plane wave equation

1. The Uniform Plane Wave
Tutorial 6
1) Calculate the impedance, the propagation constant , and wave velocity for conducting medium in
which =58Ms/m,μr=1 and r=2.5 at a frequency f=100MHz.
2) prove that the electromagnetic wave travels in space with velocity of light. i.e. 3x108
m/s.
3) An electromagnetic wave is travelling in medium with r=75 μr= 1 and =2 s/m. If the electric field in
x-direction given Hx=100Cos107
t V/m at z=0, find attenuation constant, phase constant, intrinsic
impedance and expression of H(t) at z=0.
4) A uniform plane wave in free space is given by ;
E

s=(300<45˚)e-j200z
V/m. Determine frequency of the wave, wave impedance, H

s and
magnitude of E

at z=10mm and t=8ps.
5) Find the magnetic field intensity for a TEM wave with electric field intensity of 1μV/m, in (i) air (ii)
lossless dielectric with r=5,μr=1.
6) An electromagnetic wave travelling in the z-direction in sea-water is given by Ex=100Cos107
t V/m at
z=0. Assume r=72,μr=1 and =5s/m.
Find:
(i) Attenuation Constant.
(ii) Phase Constant.
(iii) Intrinsic impedance.
(iv) The wavelength in the medium.
(v) Skin depth.
(vi) The expression for H(t) at z=10cm.
7) A uniform plane wave in free space is given by ;
E

s=(200<20˚)e-j200z
âx V/m.
Determine
(i) ,ω,, f, .
(ii) H

s, H

(z,t)
(iii) | E

| at z=8mm, t=6ps.

2. 8) A 150MHz uniform plane wave in free space is described by H

s= (4+j10) (2 âx + j ây)e-jz
A/m. find
(a) ω (b) λ (c)  (d) H

(z ,t) at t=1.5ns, z=20cm (e) Emax (f) Hmax
9) A uniform plane wave propagating in free space has E

= 2 cos (107
t-z) âx, determine, and H

.
10) A z-polarized uniform plane wave with frequency 100MHz propagates in air in the positive x-
direction and impinges normally on a perfectly conducting plane at x=0, assuming the amplitude of the
electric field vector be 3mV/m. determine phasor and instantaneous expressions for
(a) Incident electric and magnetic field vectors.
(b) Reflected electric and magnetic field vectors.
11) For a non-magnetic materials having r= 2.25 and = 10-4
mho/m, find the numeric values at 5MHz
for:
(a) The Loss Tangent (b) The attenuation constant (c) The Phase constant (d) The intrinsic impedance
12)A 9.4GHz uniform plane wave is propagating in polyethylene (r=2.25, μr=1). If the magnitude of the
magnetic field intensity is 7mA/m, and the material is lossless, find (i) Velocity of propagation (ii) the
wavelength (iii) the phase constant (iv) the intrinsic impedance (v) the magnitude of electric field
intensity.
13) A uniform plane wave in free space is propagating in the – ây direction at a frequency of 10MHz. If
E

=400 cos(ωt+z) âz, write the expressions for electric and magnetic fields i.e. E

s(x,y,z) and H

s(x,y,z)
respectively in phasor forms.
14) A Plane wave in free space represented by iE

= 2 cos(9.9x108
t-33.3y) âz makes normal incidence at
the boundaries y=0 to second medium characterized by =2o, μ=8μo, =0, find (a) H

i (b) E

r (c) H

r
(d) E

t (e) H

t
15) At frequencies of 100 and 300 MHz, the dielectric constant of ice model from pure water has value of
3.45 and 3.20 respectively, while the loss tangent is 0.035,0.0009 respectively. If a uniform plane wave
with an amplitude of 100V/m at z=0 is propagating through such ice, find the time average power density
at z=0 and z=10m for each frequency.
16) A Radar Disc antenna is needed to be covered with a transparent plastic (r= 2.25,μr =1) to protect it
from weather without any reflection of the signal back to the antenna. What should be the minimum
thickness of the plastic cover if the operating frequency of the antenna is 10GHz?
17) A steel pipe is constructed of a material for which we may assume μr=200 and =5x106
mho/m. The
outer and inner radii are 8 and 6mm respectively, and the length is 80m. If the total current carried by the
pipe is 2 cos104
t A, find (a) the skin depth (b) the effective resistance (c) the dc resistance (d) the time
average power loss.