Chapter 19
Magnetism
Problem Solutions
19.1
The direction in parts (a) through (d) is found by use of the right hand rule. You must
remember that the electron is negatively charged and thus experiences a force in the
direction exactly opposite that predicted by the right hand rule for a positively charged
particle.
(a)
horizontal and due east
(b)
horizontal and 30
N of E
°
(c)
horizontal and due east
(d)
zero force
,
(
)
sin
sin 180
0
F
qvB
qvB
θ
=
=
° =
19.3
Since the particle is positively charged, use the right hand rule. In this case, start with
the fingers of the right hand in the direction of
v
and the thumb pointing in the
direction of
F
. As you start closing the hand, the fingers point in the direction of
B
after
they have moved 90°. The results are
(a)
into the page
(b)
toward the right
(c)
toward bottom of page
19.8
The speed attained by the electron is found from
(
)
2
1
2
mv
q
V
=
Δ
, or
(
)
(
)
(
)
19
7
31
2
1.60
10
C
2 400 V
2
2.90
10 m s
9.11
10
kg
e
V
v
m


×
Δ
=
=
=
×
×
(a)
Maximum force occurs when the electron enters the region perpendicular to the
field.
(
)
(
)
(
)
max
19
7
12
sin 90
1.60
10
C
2.90
10
m
s
1.70 T
7.90
10
N
F
q vB


=
°
=
×
×
=
×
141
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142
CHAPTER 19
(b)
Minimum force occurs when the electron enters the region parallel to the field.
min
sin0
0
F
q vB
=
° =
19.9
(
)
(
)
(
)
(
)
27
13
2
19
7
1.67
10
kg
2.0
10
m s
0.021 T
1.60
10
C
1.0
10 m s
m a
F
B
qv
qv


×
×
=
=
=
=
×
×
The right hand rule shows that
B
must be in
the
direction
y

to yield a force in the
+
x
direction when
v
is in the +
z
direction.
19.11
From
sin
F
BIL
θ
=
, the magnetic field is
(
)
3
0.12 N m
8.0
10
T
sin
15 A
sin 90
F L
B
I
θ

=
=
=
×
°
The direction of
B
must be
the
direction
z
+
to have
F
in the –
y
direction when
I
is
in the +
x
direction.
19.15
(
) (
) (
)
(
)
sin
0.300 T
10.0 A
5.00 m
sin
30.0
7.50 N
F
BIL
θ
=
=
° =
19.19
For the wire to move upward at constant speed, the net force acting on it must be zero.
Thus,
sin
BIL
mg
θ
=
and for minimum field
90
θ
=
°
. The minimum field is
(
)
(
)
(
) (
)
2
0.015 kg
9.80 m s
0.20 T
5.0 A
0.15 m
mg
B
I L
=
=
=
For the magnetic force to be directed upward when the current is toward the left,
B
must be directed
out of the page
.
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 Charge, Magnetism, Force, Magnetic Field, Electric charge, Bnet, right hand rule

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