# Centre of Charge?

1. Dec 4, 2005

### neutrino

Is there anything like centre of mass for charges? Does it depend upon what type of charges are involved?

Thanks,
Navneeth

2. Dec 4, 2005

### Physics Monkey

You might be tempted to define the "center of charge" as something like
$$\vec{R} = \frac{\sum q_\alpha \vec{r}_\alpha}{\sum q_\alpha}$$
by analogy with the center of mass. The most obvious trouble with this formula is that the total charge, the thing in denominator, can be zero. This means the center of charge doesn't exist in general (at least using this definition). On the other hand, the quantity $$\vec{d} = \sum q_\alpha \vec{r}_\alpha$$ is actually important and it is given a name: the dipole moment. Perhaps you have heard of dipoles in your electromagnetism courses, if so you might try to convince yourself that the general expression I gave is equivalent to what you know. The dipole moment can tell you a lot of important things about a system. For example, when a system is charge neutral, the dipole moment (if it isn't zero) determines the electric field of your system far away from the system (this is called the multipole expansion) . Also, oscillating dipoles are very important when studying electromagnetic radiation.

Last edited: Dec 4, 2005
3. Dec 4, 2005

### neutrino

Thank you. I have come across dipoles in intro courses, but I came up with this question after going through a qualitative explanation of Van der Waals' bonds, where the symmetry of charge distribution of an atom is supposed to be 'disturbed' prior to the formation of a bond. In a book on Solid-State Physics I have (not one of those which can be recognised by the author's name alone), it is mentioned that "...due to the disturbance of the electron cloud of an atom, the centres of the positive and negative charge distributions no more coincide and an elctric dipole with a non-zero dipole moment is generated...".