Page 205 - Engineering Electromagnetics, 8th Edition

CHAPTER 7 The Steady Magnetic Field 187

Equation (9) may be used to find the magnetic field intensity caused by current
filaments arranged as a sequence of straight-line segments.

EXAMPLE 7.1
As a numerical example illustrating the use of (9), we determine H at P 2 (0.4, 0.3, 0)
in the field of an 8. A filamentary current is directed inward from infinity to the origin
on the positive x axis, and then outward to infinity along the y axis. This arrangement
is shown in Figure 7.6.

Solution. We first consider the semi-infinite current on the x axis, identifying the
−1
two angles, α 1x =−90 and α 2x = tan (0.4/0.3) = 53.1 . The radial distance ρ is
◦
◦
measured from the x axis, and we have ρ x = 0.3. Thus, this contribution to H 2 is
8 2 12
◦
H 2(x) = (sin 53.1 + 1)a φ = (1.8)a φ = a φ
4π(0.3) 0.3π π
The unit vector a φ must also be referred to the x axis. We see that it becomes −a z .
Therefore,
12
H 2(x) =− a z A/m
π
−1
For the current on the y axis, we have α 1y =− tan (0.3/0.4) =−36.9 , α 2y = 90 ,
◦
◦
and ρ y = 0.4. It follows that
8 8
◦
H 2(y) = (1 + sin 36.9 )(−a z ) =− a z A/m
4π(0.4) π

Figure 7.6 The individual fields of two semi-infinite
current segments are found by (9) and added to obtain
H 2 at P 2 .