70932

Boundary Characterisation

We will for simplicity consider piane boundaries, and will regard any smoothly curved boundary as approximately piane at an appropriate scalę of viewing. Such a piane boundary

is shown in Figurę 6.1 and is assumed to lie between region 1, in which the medium is characterized by real magnetic permeability pi, dielectric permittivity ²i, and electric

conductivity oi, and a region 2 in which the materiał is characterized by corresponding

parameters p2,²2, and 02. A unit vector *n is directed normal to the boundary from region 1 to region 2. The reference directions for E, D and B are similar to those for H which are shown.

The boundary is assumed to carry a possible surface charge density ps, and a possible surface current density Jswhich should be viewed as directed out of the paper.

In order to make a correct interpretation of some of the results to be derived below, particular relationships between the quantities just defined and the reference directions for

them as established in Figurę 6.1 must be observed. It should be noted that the reference

direction for the surface current is out of the paper. The safety pin loop to which the linę

integrals will be applied lies with its long sides both in the piane of the boundary and in the piane of the paper, that is perpendicular to the direction of the surface current. Moreover the direction of traverse of that contour, which is indicated by the arrows in

Figurę 6.1 and the reference direction for the surface current, are related according to the

right-hand rule. Finally, we notę that the reference directions for tangential components

on each side of the boundary will on one side match the direction of traverse of the contour

but on the other side will be opposite. We will later take notę of this fact in establishing

the signs of terms which appear in the equations to be derived.