What I am confused about is whether the charge of an object is concentrated within the centre of the mass itself, or does it change depending on the situation?
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1Imagine a proton and an electron separated by some distance. The charge of this system is not within its center of mass. – G. Smith Oct 02 '19 at 05:22
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1Physicists don’t define a center of charge because with both positive and negative charges it doesn’t make sense. See https://physics.stackexchange.com/questions/8221/why-isnt-there-a-centre-of-charge – G. Smith Oct 02 '19 at 05:30
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Since the center of mass is a point, nothing can be within it. Are you asking whether the center of charge & the center of mass always coincide? – D. Halsey Oct 02 '19 at 17:55
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Charge and mass are independent properties of a body. The center of mass and charge of a body depend solely on the way the mass or charge is distributed about the body. If both are distributed in the same way, their centers will coincide.

Sam
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A rod for example may have a linear charge density, this will mean that the center will not be at the middle. Simply bringing a magnet close to a body will also disturb the distribution of charge. – Sam Oct 02 '19 at 04:32