Field of Multiple Point Charges

Electric fields, like forces, are additive. If you have multiple point charges, then the net electric field at any point (that is, the electric field that a proton would actually feel if it were placed there) is the vector sum of the electric field created by each source at that point. Remember to add the fields as vectors; don't add the magnitudes together.
The figure shows a negative charge (−1µC) at the origin and a positive charge (2µC) at x=−1m on the x--axis.
The figure shows two charges on two corners of a rectangle.
One particularly important configuration of charges is the dipole, a positive and a negative charge of equal magnitude.
A positive charge q sits at the origin, and a negative charge -q sits at the point (s,0,0). Find the electric field...

As we see from the example, if we move a distance r away from the dipole in either the vertical or horizontal direction (or in any other direction) the electric field takes on a functional form proportional to \(1/r^3\). We say that the dipole field dies off as \(1/r^3\) while the electric field of a point charge dies off as \(1/r^2\). Comparing these two functions in a graph, we see that the dipole field approaches zero (or "dies off more quickly") than the field of a single charge. This should make sense: positive and negative charges create opposite fields, and so if you placed a positive and negative charge right on top of each other, the net electric field would be zero. (This corresponds to the case s =0 in the example above.) If we place the two charges so that they are almost overlapping, then the electric fields will almost cancel but not quite: in this case, "almost cancelling" means that the electric field dies off more quickly than for a point charge.