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Magnetic Fields
3.
A particle (q = –4.0 µC, m = 5.0 mg) moves
in a uniform magnetic field with a velocity
having a magnitude of 2.0 km/s and a
direction that is 50 away from that of the
magnetic field. The particle is observed to
have an acceleration with a magnitude of
5.8 m/s2. What is the magnitude of the
magnetic field?
a.
b.
c.
d.
e.
4.
5.3 mT
4.9 mT
5.1 mT
4.7 mT
3.6 mT
11.
negative y direction
positive y direction
negative z direction
positive z direction
negative x direction
13.
Bx is positive.
Bz is positive.
By is negative.
By is positive.
Bx is negative.
QVB toward the east
Zero
QVB toward the west
QVB upward
QVB toward the south
A straight wire carries a current of 40 A in a
uniform magnetic field (magnitude = 80
mT). If the force per unit length on this wire
is 2.0 N/m, determine the angle between
the wire and the magnetic field.
a.
b.
c.
d.
e.
1
39 km/s2
43 km/s2
48 km/s2
52 km/s2
25 km/s2
A charged particle (mass = M, charge = Q >
0) moves in a region of space where the
magnetic field has a constant magnitude of
B and a downward direction. What is the
magnetic force on the particle at an instant
when it is moving horizontally toward the
north with speed V?
a.
b.
c.
d.
e.
A positively charged particle has a velocity
in the negative z direction at point P. The
magnetic force on the particle at this point is
in the negative y direction. Which one of the
following statements about the magnetic
field at point P can be determined from this
data?
a.
b.
c.
d.
e.
A charged particle (mass = 4.0 µg, charge =
5.0 µC) moves in a region where the only
force on it is magnetic. What is the
magnitude of the acceleration of the particle
at a point where the speed of the particle is
5.0 km/s, the magnitude of the magnetic
field is 8.0 mT, and the angle between the
direction of the magnetic field and the
velocity of the particle is 60?
a.
b.
c.
d.
e.
An electron moving in the positive x
direction experiences a magnetic force in
the positive z direction. If Bx = 0, what is the
direction of the magnetic field?
a.
b.
c.
d.
e.
9.
10.
either 39 or 141
either 25 or 155
either 70 or 110
either 42 or 138
either 65 or 115
2
14.
CHAPTER 29
A segment of wire carries a current of 25 A
along the x axis from x = –2.0 m to x = 0 and
then along the y axis from y = 0 to y = 3.0 m.
In this region of space, the magnetic field is
equal to 40 mT in the positive z direction.
What is the magnitude of the force on this
segment of wire?
a.
b.
c.
d.
e.
17.
18.
25.
What current must be maintained in a
square loop (50 cm on a side) to create a
torque of 1.0 N  m about an axis through its
center and parallel to one of its sides when a
magnetic field of magnitude 70 mT is
directed at 40 to the plane of the loop?
a.
b.
c.
d.
e.
29.
0.41 N  m
0.14 N  m
0.38 N  m
0.27 N  m
0.77 N  m
66 A
89 A
61 A
75 A
37 A
A square loop (L = 0.20 m) consists of 50
closely wrapped turns, each carrying a
current of 0.50 A. The loop is oriented as
shown in a uniform magnetic field of 0.40 T
directed in the positive y direction. What is
the magnitude of the torque on the loop?
3.2 ILB
5.0 ILB
4.2 ILB
3.6 ILB
1.0 ILB
What is the magnetic force on a 2.0-m
length of (straight) wire carrying a current
of 30 A in a region where a uniform
magnetic field has a magnitude of 55 mT
and is directed at an angle of 20 away from
the wire?
a.
b.
c.
d.
e.
A current of 4.0 A is maintained in a single
circular loop having a circumference of 80
cm. An external magnetic field of 2.0 T is
directed so that the angle between the field
and the plane of the loop is 20. Determine
the magnitude of the torque exerted on the
loop by the magnetic forces acting upon it.
a.
b.
c.
d.
e.
2.8 N
1.6 N
1.2 N
2.0 N
0.4 N
A straight wire of length L carries a current
I in the positive z direction in a region
where the magnetic field is uniform and
specified by Bx = 3B, By = –2B, and Bz = B,
where B is a constant. What is the
magnitude of the magnetic force on the
wire?
a.
b.
c.
d.
e.
21.
2.0 N
5.0 N
1.0 N
3.6 N
3.0 N
What is the magnitude of the magnetic force
on a charged particle (Q = 5.0 µC) moving
with a speed of 80 km/s in the positive x
direction at a point where Bx = 5.0 T, By = –
4.0 T, and Bz = 3.0 T?
a.
b.
c.
d.
e.
23.
1.5 N
1.3 N
1.1 N
1.7 N
3.1 N
a.
b.
c.
d.
e.
0.21 N  m
0.20 N  m
0.35 N  m
0.12 N  m
1.73 N  m
Magnetic Fields
30.
A rectangular coil (0.20 m  0.80 m) has 200
turns and is in a uniform magnetic field of
0.30 T. When the orientation of the coil is
varied through all possible positions, the
maximum torque on the coil by magnetic
forces is 0.080 N  m. What is the current in
the coil?
a.
b.
c.
d.
e.
31.
0.37 T
1.6 T
0.50 T
1.2 T
2.5 T
A deuteron is accelerated from rest through
a 10-kV potential difference and then moves
perpendicularly to a uniform magnetic field
with B = 1.6 T. What is the radius of the
resulting circular path? (deuteron: m = 3.3 
10–27 kg,
q = 1.6  10–19 C)
a.
b.
c.
d.
e.
19 mm
16 mm
20.3 mm
10 mm
9.0 mm
A 500-eV electron and a 300-eV electron
trapped in a uniform magnetic field move
in circular paths in a plane perpendicular to
the magnetic field. What is the ratio of the
radii of their orbits?
a.
b.
c.
d.
e.
37.
A circular coil (radius = 0.40 m) has 160
turns and is in a uniform magnetic field.
When the orientation of the coil is varied
through all possible positions, the
maximum torque on the coil by magnetic
forces is 0.16 N  m when the current in the
coil is 4.0 mA. What is the magnitude of the
magnetic field?
a.
b.
c.
d.
e.
33.
5.0 mA
1.7 A
8.3 mA
1.0 A
42 mA
35.
82 km
59 km
71 km
48 km
7.5 km
An electron follows a circular path (radius =
15 cm) in a uniform magnetic field
(magnitude = 3.0 G). What is the period of
this motion?
a.
b.
c.
d.
e.
47.
2.8
1.7
1.3
4.0
1.0
A proton moves around a circular path
(radius = 2.0 mm) in a uniform 0.25-T
magnetic field. What total distance does this
proton travel during a 1.0-s time interval? (
m  1.67 1027 kg , q  1.6 1019 C )
a.
b.
c.
d.
e.
46.
3
0.12 µs
1.2 ms
0.18 µs
1.8 ms
1.8 µs
A proton with a kinetic energy of 0.20 keV
follows a circular path in a region where the
magnetic field is uniform and has a
magnitude of 60 mT. What is the radius of
this path?
a.
b.
c.
d.
e.
4.1 cm
2.9 cm
3.4 cm
5.1 cm
2.4 cm
4
48.
CHAPTER 29
A proton is accelerated from rest through a
potential difference of 150 V. It then enters a
region of uniform magnetic field and moves
in a circular path (radius = 12 cm). What is
the magnitude of the magnetic field in this
region?
a.
b.
c.
d.
e.
49.
54.
b.
c.
d.
e.
57.
15 mm
12 mm
18 mm
24 mm
8.5 mm
Equal charges, one at rest, the other having
a velocity of 104 m/s, are released in a
uniform magnetic field. Which charge has
the largest force exerted on it by the
magnetic field?
a.
b.
c.
d.
e.
The charge that is at rest.
The charge that is moving, if its
velocity is parallel to the magnetic field
direction when it is released.
The charge that is moving if its velocity
makes an angle of 45o with the
direction of the magnetic field when it
is released.
The charge that is moving if its velocity
is perpendicular to the magnetic field
direction when it is released.
All the charges above experience equal
forces when released in the same
magnetic field.
One reason why we know that magnetic
fields are not the same as electric fields is
because the force exerted on a charge +q
a.
18 mT
12 mT
15 mT
22 mT
10 mT
A proton is accelerated from rest through a
potential difference of 2.5 kV and then
moves perpendicularly through a uniform
0.60-T magnetic field. What is the radius of
the resulting path?
a.
b.
c.
d.
e.
56.
You stand near the earth’s equator. A
positively charged particle that starts
moving parallel to the surface of the earth in
a straight line directed east is initially
deflected upwards. If you know there are
no electric fields in the vicinity, a possible
reason why the particle does not initially
acquire a downward component of velocity
is because near the equator the magnetic
field lines of the earth are directed
a.
b.
c.
d.
e.
59.
is in opposite directions in electric and
magnetic fields.
is in the same direction in electric and
magnetic fields.
is parallel to a magnetic field and
perpendicular to an electric field.
is parallel to an electric field and
perpendicular to a magnetic field.
is zero in both if the charge is not
moving.
upward.
downward.
from south to north.
from north to south.
from east to west.
A magnetic field is directed out of the page.
Two charged particles enter from the top
and take the paths shown in the figure.
Which statement is correct?
a.
b.
c.
d.
e.
Particle 1 has a positive charge and
particle 2 has a negative charge.
Both particles are positively charged.
Both particles are negatively charged.
Particle one has a negative charge and
particle 2 has a positive charge.
The direction of the paths depends on
the magnitude of the velocity, not on
the sign of the charge.
Magnetic Fields
61.
The diagram below shows the position of a
long straight wire perpendicular to the page
and a set of directions labeled A through H.
69.
5
The magnetic field in a region of space is
parallel to the surface of a long flat table.
Imagine that this page is lying flat on the
table. When current is present in the coil,
which is lying on the table, the coil tends to
rotate so that the left side moves up and the
right side moves down. The magnetic field
is
When the current in the wire is directed up
out of the page, the direction of the
magnetic field at point P is
a.
b.
c.
d.
e.
65.
A.
B.
C.
D.
E.
The point P lies along the perpendicular
bisector of the line connecting two long
straight wires S and T that are
perpendicular to the page. A set of
directions A through H is shown next to the
diagram. When the two equal currents in
the wires are directed up out of the page,
the direction of the magnetic field at P is
closest to the direction of
a.
b.
c.
d.
e.
E.
F.
G.
H.
A
a.
b.
c.
d.
e.
71.
directed parallel to the page and
downwards.
directed parallel to the page and
upwards.
directed parallel to the page and to the
right.
directed parallel to the page and to the
left.
in a direction that cannot be
determined in this experiment
A magnetic field of 2.0 T is applied to a
bubble chamber to make the tracks of
protons and other charged particles
identifiable by the radius of the circles they
move in. If a high-energy proton moves
along an arc of a 3.3-m circle, what is the
momentum of the proton? [q = 1.6  10–19 C,
m = 1.67  10–27 kg]
Sources of the Magnetic Field
3.
d
4.
a
9.
a
10.
b
11.
c
13.
a
14.
d
17.
d
18.
d
21.
c
23.
c
25.
d
29.
c
30.
c
31.
c
33.
c
35.
c
37.
d
46.
a
47.
c
48.
c
49.
b
54.
d
56.
d
57.
c
59.
a
61.
c
65.
e
69.
c
71.
1.056 C 10–18 kg · m/s
6
Sources of the Magnetic Field
1.
One long wire carries a current of 30 A
along the entire x axis. A second long wire
carries a current of 40 A perpendicular to
the xy plane and passes through the point
(0, 4, 0) m. What is the magnitude of the
resulting magnetic field at the point y = 2.0
m on the y axis?
a.
b.
c.
d.
e.
2.
a.
b.
c.
d.
e.
7.
17.
5.3 A
3.8 A
4.5 A
3.0 A
0.5 A
79 µT
69 µT
59 µT
89 µT
9.4 µT
What is the magnitude of the magnetic field
at point P if a = R and b = 2R?
51 µT
33 µT
72 µT
64 µT
46 µT
Two long parallel wires carry unequal
currents in the same direction. The ratio of
the currents is 3 to 1. The magnitude of the
magnetic field at a point in the plane of the
wires and 10 cm from each wire is 4.0 µT.
What is the larger of the two currents?
a.
b.
c.
d.
e.
25.
0.5 A
1.0 A
1.5 A
2.0 A
3.0 A
A segment of wire of total length 2.0 m is
formed into a circular loop having 5.0 turns.
If the wire carries a 1.2-A current, determine
the magnitude of the magnetic field at the
center of the loop.
a.
b.
c.
d.
e.
72 µT
48 µT
24 µT
96 µT
32 µT
Two long straight parallel wires separated
by a distance of 20 cm carry currents of 30 A
and 40 A in opposite directions. What is the
magnitude of the resulting magnetic field at
a point that is 15 cm from the wire carrying
the 30-A current and 25 cm from the other
wire?
Two long parallel wires carry unequal
currents in opposite directions. The ratio of
the currents is 3 to 1. The magnitude of the
magnetic field at a point in the plane of the
wires and 10 cm from each wire is 4.0 µT.
What is the larger of the two currents?
a.
b.
c.
d.
e.
Two long parallel wires each carry a current
of 5.0 A directed to the east. The two wires
are separated by 8.0 cm. What is the
magnitude of the magnetic field at a point
that is 5.0 cm from each of the wires?
a.
b.
c.
d.
e.
6.
4.0 µT
5.0 µT
3.0 µT
7.0 µT
1.0 µT
15.
7
a.
b.
c.
d.
e.
3µ0I
4R
µ0I
4R
2µ0I
3R
µ0I
3R
3µ0 I
4R
8
CHAPTER 30
32.
27.
What is the magnitude of the magnetic field
at point P in the figure if a = 2.0 cm, b = 4.5
cm, and I = 5.0 A?
Two long parallel wires are separated by 4.0
cm. One of the wires carries a current of 20
A and the other carries a 30-A current.
Determine the magnitude of the magnetic
force on a 2.0-m length of the wire carrying
the greater current.
a.
b.
c.
d.
e.
33.
a.
b.
c.
d.
e.
28.
The figure shows a cross section of three
parallel wires each carrying a current of 5.0
A out of the paper. If the distance R = 6.0
mm, what is the magnitude of the magnetic
force on a 2.0-m length of any one of the
wires?
Three long, straight, parallel wires each
carry a current of 10 A in the positive x
direction. If the distance between each wire
and the other two is 10 cm, what is the
magnitude of the magnetic force on a 20-cm
length of either of the wires?
a.
b.
c.
d.
e.
29.
87 µT, into the paper
87 µT, out of the paper
0.23 mT, out of the paper
0.23 mT, into the paper
23 µT, into the paper
7.0 mN
6.0 mN
8.0 mN
9.0 mN
4.0 mN
57 µN
40 µN
69 µN
50 µN
20 µN
Two long parallel wires are separated by 6.0
mm. The current in one of the wires is twice
the other current. If the magnitude of the
force on a 3.0-m length of one of the wires is
equal to 8.0 µN, what is the greater of the
two currents?
a.
b.
c.
d.
e.
0.20 A
0.40 A
40 mA
20 mA
0.63 A
a.
b.
c.
d.
e.
2.5 mN
3.3 mN
2.2 mN
2.9 mN
1.7 mN
Sources of the Magnetic Field
35.
The figure shows a cross section of three
parallel wires each carrying a current of 15
A. The currents in wires A and C are out of
the paper, while that in wire B is into the
paper. If the distance R = 5.0 mm, what is
the magnitude of the force on a 4.0-m length
of wire C?
a.
b.
c.
d.
e.
90 mN
54 mN
30 mN
18 mN
36 mN
61.
53.
0.60 mT
0.85 mT
52 µT
0.40 mT
0.75 mT
A long solenoid (1000 turns/m) carries a
current of 25 mA and has an inside radius
of 2.0 cm. A long wire which is parallel to
and 4.0 cm from the axis of the solenoid
carries a current of 6.0 A. What is the
magnitude of the magnetic field at a point
on the axis of the solenoid?
a.
b.
c.
d.
e.
51 µT
61 µT
43 µT
81 µT
1.4 µT
b.
c.
d.
e.
63.
0.25
0.50
1
2
4
By using a compass to measure the
magnetic field direction at various points
adjacent to a long straight wire, you can
show that the wire’s magnetic field lines are
a.
51.
A long solenoid (n = 1200 turns/m, radius =
2.0 cm) has a current of a 0.30 A in its winding. A
long wire carrying a current of 20 A is parallel to
and 1.0 cm from the axis of the solenoid. What is
the magnitude of the resulting magnetic field at a
point on the axis of the solenoid?
a.
b.
c.
d.
e.
When the number of turns in a solenoid and
its length are both doubled, the ratio of the
magnitude of the new magnetic field inside
to the magnitude of the original magnetic
field inside is:
a.
b.
c.
d.
e.
62.
9
straight lines in space that go from one
magnetic charge to another.
straight lines in space that are parallel
to the wire.
straight lines in space that are
perpendicular to the wire.
circles that have their centers on the
wire and lie in planes perpendicular to
the wire.
circles that have the wire lying along a
diameter of the circle.
The reason the north pole of a bar magnet
free to rotate points north is because
a.
b.
c.
d.
e.
the south geographic pole of the earth
is the earth’s magnetic north pole.
the south geographic pole of the earth
is the earth’s magnetic south pole.
there is a net accumulation of negative
magnetic charge at the earth’s south
geographic pole.
there is a net accumulation of positive
magnetic charge at the earth’s north
geographic pole.
the north geographic pole of the earth
is the earth’s magnetic north pole.
10
65.
CHAPTER 30
At a point in space where the magnetic field
is measured, the magnetic field produced
by a current element
a.
b.
c.
d.
e.
67.
points radially away in the direction
from the current element to the point
in space.
points radially in the direction from the
point in space towards the current
element.
points in a direction parallel to the
current element.
points in a direction parallel to but
opposite in direction to the current
element.
points in a direction that is
perpendicular to the current element
and perpendicular to the radial
direction.
70.
a.
b.
c.
d.
e.
72.
A solenoid consists of 100 circular turns of
copper wire. Parts of three turns, A, B and
C, are shown below.
d.
e.
.
both A and C are repelled by B.
A is attracted to B; C is repelled by B.
neither A nor C is attracted to or
repelled by B.
A is repelled by B; C is attracted to B.
both A and C are attracted to B.
75.
1/4.
1/2.
1.
2
4.
Two solenoids of equal length are each
made of 2000 turns of copper wire per
meter. Solenoid I has a 5.00 cm radius;
solenoid II a 10.0 cm radius. When equal
currents are present in the two solenoids,
the ratio of the magnitude of the magnetic
field BI along the axis of solenoid I to the
magnitude of the magnetic field BII along
the axis of solenoid II, BI/BII, is
a.
b.
c.
d.
e.
When a current flows through the coil,
a.
b.
c.
Two solenoids are each made of 2000 turns
of copper wire per meter. Solenoid I is 2 m
long, while solenoid II is 1 m long. When
equal currents are present in the two
solenoids, the ratio of the magnetic field BI
along the axis of solenoid I to the magnetic
field BII along the axis of solenoid II, BI/BII,
is
1/4.
1/2.
1.
2.
4.
The magnetic field strength B within a
solenoid with n turns per unit length
(length = ) and current I has magnitude B
equal to
a.
b.
c.
d.
e.
nI.
0nI.
(1 0 )nI.
nI
.

 0nI
.

Sources of the Magnetic Field
77.
Equal currents of magnitude I travel out of
the page in wires M and N. Eight directions
are indicated by letters A through H.
The direction of the magnetic field at point
P is
a.
b.
c.
d.
e.
79.
E.
F.
G.
H.
A.
Equal currents of magnitude I travel into
the page in wire M and out of the page in
wire N. Eight directions are indicated by
letters A through H.
The direction of the magnetic field at point
P is
a.
b.
c.
d.
e.
C.
E.
F.
G.
H.
Open-Ended Problems
81.
A long solenoid (n = 80 turns/cm) carries a
current of 70 mA. If the interior of the
solenoid is filled with a ferromagnetic
material having a permeability km of 650,
determine the magnitude of the magnetic
field before and after the ferromagnetic
material is inserted.
11
82.
Two wires, each having a weight per unit
length of 10–4 N/m, are strung parallel, one
0.1 m above the other. If the wires carry the
same current, though in opposite directions,
how great must the current in each wire be
for the magnetic field of the lower
conductor to balance the weight of the
upper conductor?
83.
What current in a solenoid 15-cm long
wound with 100 turns would produce a
magnetic field equal to that of the Earth, 5 
10–5 T?
84.
A superconducting wire carries a current of
1.0  104 A. Find the magnetic field at a
distance of 1.0 m from the wire.
85.
The planetary model of the hydrogen atom
consists of an electron in a circular orbit
about a proton. The motion of the electron
of charge 1.6  10–19 C creates an electric
current. The radius of the electron orbit is
5.3  10–11 m and the electron’s velocity is
2.2  106 m/s. What is the magnetic field
strength at the location of the proton?
12
CHAPTER 30
1.
b
32.
b
70.
c
2.
c
33.
d
72.
c
6.
b
35.
d
75.
a
7.
d
51.
a
77.
e
15.
c
53.
c
79.
d
17.
c
61.
c
81.
7 gauss, 0.46 T
25.
a
62.
d
82.
7.1 A
27.
a
63.
a
83.
59.7 mA
28.
c
65.
e
84.
2  10–3 T
29.
b
67.
e
85.
12.5 T