My electromagnetics textbook has a picture of an RC circuit with a current source.
As you can see, there are three current density vectors, J_i, J_c, and J_d. The book labels them as follows:
J_i = impressed (source) electric current density
J_c = conduction electric current density
J_d = displacement electric current density = partial D / partial t, where D is electric flux density
It then uses this figure to explain the following Maxwell equation:
curl of H = J_i + J_c + J_d, where H is magnetic field intensity
What I don't understand is... Isn't J_i the same as J_c? I'm getting this from the idea that if you do a Kirchhoff Current Law evaluation at the top left node (between the source and resistor), then J_i is going in and J_c is going out, thereby making them equal? ... So wouldn't this mean that J_i and J_c are the same current? And if they're the same current, then doesn't that mean that the Maxwell equation is counting it twice?
I'm looking for a solid explanation of why J_i is different than J_c, despite Kirchhoff's Current Law. Thanks!