thwing (jrt2329) – Homework 08 – Yao – (59110)
1
This
printout
should
have
25
questions.
Multiplechoice questions may continue on
the next column or page – find all choices
before answering.
001
10.0 points
A charged particle is projected with its initial
velocity parallel to a uniform magnetic field.
What is the resulting path?
1.
circular arc.
2.
straight line parallel to the field.
correct
3.
straight line perpendicular to the field.
4.
spiral.
5.
parabolic arc.
Explanation:
The force on a moving charge due to a
magnetic field is given by
vector
F
=
qvectorv
×
vector
B .
If
vectorv
and
vector
B
are parallel, then
vectorv
×
vector
B
= 0
.
Hence the force on the particle is zero, and
the particle continues to move in a straight
line parallel to the field.
002
10.0 points
A static uniform magnetic field is directed
into the page.
A charged particle moves in
the plane of the page following a counter
clockwise spiral of increasing radius as shown.
B
B
Neglect the effect due to gravity.
What is a reasonable explanation?
1.
The
charge
is
negative
and
slowing
down.
2.
The charge is positive and slowing down.
3.
The charge is positive and with a constant
speed.
4.
The charge is neutral and slowing down.
5.
The charge is positive and speeding up.
correct
6.
None of these
7.
The charge is negative and speeding up.
8.
The charge is neutral and speeding up.
9.
The charge is negative and with a con
stant speed.
10.
The charge is neutral and with a constant
speed.
Explanation:
We know that when a charged particle
moves in a uniform magnetic field with a
constant speed, it undergoes a circular mo
tion with the centripetal force provided by
the magnetic force, namely
m
v
2
r
=
q v B ,
so we know that the radius is in fact propor
tional to the speed,
r
=
m
q B
v .
Since the particle follows a spiral of increasing
radius, we can judge that it is speeding up.
The magnetic force
vector
F
=
qvectorv
×
vector
B
must be
in the direction for the centripetal force
−
ˆ
r
(pointed inward) of this particle in counter
clockwise circular motion.
Since
vectorv
×
vector
B
is in
the negative ˆ
r
direction, the particle has a
positive charge.
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thwing (jrt2329) – Homework 08 – Yao – (59110)
2
003
10.0 points
Hint:
Use nonrelativistic mechanics to work
this problem.
A cyclotron is designed to accelerate pro
tons to energies of 3
.
6 MeV using a magnetic
field of 0
.
5 T.
The charge on the proton is 1
.
60218
×
10
−
19
C and its mass is 1
.
67262
×
10
−
27
kg.
What is the required radius of the cy
clotron?
Correct answer: 0
.
548297 m.
Explanation:
Let :
B
= 0
.
5 T
,
q
= 1
.
60218
×
10
−
19
C
,
E
= 3
.
6 MeV
= (3
.
6
×
10
6
eV)
×
(1
.
602
×
10
−
19
J
/
eV)
,
= 5
.
7672
×
10
−
13
J
,
and
m
= 1
.
67262
×
10
−
27
kg
.
The speed of the proton is
v
=
radicalbigg
2
E
m
=
radicalBigg
2 (5
.
7672
×
10
−
13
J)
(1
.
67262
×
10
−
27
kg)
= 2
.
62602
×
10
7
m
/
s
,
where
E
is the kinetic energy of the proton.
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 Spring '09
 YAO
 Physics, Electron, Charge, Work, Magnetic Field, Correct Answer, Electric charge

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