Physics 8B
11 – EM Waves
rev 4.0
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 yaxis. 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 +
ω
t)
z
ˆ
B(x, y, z, t) = B
0
sin(kx +
ω
t)
y
ˆ
y
4
B
3
x
1
z
E
•2
a)
Q:
In which direction is the wave propagating? Explain.
b)
Q:
Is the wave transverse or longitudinal? Explain.
c)
Q:
Points 1, 2 and 3 lie in the xz plane and point 4 lies in the xy plane. For the
instant shown, rank these points according to the magnitude of the electric field.
d)
Q:
Is your ranking consistent with the mathematical expression for the electric
field? Explain.
e)
Q:
For the instant shown, rank points 1, 2, 3 and 4, according to the magnitude of
the magnetic field.
f)
Q:
Is your ranking consistent with the mathematical expression for the magnetic
field? Explain.
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Physics 8B
11 – EM Waves
rev 4.0
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
A T
E
Direction of
B propagation
F
a)
Q:
Draw the electric field vector at point P at the same instant. Explain how you
chose the direction.
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 Spring '07
 SHAPIRO
 Physics, Light, Mathematical Expression, EM waves

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