The electric field at a point on the equatorial plane at a distance r from the centre of a dipole having dipole moment p → is given by ( r > > separation of two charges forming the dipole, ϵ 0 - permittivity of free space)

Step-by-step solution

Use the concept of potential gradient, then the relation, E r = - d V d r ⇒ E θ = - 1 r × d V d θ   &   V = K P r 2 cos θ , for general point, ⇒ E θ = - 1 r × d K P r 2 cos θ d θ   ⇒ E = - K P r 3 1 + 3 cos 2 θ , for the equatorial position, θ = 90 ° ⇒ E → = - k P → r 3 = - P → 4 π ϵ 0 r 3 .