[SOLVED] CS ER Mid 2 Problem 1

Mid 2 Problem 1
In a spherical coordinate system, a ring (red) with a current I=I0 generates fields as
H(r,,)=jka2I0cos()[1+ 1]ejkr r 2r2 jkr

r
H (r,,)=0
H (r,,)=(ka)2I0sin()[1+ 1 1 ]e E (r,,)=(ka)2I0sin()[1+ 1 ]ejkr
jkr 4r jkr (kr)2

Er (r,,)=0
4r jkr
E (r,,)=0
The ring radius a=20mm. The ring is in the free space. Current I0 =1A.
The frequency=2.5GHz. And phase constant k = 2 .
At every point in the 3-D space, there are two magnetic field vectors and one electrical field vector.
JCCHIAO2020
1

(1)
At every point in the space, there are two magnetic field vectors and one electrical field vector.
Plot the fields
Hr (x, y, z) at a plane at H (x,y,z)
E (x,y,z)
z
r
z = 2cm, y=0 1m x 1m
|Hr |, |H |or|E |
x
x
x JCCHIAO2020

y
2

(2)
Plot the fields in a 2-D map at a plane at |Hr ||H |or|E |
z=2cm,1mx1m, 1my1m,
z
r
y
Then convert the magnitudes of fields to normalized values.
x
Plot a heat map with red being 1 (maximum) and blue

being almost zero (minimum).
y
0.5
0 -0.5 -1.0
-1.0
Heat map example:
1.0
1.0
0.5
0.0
x JCCHIAO2020

-0.5
0
0.5
1.0
3

Now plot the heat map with red being 0dB (maximum) and blue being -30dB for the three field component magnitudes.
Heat map example:
1.0 0.5 0 -0.5
-1.0 -1.0
0dB
-15dB
-30dB
JCCHIAO2020
4
-0.5
0
0.5
1.0