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

Given:
(a)
Distance between charge and P : d
(b)
Distance between two charges +q and -q = 2a
Dipole moment : p =2qa
Formula used:
(a)
It’s a direct formula of the electric field due to a point charge:
Here, k is a constant and k= =9× 10⁹ Nm²C^-2 . q is the point charge and d is the distance between the charge and the point P
(b)
For the second configuration too we have a direct formula.
Opposite charges at both ends separated by a distance forms a dipole and electric field at a point on the perpendicular bisector of the dipole is given as:
Here, p is the dipole moment and is : p= 2qa and k is a constant and k= =9× 10⁹ Nm²C^-2 , d is the distance between Point P and the center of the dipole.
(c)
Figure (c) is made up of combination of system in (a) and (b)

Point P is influenced by two dipoles.
1.-q and +q (A and B)
2. +q and +q (B and C)
1. Is the result of (b) = E₂
2. Is the result of (a) = E₁
Hence net electric field at P in the configuration (c) would be resultant of E₁ and E₂

Hence, results for (a), (b) and (c) are , , and respectively.