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SOLUTION OF BASIC EQUATIONS OF ELECTRODYNAMICS 175

X-axis

Z-axis Z > 0 Origin Z < 0 Z-axis
Figure 4.1.5 Vector potential in space-time domain

2. Comparing Figure 4.1.3 and 4.1.4 one more time we realize that the vector potential wave
oscillates up-and-down at right angles to the direction of its propagation over -axis.
According to (4.19), (4.1) and (4.35) the EM fields associated with such transverse wave
has only two components

1 1
= × = � �
0
0 0 2 � (4.41)
2
1 2
= − � � = − = −
0 0 0 2 0 2
Then according to (4.40) for the forward wave ( − ) propagating in the positive
1
direction > 0 we obtain
+
= − � 1 1 � = − � 1 1 �
0
0
0 () 0 � (4.42)
+
= − � 1 �
0

while for the backward wave ( + ) propagating in the negative direction < 0
2
− 1 2
= � �
0
� (4.43)
0
−
= − � 2 �
0

3. According to (4.42) and (4.43) the ratio = = 377 Ohms. Therefore, the electric
⁄

0
and magnetic field oscillations are perfectly synchronized in space-time domain.