Appendix A Maxwell's Eqs.
Coupling Between E and H - Maxwell’s Curl Equations
The coupling between the electric, E and magnetic, H fields is mathematically described by Ampere’s
and Faraday’s laws. Each of these fields generates the other
as described by the Maxwell’s curl equations which are the
generalized form of Ampere’s and Faraday’s laws. The
generated fields circulate about the causative fields and are always
at right angles to them.
In Ampere’s law the causative field is the total conduction
current density, JT = JC + (∂D/∂t).
So, since JC = σE
and D = εE, the heart of the causative
field in Ampere’s law is the electric field itself and its
time variation. This is expressed as the Maxwell’s equation
| Curl H = JC + (∂D/∂t) | (A.1) |
The causative field in Faraday’s law is the time variation of the magnetic field expressed as
| Curl E = -(∂B/∂t) | (A.2) |
where, of course, B = μH.
The circulation relations are depicted in the animations below.