Question

Why dipole field falls off at large distances?

Answer 1

Imagine two charges, one +q+q and another −q−q, separated by 11m. As a system the net charge is 00, but clearly the field will not be 00 a distance of 1010m away: the fields of each charge goes off like 1/r21/r2 but only partially cancel out when you add them because of the distance between the charges; the partial cancellation will be quite direction dependent.

Imagine now you’re not 1010m but 109109m away. For large distances one can show the field of the dipole falls off like 1/r31/r3because the fields of the two charges almost cancel out but not completely. There is also: a directional effect, and the field strength depends on the ratio d/rd/r of the distance dd between the two charges to the distance rr between the center of the charges and the point where you evaluate the field.

It depends basically if you consider the constituents into a single net point source or if you still consider them separately.

[Thank You]