1. Consider the time-harmonic charge distribution
(r, t) = q [ (r h) (r + h) + (r h) (r + h)] cos(t)
in free space.
a) Write down the phasors for the charge density (r, t) and its time derivative
b) Calculate the divergenc
1. Consider a multi-slab planar geometry with n = 1 for z > 0 and z < d2 ; n = a for d1 < z < 0;
n = b for d2 < z < d1 . Also = o in all four regions.
a) Determine the reectance in terms of a and b if d1 = d2 d1 = . Here reectance is d
and the numerical values of electron mass and charge m and e in MKS:
a) Show that
80.6N 9 N Hz
if N is to be entered in elect/m3 units.
b) Calculate fp in MHz if N = 1012 elect/m3 .
2. A homogeneous colli
1. For each uniform plane TEM wave described below in terms of its wave vector k determine the
corresponding (i) wavelength , (ii) wave frequency (assume free space propagation), (iii) angles
and describing the propagation direction of
1. A Hertzian radiation source with the current density
J (r, t) = xIo x(x 100)(y)(z 100)cos(t)
is embedded in free space and its oscillation frequency f = 2 = 300 MHz. Assuming that Io x =
1 A.m, determine the numerical values (
1. A z -polarized short-dipole located at the origin is in front of a reecting (PEC) plate situated on
x = d plane, with d = 4 , and it is found that the reector/dipole-system produces an electric eld
phasor of E(s, 0, 0) = 5 mV/m on
1. In the four gures below the planar media interface coincides with the plane z = 0.
Match the descriptions below to the gures. Justify your answer.
a) There is a surface electric charge density of (1/18) 109 (C/m2 ) on the media inter
1. Consider a pair of x and y polarized identical short-dipole antennas at the origin having input currents
of Ix = Io 0 A and Iy = Io 90 A, respectively. The superposition of the radiation elds of the two
dipoles is given by
1. Consider an array of four identical z -polarized short dipoles with input currents Io = 10 A at
locations (x, y, z) = (d, 0, 0) and (0, d, 0) and Io = 1180 A at locations (x, y, z) = (d, 0, 0) and
(0, d, 0).
a) Determine the smallest
1. A small loop antenna in free space and centered about the origin on the xy-plane is producing a
(far-eld) radiation electric eld (in phasor notation)
E = 2
at a location (x, y, z) = (0, r, 0) when it is driven with a lo
1. Consider a parallel plate waveguide with a plate separation of a in x direction lled with a uniform
collisionless plasma of a plasma frequency p . Determine:
a) Permissible values of kx for the guided modes in the system imposed by