Page 210 - Engineering Electromagnetics, 8th Edition

192 ENGINEERING ELECTROMAGNETICS

Figure 7.9 The magnetic field intensity as a function of
radius in an infinitely long coaxial transmission line with
the dimensions shown.

The external field is zero. This, we see, results from equal positive and negative
currents enclosed by the path. Each produces an external field of magnitude I/2πρ,
but complete cancellation occurs. This is another example of “shielding”; such a
coaxial cable carrying large currents would, in principle, not produce any noticeable
effect in an adjacent circuit.
As a final example, let us consider a sheet of current flowing in the positive y
direction and located in the z = 0 plane. We may think of the return current as equally
divided between two distant sheets on either side of the sheet we are considering. A
sheet of uniform surface current density K = K y a y is shown in Figure 7.10. H cannot
vary with x or y.If the sheet is subdivided into a number of filaments, it is evident
that no filament can produce an H y component. Moreover, the Biot-Savart law shows
that the contributions to H z produced by a symmetrically located pair of filaments
cancel. Thus, H z is zero also; only an H x component is present. We therefore choose
the path 1-1 -2 -2-1 composed of straight-line segments that are either parallel or

Figure 7.10 A uniform sheet of surface current
K = K y a y in the z = 0 plane. H may be found by applying
Amp ` ere’s circuital law about the paths 1-1 -2 -2-1 and

3-3 -2 -2-3.