499
Chapter 26
The Magnetic Field
Conceptual Problems
1
•
[SSM]
When the axis of a cathoderay tube is horizontal in a region
in which there is a magnetic field that is directed vertically upward, the electrons
emitted from the cathode follow one of the dashed paths to the face of the tube in
Figure 2630. The correct path is (
a
) 1, (
b
) 2, (
c
) 3, (
d
) 4, (
e
) 5.
Determine the Concept
Because the electrons are initially moving at 90
°
to the
magnetic field, they will be deflected in the direction of the magnetic force acting
on them. Use the righthand rule based on the expression for the magnetic force
acting on a moving charge
B
v
F
r
r
r
×
=
q
, remembering that, for a negative charge,
the force is in the direction opposite that indicated by the righthand rule, to
convince yourself that the particle will follow the path whose terminal point on
the screen is 2.
)
(
b
is correct.
2
••
We define the direction of the electric field to be the same as the
direction of the force on a positive test charge.
Why then do we
not
define the
direction of the magnetic field to be the same as the direction of the magnetic
force on a moving positive test charge?
Determine the Concept
The direction of the force depends on the direction of the
velocity.
We do not define the direction of the magnetic field to be in the
direction of the force because if we did, the magnetic field would be in a different
direction each time the velocity was in a different direction.
If this were the case,
the magnetic field would not be a useful construct.
3
•
[SSM]
A
flicker bulb
is a light bulb that has a long, thin flexible
filament. It is meant to be plugged into an ac outlet that delivers current at a
frequency of 60 Hz.
There is a small permanent magnet inside the bulb.
When
the bulb is plugged in the filament oscillates back and forth.
At what frequency
does it oscillate?
Explain.
Determine the Concept
Because the alternating current running through the
filament is changing direction every 1/60 s, the filament experiences a force that
changes direction at the frequency of the current.
4
•
In a cyclotron, the potential difference between the dees oscillates with
a period given by
T
=
2
π
mq
B
()
. Show that the expression to the right of the
equal sign has units of seconds if
q
,
B
and
m
have units of coulombs, teslas and
kilograms, respectively.
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View Full DocumentChapter 26
500
Determine the Concept
Substituting the SI units for
q
,
B
, and
m
yields:
s
1
m
kg
s
m
kg
kg
m
s
s
m
kg
kg
m
C
s
N
C
kg
m
A
N
C
kg
T
C
2
=
⋅
⋅
=
⋅
⋅
=
⎟
⎠
⎞
⎜
⎝
⎛
⋅
⋅
=
⎟
⎠
⎞
⎜
⎝
⎛
⋅
=
⋅
5
•
A
7
Li nucleus has a charge equal to +3
e
and a mass that is equal to the
mass of seven protons. A
7
Li nucleus and a proton are both moving perpendicular
to a uniform magnetic field
B
r
. The magnitude of the momentum of the proton is
equal to the magnitude of the momentum of the nucleus. The path of the proton
has a radius of curvature equal to
R
p
and the path of the
7
Li nucleus has a radius of
curvature equal to
R
Li
. The ratio
R
p
/
R
Li
is closest to (
a
) 3/1, (
b
) 1/3, (
c
) 1/7,
(
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 Spring '12
 Goussiou
 Physics

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