Calculate electric field due to dipole of dipole momentum ‘P’ at distance ‘r’ and angle θ.
E1=14πε0×2pcosθr3 (along OC) .... (i)
Simlialry, P lies on the equatorial line of dipole with moment →p2. Hence, the magnitude of electric field intensity ]vecE2 at P due to →p2 is
E2=14πε0−psinθr3 (opposite to p2) ...(ii)Hence, the resultant intensity at P is →E=→E1+→E2.
The magnitude of →E is E=√(E21+E22) (as →E1 and →E2 are mutally perpendicular).
or E=√(2pcosθ4πε0r3)2+(psinθ4πε0r3)2
=p4πε0r3√4cos2θ+sin2θ=p4πε0r3√1+3cos2θ