Question

The distance of the field point on the axis of a small dipole is doubled. By what factor will the electric field, due to the dipole change?

Answer 1

For small dipole, $E_{axis}=\frac{1}{4\pi {ϵ}_0}\frac{2p}{r_3}\propto \frac{1}{r^3}$
When $r$ is doubled, the electric field strength become $1/8$ times of the original field.