Electric Potential Energy of a System of Charges

(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?

The distance between two horizontal parallel plates is $2.0 cm$ and the potential difference between them is $120 V$ Calculate: increase in electrical energy of the electron in moving from one plate to the other.

Three point charges$-q, + q$ and $- q$ are placed along a straight line at equal distances (say $r$ metre). Calculate the electric potential energy of this system of charges, when this charge is at one end.

Three point charges $- q, + q$ and $- q$ are placed along a straight line at equal distances (say $r$ metre). Calculate the electric potential energy of this system of charges, when $+ q$ charge is in the middle. 

A charge is moved opposite to the Coulombian force in an electric field. By whom will the work be done? What will be its effect on the field? On the energy of the system?

The electrostatic potential energy of a system of three charges $q_1, q_2$and $q_3$ is given by $U =U_{12}+U_{31}$. State very briefly in words, or by mathematical equations, what each of the terms on the right-hand side stand for.  

An electron is brought towards another electron. What happens to the electrostatic potential energy of the system?

Two electrons are released towards each other with equal velocities of ${10}^6 \mathrm{m} {\mathrm{s}}^{-1}$. What will be the closest approach between them?

The distance between two protons is $1.0\times {10}^{-10} \mathrm{m}$. If they are made free, what will be the kinetic energy of each when they are away at a very large distance from each other? If one proton is kept fixed and only other is free then what will be its kinetic energy?

 Calculate the work required to assemble each of the systems of charges (which is same as the electrostatic potential energy of the system) shown in Fig. $\left(\mathrm{a}\right)$ and $\left(\mathrm{b}\right)$.

Two positive charges of $10 \mathrm{\mu C}$ each are situated $10 \mathrm{cm}$ apart from each other. What is the increase in the electrostatic potential energy of the system when the two charges are brought closer by $2 \mathrm{cm}$?

Three equal charges of $5.0 \mathrm{\mu C}$ each are placed at the three vertices of an equilateral triangle of side $5.0 \mathrm{cm}$ each. Calculate the electrostatic potential energy of the system of charges.

Three point-charges ${\mathrm{q}}_1(=-1 \mathrm{\mu C}), {\mathrm{q}}_2(=+2 \mathrm{\mu C})$ and ${\mathrm{q}}_3(=-1 \mathrm{\mu C})$ are placed in air in a line. The distance between ${\mathrm{q}}_1$ and ${\mathrm{q}}_2$ is $1 \mathrm{m}$ and that between ${\mathrm{q}}_2$ and ${\mathrm{q}}_2$ is also $1 \mathrm{m}$. Calculate the electrostatic energy of the system.

The mutual electric potential energy between two protons in a uranium nucleus is $2.4\times {10}^5 \mathrm{eV}$ .Find the distance between the protons.

What do you understand by the term electric potential energy of two point charges distant by a finite distance? Obtain expression for it. What would happen to electric potential energy if distance is reduced between two similar and opposite charges?

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.

The electric potential energy of a system of two positive point charges of $1 \mathrm{\mu C}$ each placed in air $1 \mathrm{m}$ apart is :

A pellet carrying a charge of $0.5 \mathrm{C}$ is accelerated from rest through a PD of $2000 \mathrm{V}$. It attains a kinetic energy of: