Flores, Michael – Homework 13 – Due: Apr 27 2004, 4:00 am – Inst: Sonia Paban
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001
(part 1 of 2) 10 points
To demonstrate the generation of electromag
netic waves due to oscillations of a current
sheet in the
yz
plane at
x
= 0, one first con
siders the following situation. One turns on a
steady current flow along the negative
y
axis
at
t
= 0.
p
z
I
x
y
0
The
point
P
is
along
the
negative
x

direction.
Let
~
B
and
~
E
be the magnetic
and electric field established at
P
soon after
the switching on of the current, respectively.
The directions of
~
B
and
~
E
are
1.
~
B
is along the negative
y
axis,
~
E
is along
the positive
z
axis.
2.
~
B
is along the negative
z
axis,
~
E
is along
the positive
z
axis.
3.
~
B
is along the positive
y
axis,
~
E
is along
the positive
z
axis.
4.
~
B
is along the positive
z
axis,
~
E
is along
the negative
y
axis.
5.
~
B
is along the positive
y
axis,
~
E
is along
the negative
z
axis.
6.
~
B
is along the positive
z
axis,
~
E
is along
the positive
y
axis.
7.
~
B
is along the negative
z
axis,
~
E
is along
the positive
y
axis.
correct
8.
~
B
is along the negative
z
axis,
~
E
is along
the negative
y
axis.
9.
~
B
is along the negative
y
axis,
~
E
is along
the positive
y
axis.
10.
~
B
is along the negative
y
axis,
~
E
is along
the negative
z
axis.
Explanation:
Basic
Concepts
Electromagnetic
waves.
Since the current on the sheet is flowing along
the negative
y
axis, the magnetic field for neg
ative values of
x
is directed along the negative
z
axis.
x
y
O
O
z
P
P
E
E
B
B
B
A
C
D
⇐
About point
P
we may construct a rectan
gular window
ABCDA
in the
xy
plane.
As
the “front” of the
B
field sweeps across the
window to the left, it causes a counterclock
wise induced emf, which is generated by the
induced emf at the right side of the window
from
D
to
A
. Since the side
DA
can be placed
at any location between
O
and
P
, when the
B
field reaches
P
, there is a companion
E

field stretched out from
D
to
A
. Notice that
the electromagnetic wave is traveling along
the negative
x
axis, so
~
E
has to be directed
along the positive
y
axis (so that
~
E
×
~
B
is
directed along the correct direction).
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Flores, Michael – Homework 13 – Due: Apr 27 2004, 4:00 am – Inst: Sonia Paban
2
002
(part 2 of 2) 10 points
Now consider the current sheet which under
goes the sinusoidal oscillations with a definite
frequency where the amplitude of the mag
netic field oscillations in the waves is
B
max
.
Consider a book of area
A
located at
P
paral
lel to the
yz
plane. Find the radiation force on
the book, if it absorbs one third of the light.
1.
1
2
B
2
max
A
μ
0
2.
4
3
B
2
max
A
μ
0
3.
1
3
B
2
max
A
μ
0
4.
1
6
B
2
max
A
μ
0
5.
2
3
B
2
max
A
μ
0
6.
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 Spring '04
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 Work, Light, Sonia Paban, Michael – Homework

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