Page 201 - Engineering Electromagnetics, 8th Edition

CHAPTER 7 The Steady Magnetic Field 183

Figure 7.2 The total current I within a
transverse width b,in which there is a uniform
surface current density K,is Kb.

meter, is therefore infinite. Surface current density, however, is measured in amperes
per meter width and designated by K.If the surface current density is uniform, the
total current I in any width b is

I = Kb

whereweassumethatthewidthb ismeasuredperpendicularlytothedirectioninwhich
the current is flowing. The geometry is illustrated by Figure 7.2. For a nonuniform
surface current density, integration is necessary:

I = KdN (4)

where dN is a differential element of the path across which the current is flowing.
Thus the differential current element IdL, where dL is in the direction of the current,
may be expressed in terms of surface current density K or current density J,

IdL = K dS = J dν (5)

and alternate forms of the Biot-Savart law obtained,

K × a R dS

H = 4πR 2 (6)
s
and

J × a R dν
H = 4πR 2 (7)
vol