The continuity equation is derived from two of Maxwell's equations. It states that the divergence of the current density is equal to the negative rate of change of the charge density,
Derivation
One of Maxwell's equations states that
- .
- ,
- .
- .
- ,
In fluid dynamics, the continuity equation is an equation
of conservation of mass. Its form is
Interpretation
Current density is the movement of charge density. The continuity equation says that if charge is moving out of a differential volume (i.e. divergence of current density is positive) then the amount of charge within that volume is going to decrease, so the rate of change of charge density is negative. Therefore the continuity equation amounts to a conservation of charge.
See the Euler equations.