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8B Worksheet Answers
11. EM Waves
1. a) The wave is propagating in the
"
ˆ
x
direction.
b) The wave is
transverse
: The electric and magnetic fields are oriented in a direction
perpendicular to the direction of propagation.
c)
E
1
=
E
2
=
E
4
>
E
3
= 0
d) Yes: Points 1, 2, and 4 all have the same
x
and we are evaluating
E
at the same
time, so the fields are identical.
e)
B
1
=
B
2
=
B
4
>
B
3
= 0
f) Yes: Points 1, 2, and 4 all have the same
x
and we are evaluating
B
at the same
time, so the fields are identical.
2. a) The electric field points vertically up (see
green
vector in the figure for part (b)) for
reasons explained in part (c).
b)
Electric Field: Blue
Magnetic Field: Red
Note: Only a few vectors are explicitly shown. The sinusoidal waves you see are the ‘vector
envelope’ of the wave along the axis: That is, if we were to draw field vectors for points along
the axis, then drew a curve connecting all of their tips together, we would get the ‘vector
envelope’.
c) Point
R
is 2
d
=
λ
/ 2 away from
P
, so the
B
field has had its
phase
(the angle in the
cosine or sine when we write out the form of
B
) advance by
π
. Adding a
π
in the
argument of a sine or cosine has the effect of making the sine or cosine
negative
 i.e.
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View Full Documentsin(
θ
+
π
) = sin(
). Therefore,
r
B
(
R
)
=
"
r
B
(
P
)
=
"
r
B
1
, so
vector
C
represents the magnetic
field at
R
.
d) Point
T
is 4
d
=
λ
away from
P
, so the
E
field has had its phase advance by 2
π
, which
means the
E
field at
T
is the same as the
E
field at
P
. We know that the electric field
at
P
must be pointing either vertically up or down, since the vector
r
E
must be both
perpendicular to the vector
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 Spring '10
 CatherineBordel
 Physics, Work

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