Potential Energy of a System of Charges

The term ‘potential energy’ of charge ‘q’ at a distance ‘r’ in an external electric field can be defined as:.

Two point charges  $20\times {10}^{-6}$ C and  $-4\times {10}^{-6}$ C are separated by a distance of 50 cm in air.

(i) Find the point on the line joining the charges, where the electric potential is zero.

(ii) Also find the electrostatic potential energy of the system.

Charge $-2q$, $Q$ and $-3q$ are placed on a straight line as shown in figure. If the total potential energy of the system is zero then value of $\frac{Q}{q}$ will be

Two fixed charges $\mathrm{A}$ and $\mathrm{B}$ of $5\mu \mathrm{C}$ each are separated by a distance $6 \mathrm{m}$. $\mathrm{C}$ is the midpoint of the line joining $\mathrm{A}$ and $\mathrm{B}$. A charge $\mathrm{Q}$ of strength $-5\mu \mathrm{C}$ is shot perpendicular to the line joining $\mathrm{A}$ and $\mathrm{B}$ through $\mathrm{C}$ with a kinetic energy of $0.06 \mathrm{J}$. The charge $\mathrm{Q}$ comes to rest at a point $\mathrm{D}$. The distance $\mathrm{CD}$ is

An electron is released from a distance of $4 \mathrm{m}$ from a stationary point charge $20 \mathrm{nC}$. What will be the speed of the electron when it is $2 \mathrm{m}$ away from the point charge?
[Charge of electron $=1.6\times {10}^{-19}\mathrm{C}$, mass of electron $=9\times {10}^{-31} \mathrm{kg}$, $\frac{1}{4\pi {\epsilon }_0}=9\times {10}^9$ S.I. unit]
 

Two positive point charges of $10 \mathrm{\mu C}$ and $12 \mathrm{\mu C}$ are placed $10 \mathrm{cm}$ apart in air. The work done to bring them $6 \mathrm{cm}$ closer is

A disk of radius $R$ with uniform positive charge density $\sigma$ is placed on the $xy$ plane with its center at the origin. The Coulomb potential along the $z$-axis is
$V\left(z\right)=\frac{\sigma }{2{ϵ}_0}\left(\sqrt{R^2+z^2}-z\right)$

A particle of positive charge $q$ is placed initially at rest at a point on the $z$-axis with $z=z_0$ and $z_0>0$. In addition to the Coulomb force, the particle experiences a vertical force $\overrightarrow{F}=-c\hat{k}$ with $c>0$. Let $\beta =\frac{2c{\epsilon }_0}{q\sigma }$. Which of the following statement(s) is(are) correct?

The energy required to move a charge of $0.25 \mathrm{C}$ between two points is $4\times {10}^{20}\mathrm{eV}$. The potential difference between them is

A tin nucleus has a charge of $+50e$ where $e$ is equal to $1.6\times {10}^{-19}\mathrm{C}$. If a proton is at a distance of ${10}^{-12} \mathrm{m}$ from a tin nucleus, then its potential energy is about

Two different equipotential surfaces $S_{1}$ and $S_{2}$ at electric potential $V_{1}$ and $V_{2}$ respectively are as shown in figure. The work done in moving a charge $q$ from $P$ to $Q$ is

There is a point charge $Q$ at a distance $\frac{R}{2}$ from the centre of a circle of radius $R$. Another point charge $q$ is to be moved from $A$ to $B$, where $A$ and $B$ are two points on the circle diametrically opposite to each other. How much work is done by the electrostatic force exerted by $Q$ on $q$?

Four identical charge particles having charge $q$ are placed fixed at the vertices of a square of side length $a$. A negative charge $-Q$ having mass $m$ is situated at the centre of the square. The minimum velocity given to $-Q$ so that it can escape from there is,

In which of the following stores maximum energy?

Four point charges $q,-2q,-3q$ and $4q$ are placed at the four vertices of a regular tetrahedron of side $L$, while a charge $5q$ is placed at its center. What is the total electrostatic energy of the system? (Vacuum permittivity is denoted by ${\epsilon }_0$).

Two equal points charges $q$ are fixed at $x=-a$ & $x=+a$ on $x$-axis. Another point charge $Q$ is placed at the origin. The change in electrical potential energy of $Q$, when it is displaced by a small amount or along $x$-axis, is approximately proportional to.

How much work has to be done in assembling three charged particles at the vertices of an equilateral triangle as shown in figure?

A metallic sphere has a charge of $10\mu \mathrm{C}$. A unit negative charge is brought from $\left(\mathrm{A}\right)$ to $\left(\mathrm{B}\right)$, both $100\mathrm{cm}$ away from the sphere but $\left(\mathrm{A}\right)$ being east of it while $\left(\mathrm{B}\right)$ being on west. The net work done on the unit negative charge is

The velocity $v$ acquired by an electron starting from rest and moving through a potential difference $V$ is shown by the graph.

Three charges $-q,+2q$ and $-q$ are placed at the vertices $AB$ and $C$ respectively of an isosceles right angled triangle $ABC$, angle $B$ being $90°$ and $AB=BC=a$. If $q=1.6\times {10}^{-19}\mathrm{C}$ and $a=1.5\times {10}^{-10}\mathrm{m}$ then energy required to dissociate the system of charges is $x\times {10}^{-18}\mathrm{J}$, then the value of $x$ rounded off to closest integer is -

Three charges, $-q,\mathrm{ }Q$ and $-q$, are placed at equal distances, on a straight line. If the potential energy of the system of three charges is zero, then what is the ratio of $Q:q$?