Question

Establish the formula for electric field intensity at a point on the axis of an electric dipole.

Answer 1

An electric dipole is an object which has positive electric charge on one end and a negative on the other end.

Electric field intensity $E$ at a point is defined as the electric force acting on a unit charge kept at that point.

By Coulomb's law, $E_1=\frac{q}{4\pi {ϵ}_{{}_0}{r}_{{}_1}^2}$

Here q is the positive charge of the dipole, $r_{{}_1}$ is its distance from the given point on the axis and ${ϵ}_0$ is the electric permitivity of air or vacuum.

Similarly for the negative charge, $E_2=\frac{-q}{4\pi {ϵ}_{{}_0}{r}_{{}_2}^2}$

By adding both the equations, we get,

$E=\frac{q}{4\pi {ϵ}_{{}_0}}\times \frac{1}{r_{{}_1}^2-r_{{}_2}^2}$

This is the final equation.