From Kirchoff’s laws, the loop equations for
the right and left loops respectively are
right loop :
1
5
E
+
i
1
R
= 0
(1)
left loop :
4
5
E
+
i
2
R
= 0
(2)
004
(part 1 of 1) 10 points
In the figure shown, the north pole of the
magnet is first moved down toward the loop
of wire, then is withdrawn upward.
Clockwise
Counter
clockwise
N
As viewed from above, the induced current
in the loop is
1.
first clockwise, then counterclockwise.
2.
for both cases counterclockwise with de
creasing magnitude.
3.
first counterclockwise,
then clockwise.
correct
Husain, Zeena – Exam 3 – Due: Apr 13 2004, 10:00 pm – Inst: Sonia Paban
3
4.
for both cases counterclockwise with in
creasing magnitude.
5.
for both cases clockwise with decreasing
magnitude.
6.
for both cases clockwise with increasing
magnitude.
Explanation:
From Ohm’s law and Faraday’s law, the
current in magnitude is
I
=
V
R
=

1
R
d
Φ
dt
,
where Φ is the magnetic flux through the loop.
We know the sign of the rate of change of the
magnetic flux is changed when the magnet is
withdrawn upward, which, according to the
equation the direction of the current is also
changed.
From Lenz’s law, we know when the magnet
is moved down toward the loop, the current
in the loop is counterclockwise as viewed from
above.
005
(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 positive
z
axis,
~
E
is along
the negative
y
axis.
2.
~
B
is along the negative
y
axis,
~
E
is along
the positive
z
axis.
3.
~
B
is along the negative
z
axis,
~
E
is along
the negative
y
axis.
4.
~
B
is along the negative
y
axis,
~
E
is along
the positive
y
axis.
5.
~
B
is along the positive
z
axis,
~
E
is along
the positive
y
axis.
6.
~
B
is along the positive
y
axis,
~
E
is along
the negative
z
axis.
7.
~
B
is along the positive
y
axis,
~
E
is along
the positive
z
axis.
8.
~
B
is along the negative
y
axis,
~
E
is along
the negative
z
axis.
9.
~
B
is along the negative
z
axis,
~
E
is along
the positive
z
axis.
10.
~
B
is along the negative
z
axis,
~
E
is along
the positive
y
axis.
correct
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.
Husain, Zeena – Exam 3 – Due: Apr 13 2004, 10:00 pm – Inst: Sonia Paban
4
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