Charge Conservation - Formal Statement of The Law

Formal Statement of The Law

Vector calculus can be used to express the law in terms of charge density ρ (in coulombs per cubic meter) and electric current density J (in amperes per square meter):

The term on the left is the rate of change of the charge density ρ at a point. The term on the right is the divergence of the current density J. The equation equates these two factors, which says that the only way for the charge density at a point to change is for a current of charge to flow into or out of the point. This statement is equivalent to a conservation of four-current.