(i) Write two properties by which electric potential is related to the electric field. (ii) Two point charges q₁ and q₂ separated by a distance of r₁₂ are kept in an external electric field. Derive an expression for the potential energy of the system of two charges in the field.

(i) Derive the expression for the electric potential due to an electric dipole at a point on its axial line. (ii) Depict the equipotential surface due to electric dipole.

Define an equipotential surface. Draw equipotential surfaces : (i) in the case of a single point charge and (ii) in a constant electric field in z-direction. Why the equipotential surfaces about a single charge are not equidistant ? (iii) Can electric field exist tangential to an equipotential surface ? Give reason.

Obtain the expression for the potential due to an electric dipole of dipole moment p at a point ‘d’ on the axial line.

Four point charges Q, q, Q and q are placed at the corners of a square of side ‘a’ as shown in the figure.

(i) Three point charges q, – 4q and 2q are placed at the vertices of an equilateral triangle ABC of side ‘l’ as shown in the figure. Obtain the expression for the magnitude of the resultant electric force acting on the charge q.

A particle, having a charge +5 µC, is initially at rest at the point x = 30 cm on the x-axis. The particle begins to move due to the presence of a charge Q that is kept fixed at the origin. Find the kinetic energy of the particle at the instant it has moved 15 cm from its initial position if (a) Q = +15 µC and (b) Q = – 15 µC