Continuity Equation and Maxwell Equation
Continuity Equation
Continuity Equation
According to principle of charge conservation, the time rate of
decrease of charge within a given volume must be equal to the net
outward current flow through the closed surface of the volume.
The current Iout coming out of the closed surface
(i)
where Qin is the total charge enclosed by the closed surface.
Using divergence theorem
But
Equation (i) now becomes
or
This is called the continuity of current equation.
(ii)
Summary
According to Ohm’slaw (How)
According to Gauss’s law
Maxwell Equation
Explanation
Maxwell Contribution?
 Inconsistency with Ampere's law
Taking Divergence:
But, from continuity Eqn.:
Maxwell added “displacement current” in Ampere’s law
Displacement Current?
Maxwell contribution in
Ampere’s Law
How current flow across the capacitor plates?
Complete Maxwell Equation