Conserved quantities in physics obey the continuity equation.
If a quantity Q (such as charge) is conserved, neither
spontaneously created or destroyed, then the time rate of change
of
the amount of that quantity in a closed region of space V
must equal the total rate S at which the quantity is
pumped into or removed from the region by any sources or sinks in the
region minus the net rate (current) I at which that quantity
flows through the
surface of the region,
We may turn this condition into an integral equation by defining
a density field for the conserved quantity (such as charge density)
, a sink/source density 
, and a current density
(like the usual electric current density) 
defined so that the
rate at which the conserved quantity crosses a surface element 
is 
. Our condition for conservation in the
region of space V may now be expressed as the integral condition,
If we express this relation on a per unit volume basis and take the
limit as the volume of the region vanished 
, we find a
differential equation describing conservation, the continuity
equation,
The continuity equation is most often written in the form,
