An antenna of size L is embedded in a material with relative permittivity, !2 . A radio wave at frequency f
impinges on material 2 from air, along the surface normal. What is the wavelength in air and at the antenna?
What is the fraction of power reflecte

A uniform plane wave travels in a lossless, nonmagnetic, dielectric material in the -y-direction. The material
has relative dielectric constant, !r = 4. The wave frequency is 3 GHz, and wave is linearly polarized to fall
along the x-axis. Find the followi

A rectangular loop with N-turns, side length L, and width W, spins around the z-axis in the +-direction
at
a constant rate, in a uniform B-field, B = x
Bo . If the loop has internal resistance, R, find
the time-dependent magnetic flux, assuming the loop

A uniform volume current density, J, is carried along an infinite straight cylinder from 0 < r < ra . A
current, I, equal in magnitude to the total current in the inner cylinder is carried in the opposite direction
on a cylindrical surface at r = rb . Fin

The voltage on a lossless transmission line was found to have a maximum magnitude of 2.0 V and a minimum
magnitude of 1.0 V. Find the standing wave ratio and the magnitude of the loads reflection coefficient. If the
transmission line characterisitic imped

A line of charge with uniform density, l , extends from 0<z<h along the z-axis. Find the electric field on the
y-axis, at y=a.
(a2
dx
x
=
2
3/2
2
+x )
a a2 + x2
(a2
1
xdx
=
2
3/2
2
+x )
a + x2
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A coaxial transmission line has a solid inner conductor with radius ra , and an outer conductor with inner
radius rb . Assume a total charge on the inner conductor surface of q, and a total charge on the outer
conductor inner surface of -q. Use Gausss law

A square loop carries current I, has N-turns, side length of L, and spins around the z-axis. A magnetic flux
density, B = Bo x
, is present in the problem. Show the correct direction of current flow if the torque is
negative when = 0. Write an expression

An antenna with impedance ZL = 64 is connected to a 128-V amplitude rf-generator with internal
impedance Zg = 64, by a transmission line with length l = 5/2 and characteristic impedance Zo = 128.
Find the voltage reflection coefficient, the input impedanc

Complex numbers z1 and z2 are given by
z1 = 5 60
z2 = 245
Plot both in the complex plane. Also, determine the following.
1. The product z1 z2 in polar form
2. The product z1 z2 in polar form
3. The ratio z1 /z2 in polar form
4. The ratio z1 /z2 in polar f

For the vector field, E =
rr, confirm the divergence theorem on the cylinder (r = ro , 0 < z < l) by doing the
following:
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1. Compute the divergence of E. Note that in cylindrical coordinates, E =
r 1r r
(rEr )+
r
E
z
+
z E
z .
2. Set up the volume in

=x
ejkz + y
2ejkzj/2 , and travels through free space. Find direction
A wave has magnetic field phasor H
of travel, polarization state (linear, circular or elliptical and direction of rotation if applicable). Also find E
from H.
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