Dipole Moment between two charges of different magnitudes but opposite signs

Question

If I had a charge of -2q and +q separated by a distance d, then is the following way of computing the net dipole of the system correct?

To compute the net dipole of the system, I take into consideration the dipole produced by each pair of two charges of opposite signs. So, I can look at the -2q as two -q charges with distance d=0 between them, hence the first dipole moment for the first -q and +q would be qd and for the second q it will be qd, so the net dipole moment is 2*q*d.

Would this be correct if I had -2q and +3q? Will the net dipole here be 6q?

Answer 1

If the net charge in your system is non zero, the dipole moment is not unique and depends on the origin. Hence the question "what is the dipole moment?" is meaningless without specifying the origin.

Even then, the method you suggest is problematic. If the two charges were $+2q$ and $-2q$, your method suggests that the net dipole moment is $4qd$ which is wrong. This is essentially because the dipole moment should be linear and your method is not.

To make sure that things work, fix an origin and define the dipole moment as $$\sum\limits_i q_i \vec r_i$$ where $q_i$ and $\vec r_i$ are the magnitudes of the charges and their locations, and you will get the dipole moment with respect to that origin without error.

Answer 2

It should be -2q*(d/2) + q*(-d/2) = -3q/2d Assuming the origin as the center of the line joining -2q and q and positive r vector to the right of origin. Also i have assumed the +q charge to be left to the origin and -2q to the right of the origin.