Page 291 - Engineering Electromagnetics, 8th Edition

CHAPTER 8 Magnetic Forces, Materials, and Inductance 273

Figure 8.15 See Problem 8.18.

8.23 Calculate values for H φ , B φ , and M φ at ρ = c for a coaxial cable with
a = 2.5mmand b = 6mmifit carries a current I = 12 A in the center
conductor, and µ = 3µH/m for 2.5mm <ρ < 3.5 mm, µ = 5 µH/m for
3.5mm <ρ < 4.5 mm, and µ = 10 µH/m for 4.5mm <ρ < 6 mm. Use
c =:(a)3 mm; (b)4 mm; (c)5 mm.
8.24 Two current sheets, K 0 a y A/m at z = 0 and −K 0 a y A/m at z = d, are
separated by an inhomogeneous material for which µ r = az + 1, where a is
a constant. (a) Find expressions for H and B in the material. (b) Find the total
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flux that crosses a 1m area on the yz plane.
8.25 A conducting filament at z = 0 carries 12 A in the a z direction. Let µ r = 1
for ρ< 1 cm, µ r = 6 for 1 <ρ < 2 cm, and µ r = 1 for ρ> 2 cm. Find:
(a) H everywhere; (b) B everywhere.
8.26 A long solenoid has a radius of 3 cm, 5000 turns/m, and carries current
I = 0.25 A. The region 0 <ρ < a within the solenoid has µ r = 5, whereas
µ r = 1 for a <ρ < 3 cm. Determine a so that (a)a total flux of 10 µWb is
present; (b) the flux is equally divided between the regions 0 <ρ < a and
a <ρ < 3 cm.
8.27 Let µ r1 = 2inregion 1, defined by 2x + 3y − 4z > 1, while µ r2 = 5
in region 2 where 2x + 3y − 4z < 1. In region 1, H 1 = 50a x − 30a y +
20a z A/m. Find (a) H N1 ;(b) H t1 ;(c) H t2 ;(d) H N2 ;(e) θ 1 , the angle between
H 1 and a N21 ;( f ) θ 2 , the angle between H 2 and a N21 .

8.28 Forvalues of B below the knee on the magnetization curve for silicon steel,
approximate the curve by a straight line with µ = 5 mH/m. The core shown
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in Figure 8.16 has areas of 1.6 cm and lengths of 10 cm in each outer leg,
and an area of 2.5 cm and a length of 3 cm in the central leg. A coil of
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1200 turns carrying 12 mA is placed around the central leg. Find B in the
(a) center leg; (b) center leg if a 0.3 mm air gap is present in the center leg.