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33.1.
Model:
A magnetic field is caused by an electric current.
Visualize:
Please refer to Figure EX33.1.
Solve:
The magnitude of the magnetic field at point 1 is 2.0 mT and its direction can be determined by using
the righthand rule. Grab the current carrying wire so that your thumb points in the direction of the current.
Because your fingers at point 1 point into the page,
1
B
G
=
(2.0 mT, into the page). At point 2, the magnetic field
due to the bottom wire is into the page. The righthand rule tells us that the magnetic field from the top wire is
also into the page. At point 2,
2
B
G
=
(4.0 mT, into the page).
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View Full Document 33.2.
Model:
A magnetic field is caused by an electric current.
Visualize:
Please refer to Figure EX33.2.
Solve:
The current in the wire is directed to the right.
B
2
=
20 mT
+
20 mT
=
40 mT because the two overlapping
wires are carrying current in the same direction and each wire produces a magnetic field having the same direction at
point 2.
B
3
=
20 mT – 20 mT
=
0 mT, because the two overlapping wires carry currents in opposite directions and
each wire produces a field having opposite directions at point 3. The currents at 4 are also in opposite directions, but
the point is to the right of one wire and to the left of the other. From the righthand rule, the field of both currents is
out of the page. Thus
B
4
=
20 mT
+
20 mT
=
40 mT.
33.3.
Model:
The magnetic field is that of a moving charged particle.
Visualize:
The first point is on the
x
axis, with
θ
a
=
90°. The second point is on the
y
axis, with
b
=
180°, and the third
point is on the
−
y
axis with
c
=
0°.
Solve:
(a)
Using Equation 33.1, the BiotSavart law, the magnetic field strength is
( )( )( )
()
71
9
7
15
0
a
2
2
2
10 T m/A 1.60 10
C 1.0 10 m/s sin90
sin
1.60 10
T
4
1.0 10 m
qv
B
r
μθ
π
−−
+
−
−
××
°
==
=
×
×
To use the righthand rule for finding the direction of
,
B
G
point your thumb in the direction of
.
v
G
The magnetic
field vector
B
G
is perpendicular to the plane of
r
G
and
v
G
and points in the same direction that your fingers point.
In the present case, the fingers point along the
ˆ
k
direction. Thus,
15
a
ˆ
1.60 10
T.
B
k
−
=×
G
(b)
B
b
=
0 T because sin
b
=
sin 180°
=
0.
(c)
B
c
=
0 T because sin
c
=
sin 0°
=
0.
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View Full Document33.4.
Model:
The magnetic field is that of a moving charged particle.
Visualize:
The first point is on the
x
axis, with
θ
a
=
90°. The second point is on the
z
axis, with
b
=
0°, and the third point
is in the
yz
plane with
c
=
45°.
Solve:
(a)
Using Equation 33.1, the BiotSavart law, the magnetic field strength is
( )( )( )
()
71
9
7
15
0
a
2
2
2
10 T m/A 1.60 10
C 2.0 10 m/s sin90
sin
3.2 10
T
4
1.0 10 m
qv
B
r
μθ
π
−−
+
−
−
××
°
==
=
×
×
To use the righthand rule for finding the direction of
a
,
B
G
point your thumb in the direction of
.
v
G
Your fingers
point along the –
y
axis, but since the charge is negative,
a
B
G
points along the +
y
axis.
Thus,
15
a
ˆ
3.2 10
T.
B
j
−
=×
G
(b)
B
b
=
0 T because sin
b
=
sin 0°
=
0.
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This note was uploaded on 01/30/2011 for the course PHYS 131 taught by Professor E.salik during the Winter '10 term at Cal Poly Pomona.
 Winter '10
 E.Salik
 Current

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