PHYS 196 Home Work 10
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1. The diagram shows a ring of radius 2.0m and mass 5.0kg being subjected to a torque  of 30.0 N-m
pointing into the paper. Find the direction and magnitude of the resulting angular acceleration.
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
2. The diagram shows a rod spinning faster and faster in such a direction that the end marked A is
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travelling into the paper and the other end marked B is out of the paper. Draw in the vector torque  .
.
A
B
3. The ring of Problem 1 carries a 3.0 A current in the clockwise direction, and it is in a magnetic field of
0.5T pointing upward as shown. Find (a) the magnitude and direction of the magnetic moment vector
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
 , (b)the magnitude and direction of the torque vector  , (c) the angular acceleration of the ring and (d)
the direction of acceleration of the point A at the top of the ring.
B
A
4. A 20-turn circular coil of radius 4.0cm carrying a 3.0A current is placed in a 0.5T magnetic field in a
direction making 30° with the plane of the coil. Find the magnitude of the torque.
5. The diagram shows a triangular wire frame with vertices a,b,c whose rectangular coordinates in meters
are (0,0,0), (3,0,0), (0,2,0) respectively. The frame carries a 12A current in the direction a,b to c, and is
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situated in a magnetic field B  0.5iˆ  0.7 ˆj  0.2kˆ T  . Find the magnetic moment vector  and the
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torque vector 
z
a
x
c
y
b
1
6. A rectangular current-carrying 50-turn coil as shown is pivoted about the z-axis. (a) If the wires in the
z=0 plane make an angle   37  with y-axis, what angle does the magnetic moment of the coil make
with the unit vector iˆ ? (b) Write an expression for n̂ in terms of the unit vectors iˆ and ĵ , where n̂ is a
unit vector in the direction of the magnetic moment. (c) What is the magnetic moment of the coil? (d)
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Find the torque on the coil when there is a uniform magnetic field B  1.5(T ) ˆj in the region occupied by
the coil, (e) Find the potential energy of the coil in this field
(The potential energy is zero when   0 .
7. Referring to Problem 3, if the ring is turned through a 90°
angle to assume the position as shown, how much work must
be done?
B
.I
I
I
8. Find the magnetic moments of the following objects rotating with angular velocity 
(a) a ring of radius a with uniform linear charge density 
(b) a circular disk of radius a with uniform surface charge density 
(c) a sphere of radius a with uniform volume charge density 
9. Show the following relation between the magnetic moment  and angular momentum L of an electron
in uniform circular motion around the nucleus of an atom:
e

L
2me
10. A small line segment 2.0mm long carries a 5.0A current in the x-direction. Find the magnitude of the
magnetic field and the angle between the magnetic field and the z-axis at the points (3,0,0) and (1,2,3)
where the coordinates are in meters.
11. A single conducting loop has a radius equal to 3.0cm and carries a current equal to 2.6A. What is the
magnitude of the magnetic field on the line through the center of the loop and perpendicular to the plane
of the loop (a) at the center of the loop, and (b) 2.0cm from the center.
12. A 50-turn coil of radius 10.0cm carries a current of 4.00A and a concentric 20-turn coil of radius 0.500
cm carries a current of 1.00A. The planes of the two coils are perpendicular to each other. Find the
magnitude of the torque exerted by the large coil on the small coil. (Neglecting any variation of the
magnetic field due to the large coil in the region of the small coil.)
13. A 450- turn solenoid of length 30cm carries a current of 2.0A. The radius of the solenoid is 1.2 cm. Find
the magnetic field on its axis (a) at the center using the exact formula and the approximate formula that
treats the solenoid as infinitely long, (b) at one end of the solenoid
14. A 20.0-meter long cooper wire, 2.00mm in diameter including insulation, is tightly wrapped in a single
layer with adjacent coils touching, to form a solenoid of diameter 2.5 cm (outer edge), What is (a) the
length of the solenoid, (b) the field at the center when the current is 16.7 A?
15. A infinitely long wire lies along the z-axis, carrying 1 current of 2.5 A in the +z direction. Find the
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magnetic field in component form ( B  ? iˆ  ? ˆj ) at the point (0.005, 0.01, 0) where the coordinates are
in meters.
16. The diagram shows two infinitely long wires carrying equal currents of 8.0A running anti-parallel to
each other. They are both parallel to the z-axis, and are located on the x-axis at x=3.0m and x=0.0m
2
respectively. Find the magnetic field at the following points on the x-y plane: (a) (5,0,0) (b) (1,0,0) and
(c) (3,1,0).
y
3m
x
17. Referring to the previous problem, find the force per meter on a wire carrying a current of 2.0A in the
positive z direction when placed at each of the three locations in the problem.
18. Three long, parallel straight wires pass through the vertices of an equilateral triangle that has sides equal
to 10cm as shown. The current in the upper wire is out of the paper while those in the two lower wires
are into the paper. If each current is 15A, find (a) the magnetic field at the location of the upper wire due
to the current in the two lower wires and (b) the force per unit length on the upper wire.
19. Three long parallel wires are at the corners of a square. Thewire each carries a current I . Find the
magnetic field at the unoccupied corner of the square when (a) all the currents are into the page, (b)
I 1 , I 3 are into the page, and I 2 is out, (c) I1 , I 2 are into the page, and I 3 is out. Your answer should be in
terms of I and L
I1
L
I2
I3
20. The diagram shows a long straight wire attached to a circular loop of radius 2.0m. A 15.0A current runs
downward along the straight wire. What must be the direction and magnitude of the current in the loop
so that the magnetic field is zero at the center of the loop?
3
Answers:
1. 1.5rad / s clockwise
2.
3. (a) 37.7 A  m 2 int o paper (b) 18.9 N to the right
4. 0.13 N  m
5. 25.2iˆ  18 ˆj ( N  m)
(c) 0.95rad / s (d ) out of the paper
(b) 0.8iˆ  0.6 ˆj (c) 0.35 N  m (d ) 0.42kˆN  m 
6. (a) 37 
7. 18.9J
1
1
1
8. (a) a 2 Q (b) a 2 Q (c) a 2 Q
2
4
5
9.
10. 0.25nT 33.7 
11. 54 T 31T
12. 2.0  10 6 N  m
13. (a) 3.77mT (b)1.89mT
14. (a) 0.51m (b)10.5mT
15.  40mT 20mT
16. 4.8T 2.4T 1.52T
17. 0.96N / m 0.48N / m 0.30N / m
18. (a) 52T (b) 0.78mN / m
3 2 0 I
4L
20. 4.78 A
19. (a)
(b)
2 0 I
4L
(c )
10  0 I
4L
4