Find the magnitude of the electric field at the point P in the configuration shown in figure for d>>a. Take 2qa = p.

The given situation is similar to the dipole at a point on an equatorial line (as shown in the following figure).From the figure, we can see that sinθ components cancel out each other and cosθ components add up. That is,Enet =2E(cos ⁡θ)=2×kqx2(cos ⁡θ)=2×14πε0qa2+d23/2aThe dipole moment is given as p = 2qa. Substituting this value of p in the above relation, we get the magnitude of the net electric field at the point P (in the given configuration) due to dipole= p4πεo1a2+d23/2Now net electric field= k2q2d4+k2p2a2+d23 = k2d4(q2+p2d2) =k2d6(q2d2+p2) =kd3q2d2+p2as Enet =14πε0d3q2d2+p2