johnson (rj6247) – hw 9 – Opyrchal – (121014)
1
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printout
should
have
18
questions.
Multiplechoice questions may continue on
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before answering.
001
10.0 points
An electron in a vacuum is first accelerated by
a voltage of 54300 V and then enters a region
in which there is a uniform magnetic field of
0
.
556 T at right angles to the direction of the
electron’s motion.
What is the force on the electron due to the
magnetic field?
Correct answer: 1
.
23115
×
10
−
11
N.
Explanation:
Let :
V
= 1
.
38206
×
10
8
m
/
s
and
B
= 0
.
556 T
.
The kinetic energy gained after acceleration
is
KE
=
1
2
m
e
v
2
=
q
e
V
, so the velocity is
v
=
radicalbigg
2
q
e
V
m
=
radicalBigg
2(1
.
60218
×
10
−
19
C)(54300 V)
9
.
10939
×
10
−
31
kg
= 1
.
38206
×
10
8
m
/
s
.
Then the force on it is
f
=
qvB
= (1
.
60218
×
10
−
19
C)
×
(1
.
38206
×
10
8
m
/
s)(0
.
556 T)
=
1
.
23115
×
10
−
11
N
.
002
10.0 points
A negatively charged particle moving paral
lel to the
x
axis enters a magnetic field (point
ing into of the page), as shown in the figure
below.
×
×
×
×
×
×
×
×
×
×
×
×
×
×
×
×
×
×
×
×
×
×
×
x
y
v
z
vector
B
vector
B
−
q
Figure:
ˆ
ı
is in the
x
direction, ˆ
is
in the
y
direction, and
ˆ
k
is in the
z
direction.
What is the initial direction of deflection?
1.
hatwide
F
= +ˆ
ı
2.
hatwide
F
= +
ˆ
k
3.
hatwide
F
=
−
ˆ
k
4.
vector
F
= 0 ; no deflection
5.
hatwide
F
= +ˆ
6.
hatwide
F
=
−
ˆ
ı
7.
hatwide
F
=
−
ˆ
correct
Explanation:
Basic Concepts:
Magnetic Force on a
Charged Particle:
vector
F
=
qvectorv
×
vector
B
Righthand rule for crossproducts.
hatwide
F
≡
vector
F
bardbl
vector
F
bardbl
;
i.e.
, a unit vector in the
F
direc
tion.
Solution:
The force is
vector
F
=
qvectorv
×
vector
B
.
vector
B
=
B
parenleftBig
−
ˆ
k
parenrightBig
,
vectorv
=
v
(+ˆ
ı
)
,
and
q <
0
,
therefore
,
vector
F
=
−
q

vectorv
×
vector
B
=
−
q

v B
bracketleftBig
(+ˆ
ı
)
×
parenleftBig
−
ˆ
k
parenrightBigbracketrightBig
=
−
q

v B
(
−
ˆ
)
hatwide
F
=
−
ˆ
.
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johnson (rj6247) – hw 9 – Opyrchal – (121014)
2
This is the third of eight versions of the
problem.
003
10.0 points
A positively charged particle moving paral
lel to the
z
axis enters a magnetic field (point
ing toward the righthand side of the page),
as shown in the figure below.
z
x
v
y
vector
B
vector
B
+
q
Figure:
ˆ
ı
is in the
x
direction, ˆ
is
in the
y
direction, and
ˆ
k
is in the
z
direction.
What is the initial direction of deflection?
1.
hatwide
F
= +ˆ
ı
2.
vector
F
= 0 ; no deflection
correct
3.
hatwide
F
= +ˆ
4.
hatwide
F
=
−
ˆ
5.
hatwide
F
=
−
ˆ
k
6.
hatwide
F
= +
ˆ
k
7.
hatwide
F
=
−
ˆ
ı
Explanation:
Basic Concepts:
Magnetic Force on a
Charged Particle:
vector
F
=
qvectorv
×
vector
B
Righthand rule for crossproducts.
hatwide
F
≡
vector
F
bardbl
vector
F
bardbl
;
i.e.
, a unit vector in the
F
direc
tion.
Solution:
The force is
vector
F
=
qvectorv
×
vector
B
.
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 Spring '08
 Opyrchal
 Electron, Force, Work, Magnetic Field, Righthand rule

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