Consider we have both a positive and negative charge, separated by a distance. When applying supperposition of the electric force and electric field generated by the two charges on a target point, it is said that the positive and negative charges create an effect called a dipole moment. Let’s consider a few example of how an electric field will be generated for a point charge in the presence of both a positive and negative charge. Molecules also often have a dipole moment.
Here, the target point is at distance b at the center between the negative and positive charges. Where both charges are of the same magnitude, both the vertical attraction and repulsion components are cancelled, leaving the electric field to be generated in a direction parallel to the axis of the two charges.
Now, we’ll consider a target point along the axis of the two charges. Remember that a positive charge will produce an electric force and electric field that radiates from itself outward, while the force and field is directed inwards towards a negative charge. We can expect then, that the electric field will be different on either side. We can expect that the side of the positive charge will repel and the negative side will attract. This works, because the distance inverse proportionality is squared, making it so that the effect from the other charge will be less. This is a dipole.
Given how a dipole functions, it would be nice to have a different set of formulas and a more refined approach to solving electric field problems with dipoles. The dipole moment p is found using the formula, p=qI with units Couolumb*meter. I is the vector which points from the negative charge to the positive charge. The dipole moment is drawn as one point at the center of the dipole with vector I through it.
In order to treat the two charges as a center of a dipole, there should be a minimum distance between the dipole and the target point. The distance between the dipole and the target should be much larger than the length l of the magnitude of vector I.
Finally, the formula for these electric fields using a dipole moment are
E1 = 2kep/b13
E2 = 2kep/b23