Question

(i) An electric dipole (dipole moment p = pî), consisting of charges − q and q separated by distance 2a, is placed along the x-axis, with its centre at the origin. Show that the potential V, due to this dipole, at a point x, (x >> a) is equal to (1/4πε₀) · (p·î/x²). (ii) Two isolated metallic spheres S₁ and S₂ of radii 1 cm and 3 cm respectively are charged such that both have the same charge density (2/π × 10⁻⁹) C/m². They are placed far away from each other and connected by a thin wire. Calculate the new charge on sphere S₁.

Assertion (A): The electric potential due to a small electric dipole is zero at every point on its equatorial plane. Reason (R): Every point on the equatorial plane of a dipole is equidistant from the two charges +q and –q, so the magnitudes of the potentials due to the two charges are equal and opposite in sign.

Draw an equipotential surface for a system consisting of two charges Q, –Q separated by a distance r in air. Locate the points where the potential due to the dipole is zero.

A charge 'q' is moved from a point A above a dipole of dipole moment 'p' to a point B below the dipole in equatorial plane without acceleration. Find the work done in the process.