Potential Energy of a System of Charges

 Three point charges $+1 \mu C, -1 \mu C$ and $+2 \mu C$ are initially infinite distance apart. Calculate the work done in assembling these charges at the vertices of an equilateral triangle of side $10 \mathrm{cm}$. Take $\left(\frac{1}{4\pi {\epsilon }_o}\right)=9\times {10}^9 \mathrm{N} {\mathrm{m}}^2{\mathrm{C}}^{-2}$

At the four vertices of a square A B C D of side $2a$, there are four point charges q,-q, q,-q in that order. Find the work done to take the four charges at the centre of the square.

Two charges $q_1$ and $q_2$ are placed $30 \mathrm{cm}$ apart, as shown in Fig. $2.126$. $A$ third charge $q_3$ is moved along the arc of a circle of radius $40 \mathrm{cm}$ from $C$ to $D$. The charge in the potential energy of the system is $\frac{q_3}{4\pi {\epsilon }_0}k$, where $k$ is

(ii) A charge $q_0$ is brought from infinity to the centre of the square, the four charges being held fixed at its comers. How much extra work is needed to do this?

What do you mean by the potential energy of a system of charges? Derive energy expression for two point charges separated by a distance. Generalise the result for a system of $\mathrm{n}$ point charges.

Three-point charges $q, 2q$ and $8q$ are to be placed on a $9 \mathrm{cm}$ long straight line. Find the separation between $q$ and $2q$ where the charges should be placed such that the potential energy of this system is minimum.

Consider the D–T reaction (deuterium–tritium fusion)
${}_1{}^2\mathrm{H}+{}_1{}^3\mathrm{H}\to {}_2{}^4\mathrm{He}+\mathrm{n}$
Consider the radius of both deuterium and tritium to be approximately $2.0 \mathrm{fm}$. What is the kinetic energy needed to overcome the Coulomb repulsion between the two nuclei? To what temperature must the gas be heated to initiate the reaction? Take,$\frac{1}{4{\text{πε}}_0}=9\times {10}^9 \mathrm{N} {\mathrm{m}}^2{\mathrm{C}}^{-2}$, Boltzmann constant, $k = 1.38\times {10}^{-23} {\mathrm{m}}^2 \mathrm{kg} {\mathrm{s}}^{-2} {\mathrm{K}}^{-1}$.