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Is there a momentum for charge?

Since mass and charge behave similarly, so, just like center of mass, I define a point center of charge, that is defined by

$$\vec r_{qm} = \frac {\sum{q_i \vec r_i}} {\sum{q_i}}$$

where $\vec r_i$ is a position vector w.r.t. the origin.

Now suppose just like momentum,there is a quantity we call charge-momentum $q \vec v$ for a system which is changed iff there is an external quantity denoted by $q \vec a$ where $\vec a= \frac{d\vec v}{dt}$ . Let us name this new quantity $ q\vec a$ as charge-force.

Now I conjecture, for every charge force, there is an equal and opposite charge force.

And that charge-momentum of an isolated system will be conserved. Just like momentum, can this be a conserved quantity of the universe? Does this make any sense ?

user23503