Potential Energy of a System of Charges

• Assertion (A): Work done in moving a charge around a closed path, in an electric field is always zero.
• Reason (R): Electrostatic force is a conservative force.

In the circuit shown in figure initially, key K₁ is closed and key K₂ is open. Then K₁ is opened and K₂ is closed (order is important). [Take Q₁′ and Q₂′ as charges on C₁ and C₂ and V₁ and V₂ as voltage respectively.]

Then

1. charge on C₁ gets redistributed such that V₁ = V₂
2. charge on C₁ gets redistributed such that Q₁′ = Q₂′
3. charge on C₁ gets redistributed such that C₁V1 + C₂V₂ = C₁E
4. charge on C1 gets redistributed such that Q₁′ + Q₂′ = Q

A point charge Q is placed at point 'O' as shown in the figure. Is the potential at point A, i.e. V_A, greater, smaller or equal to potential, V_B, at point B, when Q is (i) positive, and (ii) negative charge?

1. In a quark model of elementary particles, a neutron is made of one up quarks [charge (2/3) e] and two down quarks [charges –(1/3) e]. Assume that they have a triangle configuration with side length of the order of 10^–15 m. Calculate electrostatic potential energy of neutron and compare it with its mass 939 MeV.
2. Repeat above exercise for a proton which is made of two up and one down quark.

Charges (+q) and (–q) are placed at points A and B respectively which are a distance 2L apart. C is the midpoint between A and B. What is the work done in moving a charge +Q along the semicircle CRD?

Calculate potential energy of a point charge – q placed along the axis due to a charge +Q uniformly distributed along a ring of radius R. Sketch P.E. as a function of axial distance z from the centre of the ring. Looking at graph, can you see what would happen if – q is displaced slightly from the centre of the ring (along the axis)?

Figure shows the field lines due to a positive point charge. Give the sign of potential energy difference of a small negative charge between the points Q and P.

Justify your answers for each case.

State the significance of the negative value of electrostatic potential energy of a system of charges.

Three charges are placed at the corners of an equilateral triangle ABC of side 2.0 m as shown in the figure. Calculate the electric potential energy of the system of three charges.