that the surface charge densities on the two spheres are equal. The electric potential at the common centre is

DifficultIIT 1981

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Electric charges having the same magnitude $q$ are placed at $x = 1 \, m, 2 \, m, 4 \, m, 8 \, m, \dots$ and so on. If any two consecutive charges have opposite signs but the first charge is necessarily positive,what will be the potential at $x = 0$?

Medium

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If $3$ charges of magnitude $q$ each are placed at the vertices of an equilateral triangle of side $l \ cm$,what is the net potential energy of the system?

Easy

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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

An electric dipole is placed as shown in the figure. The electric potential (in $10^2 \ V$) at point $P$ due to the dipole is ($\epsilon_0 =$ permittivity of free space and $\frac{1}{4 \pi \epsilon_0} = K$):

As shown in the figure,positive and negative charges of $1\ \mu C$ are placed at two points. Find the potential difference between $A$ and $B$ in $volt$.

$A$ charge of total amount $Q$ is distributed over two concentric hollow spheres of radii $r$ and $R$ $(R > r)$ such that the surface charge densities on the two spheres are equal. The electric potential at the common centre is

Electric charges having the same magnitude $q$ are placed at $x = 1 \, m, 2 \, m, 4 \, m, 8 \, m, \dots$ and so on. If any two consecutive charges have opposite signs but the first charge is necessarily positive,what will be the potential at $x = 0$?

If $3$ charges of magnitude $q$ each are placed at the vertices of an equilateral triangle of side $l \ cm$,what is the net potential energy of the system?

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