Potential Energy of a System of Charges

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 $Q:q$?

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 $Q:q$?

A charged particle $q$ is shot towards another charged particle $Q$ which is fixed, with a speed$v$. It approaches $Q$ up to the closest distance $r$ and then returns. If $q$ is shot with speed $2v$, the closest distance of approach would be

There is an electric field E in $x$ - direction. If the work done on moving a charge of 0.2C through a distance of 2m along a line making an angle ${60}^o$ with $x$ - axis is 4J, then what is the value of E ?

If one charge $\mathrm{q}$ is fixed and another charge $\mathrm{q}$ is taken around the other one in a circular path, the work done will be equal to -

Two points $\mathrm{P}$ and $\mathrm{Q}$ are maintained at the potentials of $10\mathrm{V}$ and $-4 \mathrm{V}$, respectively. The work done in moving $100$ electrons from $\mathrm{P}$ to $\mathrm{Q}$ is.

Work done by an external agent to move slowly a charge $\mathrm{Q}$ from rim of a uniformly charged horizontal disc of radius $\mathrm{a}$ and charge per unit area $\mathrm{\sigma }$, to center of this disc is -

The mass of a particle is $400$ times that of an electron and the charge is double. The particle is accelerated by $5\mathrm{ }\mathrm{V}$. Initially, the particle remained at rest. Then, its final kinetic energy will be

15 joule of work has to be done against an existing electric field to take a charge of $0.01\mathrm{ }\mathrm{C}$ from $\mathrm{A}$ to $\mathrm{B}$. Then the potential difference $({\mathrm{V}}_{\mathrm{B}}\mathrm{ }–\mathrm{ }{\mathrm{V}}_{\mathrm{A}})$ is -

tialThere is cube of edge length $\left(\frac{\sqrt{3}-1}{\sqrt{3}}\right)\mathrm{m}$ . Four point charges each having charge $3\mathrm{\mu }\mathrm{C}$ are kept at points $\mathrm{A}$, $\mathrm{C}$ $\mathrm{E}$ and $\mathrm{G}$ respectively as shown in the figure. The work done to move a charge of $5\mathrm{ }\mathrm{\mu }\mathrm{C}$ from point $\mathrm{O}$ to point $\mathrm{F}$ is

A point charge is surrounded by eight identical charges, at a distance $r$, as shown in the figure. How much work is done by the force of electrostatic repulsion, when the point charge at the centre is removed to infinity?

Potential energy of two equal negative point charges, $2 \mathrm{\mu C}$ each, held $1 \mathrm{m}$ apart in air, is

Two positive point charges of $12 \mathrm{\mu }\mathrm{C}$ and $5 \mathrm{\mu C}$ are placed $10 \mathrm{cm}$ apart in the air. The work needed to bring them $4 \mathrm{cm}$ closer is

An automobile spring stretches upto $0.2 \mathrm{m}$ for a $5000 \mathrm{N}$ load. The ratio of potential energy stored in this spring when it is compressed by $0.2 \mathrm{m}$ to the potential energy stored in a $10 \mathrm{\mu F}$ capacitor at a potential difference of $10,000 \mathrm{V}$ will be,

A ball of mass $1$ carrying a charge ${10}^{-8}$ $\mathrm{C}$ moves from a point A at potential $600 \mathrm{V}$ to a point $B$ at zero potential. The change in its KE is

A charge ($-q$) and another charge ($+Q$) are kept at two points $A$ and $B$ respectively. Keeping the charge ($+Q$) fixed at $B$, the charge ($-q$) at $A$ is moved to another point $C$ such that $ABC$ forms an equilateral triangle of side $l$. The net work done in moving the charge ($-q$) is

Potential energy of two equal negative point charges $2 \mathrm{\mu C}$ each held $1 \mathrm{m}$ apart in air is,