Centre of gravity,centre of charge

Kolahal Bhattacharya

In mechanics, we often use centre of centre of mass,but, I have never found anywhere to consider centre of charge even in problems of symmetrical charge distribution.Where is the difference of the two subjects?

Andrew Mason

Interesting question.

Mass has two important aspects in physics: inertia and gravity. The centre of mass is useful because mass has the quality of inertia. We don't often care about the gravitational attraction force between two masses as it is so small. The centre of mass of a system of mass is a useful concept in determining how a system of masses will move in response to forces.

Charge has no equivalent to inertia. It is the Coulomb force that we are interested it when it comes to charge. The geometric centre of charge is not particularly useful unless the charge is symetrically distributed about a point (ie a uniformly charged sphere). Then we can treat the sphere as a point charge located at its centre. Otherwise the centre of charge distribution is not particularly useful. We have to analyse the forces based on the actual distribution of charge.

AM

lightgrav

Another way of looking at it:

mass (or charge) is the sum of m_i * (r_i)^0 .

the mass center is found by "normalizing" the sum of m_i * (r_i)^1 .
When you do that with charge, you get the dipole moment q_i * r_i .

The big difference is that all masses are positive,
so the mass monopole (r^0) term almost always dominates the situation.

Charges can be positive or negative ...
when the monopole term (Q_total) is zero, it can't dominate ...
so the dipole term (r^1) dominates [over quadrupole, octopole...].