Problem Set #5
1. Find the E and H fields produced by a current sheet of the form
JS(x)=ˆ
x J0e−jkxx
located in the z = 0 plane, in free space.
2. In class, we determined the fields of a line source for the perpendicular
polarization (TM to y). Using your answer from problem (1), find the y-
component of the H-field produced in free space by a line source of the form
JS(x)=ˆ
x I0
δ
(x)
δ
(y)
In that manner, you will determine the fields of the line source for the parallel
polarization (TE to y). Hint: The initial form of the superposition integral looks
simple, but the easiest approach is actually to manipulate this into the form of the
integral that we did for the TM-to-y case, namely
I=e−j k2−kx
2 z
k2−kx
2
−∞
∞
∫ e−jkxxdkx=
π
H0
(2 ) (k
ρ
)
There is a little trick to getting it into that form, but it is the most straightforward
way to construct the solution!
3. Using the results from Note #13, and problem set 4, determine an expression for
the H-field components (x, y, and z) of the point source in (13.1). Express your
answers in the form of derivatives of the quantity
I0
e−jk0r
4
π
r
⎛
⎝
⎜⎞
⎠
⎟
Hint: You should be able to do this by inspection!