Potential Energy of a System of Charges

Two point charges ${\mathrm{q}}_1$ and ${\mathrm{q}}_2$ are repatriated by distance $\text{'}\mathrm{r}\text{'}$ in in external electric field. Potential energy $\mathrm{U}$ is expressed as $\mathrm{U}=\frac{1}{4{\mathrm{\pi \epsilon }}_0}·\mathrm{x}$

value of $\mathrm{x}$ is 

Three point charges $Q\mathit{,}\mathit{ }\mathit{+}q$ and $\mathit{+}q$ are placed at the vertices of a right-angled isosceles triangle as shown in the figure. If the net electrostatic energy of the configuration is zero, find the value of $\left|10\frac{Q}{q}\right|·$ [Take $\sqrt{2}=1.4$ ]

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

Three charges, $+q,+2 q$ and $xq$ respectively are placed at the vertices of an equilateral triangle of side $r$. Find the value of $\mathrm{x}$ for which the potential energy of system becomes zero.

No external electric field is applied on a system of two charges $7 \mathrm{\mu C}$ and $-2 \mathrm{\mu C}$ located at $(-9 \mathrm{cm},0,0)$and $(+9 \mathrm{cm},0,0).$ Determine the electrostatic potential energy of this system. (b) How much work is needed to make the charges separate by infinite distance.

How much work has to be done in putting charges $+q, 2q \mathrm{and} +4q$ respectively at the corners of an equilateral triangle of side '$a$'.

Find the work done in bringing another $2\times {10}^9 \mathrm{C}$ charge from infinity to a point at a distance $9 \mathrm{cm}$ from a point charge $4\times {10}^{-7}\mathrm{C}$ .

Four charges, $-2 \mathrm{\mu c},+3 \mathrm{\mu c},-4 \mathrm{\mu c}$ and $+5 \mathrm{\mu c}$ respectively are placed on corners of a square of edge $0.9 \mathrm{m}$. Find the electric potential at the centre of the square. 

Two charges $10 \mathrm{\mu C}$ and $5 \mathrm{\mu C}$ are $1 \mathrm{m}$ apart. To decreases the separation to $0.5 \mathrm{m}$. How much work has to be done? 

Write expression for electrostatic potential energy for a system of two point charges $q_1$ and $q_{\mathit{2}}$ placed at positions given by position vectors ${\overrightarrow{\mathit{r}}}_{\mathit{1}}$ and ${\overrightarrow{\mathit{r}}}_{\mathit{2}}$ in a uniform electric field.

Determine the expression for potential energy for a system of three point charges.

Write the expression for potential energy for a system of three point charges.

Write the expression for potential energy of a two point charge system

In a hydrogen atom, the electron and proton are bound at a distance of about $0.53 {\mathrm{A}}^{°}$, where the potential energy of the system is $-27.2 \mathrm{eV}$.  What will be the the potential energy of the system and the minimum work required to free an electron, given that the Kinetic energy is half the potential energy, if the zero of potential energy is taken at $1.06 {\mathrm{A}}^{°}$ separation?

Three charge particles $Q, q$ , and $q$ are placed at the vertices of an isosceles right-angled triangle as shown in the figure. Find out the value of $Q$ so that electrostatic potential energy is zero.

Two $C{u}^{64}$ nuclei touch each other. The electrostatics repulsive energy of the system will be

A small positively charged ball of mass $m$ is suspended by an insulating thread of negligible mass. Another positively charged small ball is moved very slowly from a large distance until it is in the original position of the first ball. As a result, the first ball rises by $h$. How much work has been done ?

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

Three charges $Q_o,–q$ and $–q$ are placed at the vertices of an isosceles right-angle triangle, as in the figure. The net electrostatic potential energy is zero if $Q_o$ is equal to 

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?