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Question

Sir is there anything called centre of charge ? Like centre of mass.

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Solution

We don't usually use the term centre of charge as it is irrelevant.
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 symmetrically 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.
As well As:

Defining a centre of mass relies on the symmetry of particles with a mass charge. Namely that they are all of the same sign. This often allows the problem to be reduced to a geometrically simple description. For electric charge there are two signs and therefore this simple symmetry doesn’t exist at short distances, though it can be approximated to at large distance.

Hope this helps :)


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