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

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. 

If the electric potentials at two points A and B are $2 \mathrm{V}$ and $4 \mathrm{V}$ respectively, then find the work need to move a $8 \mathrm{\mu C}$ charge from A to B.

$6 \mathrm{J}$ of work is needed to move a $3 \mathrm{C}$ point charge between two points. Find the potential difference between the two points. 

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.

What is meant by electrostatic potential energy? Derive expression for potential energy of a system of point charges.

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

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 ?

Assertion: Work done in moving a charge between any two points in an electric field is independent of the path followed by the charge, between these points.

Reason: Electrostatic forces are non-conservative.

Assertion: For a charged particle moving from point $P$ to point $Q$, the net work done by an electrostatic field on the particle is independent of the path connecting point $P$ to point $Q$.

Reason: The net work done by a conservative force on an object moving along a closed loop is zero.

Assertion: Four electric charges of equal magnitude are placed at four corners of a square. Out of these four charges two are positive and two are negative. Then the electrostatic potential energy of system of these four charges must be positive.

Reason: Electrostatic force may be attractive or repulsive.