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PHYS 196 Home Work 9
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1. The following diagrams apply to a positive point charge. Draw the missing member in the list  , B, F ,
which are mutually perpendicular to each other.
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2. The following diagrams apply to a negative point charge. Draw the missing member in the list  , B, F ,
which are mutually perpendicular to each other.
3. An electron with kinetic energy 30.0 keV travels in the direction 50°N of W in a location where the
magnetic field is due north and has strength 0.25G. Find the magnitude and direction of the force on the
electron.
4.
A point charge has a charge equal to  3.64nC and a velocity equal to 2.75  10 3 m / s iˆ . Find the force
on the charge if the magnetic field is (a) 0.38T ˆj , (b) 0.75T iˆ  0.75T ˆj , (c) 0.65T iˆ , and (d)
0.75T iˆ  0.75T kˆ
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5. The force on an electron is F  (3.8iˆ  2.7 ˆj )  10 13 N due to a magnetic field B  (0.85T )kˆ . Find its
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velocity vector  assuming it has no z-component.
6. Calculate the magnitude of the magnetic force on a 240m length wire running North-South, stretched
between two towers and carrying a 150-A current. The strength of the Earth’s magnetic field is 5.0×10-5
T . The magnetic declination is 0°and the inclination is 68°.
7. A long wire stretches along the x axis and carries a 3.0-A current to the right (+x). The wire is in a
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uniform magnetic field B  (0.20 iˆ  0.36 ˆj  0.25 kˆ) T . Determine the components of the force on the
wire per cm of length.
8. The diagram shows a horizontal 1.5m long copper rod weighing 40.0N suspended at its two ends by two
wires attached to the ceiling. It is in a region where the magnetic field is 2.4T pointing into the paper. A
current runs in the rod. What must be the direction and magnitude of the current so that tension in each
wire is 25N?
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9. Suppose a straight 1.00mm diameter copper wire could just float horizontally in air because of the force
due to Earth’s magnetic field, which is horizontal, perpendicular to the wire, and of magnitude 0.5 G.
What current would the wire carry? (density of copper = 9.0 g/cc.)
10. The section of wire shown carries a current equal to 1.8A from a to b. The segment is in a region where
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the magnetic field is B  1.2T kˆ . Find the total force on the wire and show that the total force is the
same as if the wire were in the in form of a straight wire directly from a to b and carrying the same
current.
b
y
4.0cm
a
3.0cm
I
x
z
11. The diagram shows a triangular wire loop with vertices a, b, and c, whose coordinates in meters are
(2,0,0), (0,3,0) and (0,0,4) respectively. A current of 5.0A runs in the loop in the direction shown. The
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loop is in a region where the magnetic field is B  2.0T kˆ . Find the forces on the three sides of the
triangle in component form. Show that the sum of these forces is zero.
c
z
B
a
y
b
x
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12. A current carrying wire is bent into a closed semicircular loop of radius R that lies on the x-y plane. The
wire is in a uniform magnetic field that is in the +z direction. Find the force on the circular segment and
the straight segment separately. Hence show that the total force on the loop is zero.
y




B




x
13. A wire loop is in the form of a quadrant of a circle of radius R as shown. It is in a region where the
magnetic field B is uniform and parallel to one of its straight edge. A counter clockwise current I runs in
the loop. Find the forces on the two straight segments and the circular portion of the loop. Hence show
that the total force is zero.
B
14. A proton moves in a 65-cm-radius circular orbit that is perpendicular to a uniform magnetic field of
magnitude 0.75T. (a) What is the orbital period of the motion? (b) What is the speed of the proton? (c)
What is the kinetic energy of the proton?
15. What are the radius and frequency of the gyromotion of an alpha particle of kinetic energy 5.0MeV in a
3.0T magnetic field?
16. In the figure, the magnetic field has a magnitude of 60mT, the distance d is 40cm, and θ is 24°. Find the
speed at which a particle enters the region and the exit angle φ if the particle is (a) a proton, (b) a
deuteron. Assume that md=2mp.
φ
d
B
θ
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17. (Hard) A particle with charge q and momentum p , initially moving along the x-axis, enters a region
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where a uniform magnetic field B  B0 kˆ extends over a width x   as shown. The particle is deflected
a distance d in the  y direction as it traverses the field. Determine (a) whether q is positive or negative,
(b) the magnitude of the momentum p .


B0
q
p

d

18. In a mass spectrometer, a singly ionized Mg24 ion has a mass equal to 3.983×10-26 kg and is accelerated
through a 2.50-kV potential difference. It then enters a region where it is deflected by a magnetic field of
0.557 T. (a) Find the radius of curvature of the ion’s orbit. (b) What is the difference in the orbital radii
of the Mg26 and Mg24 ions? Assume that their mass ratio is 26:24.
19. A mass spectrometer is being used to monitor air pollutants. It is difficult, however, to separate
molecules with nearly equal mass, such as CO (28.0106u) and N2 (28.0134u). How large a radius of
curvature must a spectrometer have if these two molecules are to be separated at the film or detectors by
0.65mm?
20. A cyclotron for accelerating protons has a magnetic field strength of 1.4 T and a radius of 0.70m. (a)
What is the cyclotron frequency? (b) Find the kinetic energy of the protons when they emerge. (c) How
will your answers change if deuterons are used instead of protons?
21. A certain cyclotron that has a magnetic field strength of 1.8 T is designed to accelerate protons to a
kinetic energy of 25 MeV. (a) What is the cyclotron frequency for this cyclotron? (b) What must the
minimum radius of the magnet be to achieve this energy? (c) If the alternating potential difference
applied to the dees has a maximum value of 50 kV, how many revolutions must the proton make before
emerging with kinetic energy of 25 MeV?
22. A velocity selector has a magnetic field of magnitude 0.28 T perpendicular to an electric field of
magnitude 0.46 MV/m. (a) What must the speed of a particle be for it to pass through the velocity
selector undeflected? What kinetic energy must (b) protons and (c) electrons have in order to pass
through the velocity selector undeflected?
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Answers:
1.
2.
3. 2.65  10 16 N
4. - 3.80(m N)k̂, - 7.50(m N)k̂, 0, 7.50(m N) ĵ
5.  1.99  10 6 (m / s )iˆ  2.79  10 6 (m / s ) ˆj
6. 1.67N
7. -7.5 ( mN ) ĵ -10.8 ( mN ) k̂
8. 2.78 A to the left
9. 1.39kA
10. 0.0864  N iˆ  0.0648  N  ˆj
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11. Fab  30( N )iˆ  20( N ) ˆj, Fac  20( N ) ˆj, Fbc  30( N )iˆ
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12. Farc  2IRBˆj, Fdiameter  2IRBˆj
13. IRB, 0, IRB
14. 87 .4ns, 4.67  10 7 m / s, 11 .4MeV
15. 0.108 m, 1.55  10 7 m / s
16. 1.25´106 m / s, 0.63´106 m / s
 d 2  2 

17. p  qB
 2d 
18. 0.0633m, 2.6mm
19. 6.5m
20. 21.3MHz, 46.0MeV , 23.0MeV
21. 27.4MHz, 0.40m, 250
22. 1.64  10 6 m / s, 14 .0keV , 7.6eV
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