# Where will the charge of a mass will go (having some net charge) when completely converted to energy?

All my confusion began while thinking of can charge be related to energy. Now Coulomb's law state that two body having some charges apply forces on each other which is true. And according to Newton $F=ma$ means force can be exerted on a body having some mass. Since charges apply forces so it should not possible that they exist without mass! Either it is negligible, but there should some mass if charge exists but that shouldn't be zero.

Now $F=k\frac{q_1q_2}{r^2}=ma$ where $F$ is force on $q_2$ of mass $m$ due to $q_1$. Now if we start converting mass $m$ into energy keeping $q_1$ fixed at it's position and $q_1$ constant, the acceleration of the mass will increases and charge $q_2$ will be there on the mass till traces of $m$ exists and making force due to charges constant, by this concept I concluded that any amount of charge can exist on any amount of mass means $1\,\text{C}$ of charge can exist on a body of mass of order $10\,\text{kg}$ or $10\,\text{mg}$ or $10\,\text{ng}$.

Now coming to point that if I take a mass and given it some net charge $q$ and started converting that mass into energy (somehow) till that mass completely gets converted into energy so that no mass exist for the charge to gather on, then where should that charge $q$ will go, will it get destroyed or it also gets converted into energy? If it gets converted into energy then there shouldn't some more energy released rather than $mc^2$

This is my approach to prove $E=mc^2$ hope someone will tell me what I am missing or may be I am right!

• "as charges can not exist without mass because..." I got lost at that point; looks like you have a few sentence stubs and it's pretty confusing. Could you revisit the punctuation and expand that rationale behind $E=mc²+ kq$? That doesn't make much sense to me. – user191954 Sep 7 '18 at 16:52

First thing to note is that only certain interactions can result in annihilation, and thus to energy given out via $E=mc^2$. This can only happen between a particle and its anti-particle (to my knowledge). However, even were annihilation between two particles which were not mutual anti-particles possible, it still wouldn't occur in the scenario you describe, because of conservation of charge, which states that charge can't be lost or gained in an interaction.
There would be some energy implicit within the collision, because the particles, as they got closer, would accelerate faster and faster due to their increased proximity, and the effects of the inverse square law. All of their potential energy caused by their mutual interactions would be converted to kinetic energy - that's about as close as I can get to a $+kq$, I'm afraid.