Physics 8B
11 – EM Waves
rev 4.0
1
11 – EM Waves
1.
Shown below are mathematical and pictorial representations of an electromagnetic
plane wave propagating through empty space. The electric field is parallel to the z-
axis; the magnetic field is parallel to the y-axis. Note:
x
ˆ
,
y
ˆ
, and
z
ˆ
are unit vectors
along the +x, +y, and +z directions, respectively.
E(x, y, z, t) = E
0
sin(kx +
!
t)
z
ˆ
B(x, y, z, t) = B
0
sin(kx +
!
t)
y
ˆ
y
4
B
3
x
1
z
E
•2
a)
In which direction is the wave propagating? Explain.
b)
Is the wave transverse or longitudinal? Explain.
c)
Points 1, 2 and 3 lie in the x-z plane and point 4 lies in the x-y plane. For the
instant shown, rank these points according to the magnitude of the electric field.
d)
Is your ranking consistent with the mathematical expression for the electric field?
Explain.
e)
For the instant shown, rank points 1, 2, 3 and 4, according to the magnitude of the
magnetic field.
f)
Is your ranking consistent with the mathematical expression for the magnetic
field? Explain.
Physics 8B
11 – EM Waves
rev 4.0
2
2.
A simple periodic wave of electromagnetic radiation is moving in the direction shown
below. P, Q, R, S and T are equally spaced points in the path of the wave. The
distance PQ = d, the velocity of the wave is c, and its wavelength is 4d. An observer
at T, looking towards P, would see H and D as vertically upwards, while E, A and B
1
would be horizontal and to their left. At a given instant, the magnetic field at P is a
maximum, and is represented by the vector B
1
.
D
H
P C
Q
R G
B
1
S