Bài giảng Electromagnetic Fields – Prob - Chapter 4 - Trần Quang Việt
Electromagnetic Fields – Prob – ch_4
D4.7. Compute the propagation constant and instrinsic inpendance
for the following cases: (a) σ = 10-5S/m, ε=5ε0, µ=µ0, and f=105Hz;
(b) σ = 4S/m, ε=80ε0, µ=µ0, and f=109Hz
Ans :( a ) (0.0083+j0.00476) (m-1), 163.54∠9.90(Ω );
(b) (77.84 + j202.86)( m−1 ),36.34∠20.990(Ω )
D4.8. For a uniform plane wave of frequency 106Hz propagating in a
nonmagnetic (µ=µ0) material medium, the propagation constant is
known to be (0.05+j0.1) m-1. Find the following: (a) the distance in
which the fields are attenuated by e-1; (b) the distance in which the
fields undergo a change of phase by 1 rad; (c) the distance that a
constant phase of the wave travels in 1µs; (d) the ratio of the
amplitudes of the electric and magnetic fields; and (e) the phase
difference between the electric and magnetic fields.
Ans :( a ) 20m; (b) 10m; (c) 62.83m; (d) 70.62Ω; (e) 0.1476π
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Electromagnetic Fields – Prob – ch_4
D4.9. The magnetic field associated with a uniform plane wave
propagating in the +z-direction in a nonmagnetic (µ=µ0) material
medium is given by:
H = H e−z cos( 6π .107t − 3z )ay( A/ m )
0
Find the following : (a) the instantaneous power flow across a surface
of area 1m2 in the z=0 plane at t=0; (b) the time-average power flow
across a surface of area 1m2 in z=0 plane; and (c) the time-average
power flow across a surface of area 1m2 in the z=1 plane
Ans :( a ) 102.57H02 (W); (b) 51.28H02 (W); (c) 6.94H02(W )
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Electromagnetic Fields – Prob – ch_4
D4.15. The plane z=0 forms the boundary between free space (z>0)
and another medium. Find the following: (a)
at t=0 if
J s (0,0,0 )
H( 0,0,0+ ) = H0(3ax − 4ay )cosωt
z<0 is a perfect conductor and
(b) if z<0 is a magnetic material of µ=20µ and
;
H( 0,0,0+ )
H( 0,0,0− ) = H0(10ax + az )
to for the case of (b)
0
; and (c) the ratio of
B(0,0,0− )
B(0,0,0+ )
Ans :( a ) H0 (4ax +3ay ); (b) 10H0 (ax +2az ); (c) 8.989
P4.17. The magnetic field of a uniform plane wave propagating in a
nonmagnetic (µ=µ0) material medium is given by:
H = H e−z cos( 2π.106 t − 2z )ax( A/ m )
0
Find : (a) the time-average power flow per unit area normal to the z-
direction; and (b) the time-average power dissipated in the volume
bounded by the planes x=0, x=1, y=0, y=1, x=0, z=1.
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Electromagnetic Fields – Prob – ch_4
P4.21. For uniform plane wave propagation in ice (σ=10-6S/m, ε=3ε0,
and µ=µ0), compute α, β, vp, λ, and η for f=1MHz. What is the
distance in which the fields are attenuated by the factor e-1
P4.22. For uniform plane wave propagation in seawater (σ=4S/m,
ε=80ε0, and µ=µ0), compute α, β, vp, λ, and η for two frequencies:
(a) f=10GHz; and (b) f=100KHz
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