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Consequences at a boundary

As said above we make medium 1 the perfect conductor. This is so that the vector ^An points out into the adjacent space, as shown in Figurę 6.3. For d.c.fields we would havethe forms already quoted as equation 6.1 to 6.4 with Eti and Dm set to zero, viz Etz = 0(6.13)

Dnz = ps(6.14)

^An x (Ht2 -Hti) = Js(6.15)

Bn2-Bm = 0(6.16)

For time varying fields we will consider in particular the sinusoidal steady State in which we represent vector fields by błock capitals as shown in Figurę 6.3.

Because in the sinusoidal steady State all fields in the perfect conductor are now zero we will drop the subscript 2 from the fields in the adjacent space.

In the light of the above discussion, and realising that both Jsand psare allowed, we now have boundary conditions in the form Et= 0(6.17)

Dn= ps(6.18)

^An x Ht= Js(6.19)

Bn= 0 (6.20)

We should notę the change in notation to that appropriate to the sinusoidal stead State.

This finał set of boundary conditions is the most commonly encountered in

electromagnetic

theory.

We notę in relation to Figurę 6.3 above, the reference directions for Jsand Htare easily established through the right hand rule applied to Js.