Electric quadrupole. Figure shows a generic electric quadrupole. It consists of two dipoles with dipole moments that are equal in magnitude but opposite in direction. Show that the value of $$E$$ on the axis of the quadrupole for a point $$P$$ as distance $$z$$ from its centre ( assume $$z \|| d$$) is given by
$$E=\dfrac{3Q}{4\pi \varepsilon_0z^4}$$
in which $$Q(=2qd^2)$$ is known as the quadrupole moment of the charge distribution.