20-1
M
AGNETIC
F
IELD AND
M
AGNETIC
F
ORCES
20
Answers to Multiple-Choice Problems
1.
E
2.
C
3.
C
4.
B
5.
D
6.
A
7.
C
8.
C
9.
B
10.
A
11.
C
12.
B
13.
A
14.
B
15.
A
Solutions to Problems
20.1.
Set Up:
The force
on the particle is in the direction of the deflection of the particle. The directions of
and
are shown in Figure 20.1. Apply the right-hand rule to the directions of
and
See if your thumb is in the
direction of
or opposite to that direction. Use
with
to calculate
F
.
Figure 20.1
Solve: (a)
When you apply the right-hand rule to
and
your thumb points east.
is in this direction, so the charge
is positive.
(b)
20.2.
Set Up:
The force
on the ion is downward, in the direction of the deflection. The directions of
and
are
shown in Figure 20.2a. Use the right-hand rule to relate the directions of
and
The charge is positive. Use
with
to calculate
B.
Figure 20.2
(
a
)
(
b
)
v
S
v
S
F
S
F
S
B
S
e
5
1.60
3
10
2
19
C.
f 5
90°
F
5
0
q
0
v
B
sin
f
F
S
.
B
S
,
v
S
,
F
S
v
S
F
S
F
5
0
q
0
v
B
sin
f 5
1
8.50
3
10
2
6
C
21
4.75
3
10
3
m
/
s
21
1.25 T
2
sin
90°
5
0.0505 N
F
S
B
S
,
v
S
E
N
S
W
v
S
F
S
B
S
f 5
90°
F
5
0
q
0
v
B
sin
f
F
S
,
B
S
.
v
S
F
S
B
S
v
S
,
F
S

Solve:
is perpendicular to both
and
so
is either toward the top of the page or toward the bottom of the page.
If
is toward the top of the page, as shown in Figure 20.2b, then when you apply the right-hand rule your thumb
points into the page. This is the specified direction of
so
is directed as shown in Figure 20.2b.
gives
20.3.
Set Up:
The directions of
and
are shown in Figure 20.3. A proton has charge
In part (a),
An electron has charge
Figure 20.3
Solve: (a)
The right-hand rule says
is into the page in Figure 20.3.
(b)
F
is maximum when
when
is perpendicular to
F
is minimum
when
or
when
is either parallel or antiparallel to
(c)
is the same for an electron and a proton, so
the same as for a proton. Since the proton
and electron have charges of opposite sign, the forces on them are in opposite directions. The force on the electron is
directed out of the page in Figure 20.3.
Reflect:
Only the component of
perpendicular to
contributes to the magnetic force. Therefore, this force is zero
when the charged particle moves along the direction of
and the force is maximum when the particle moves in a
direction perpendicular to
When the sign of the charge changes, the force reverses direction. And, even though the
force magnitude is the same for the electron and proton, the effect of the force (the acceleration) for the electron
would be much greater, because of its smaller mass.
20.4.
Set Up:
The gravity force is downward so the force from the magnetic field must be upward. The charge’s
velocity and the forces are shown in Figure 20.4. Since the charge is negative, the magnetic force is opposite to the
right-hand rule direction. The minimum magnetic field is when the field is perpendicular to
The force is also
perpendicular to
so
is either eastward or westward.