Physics 196 Fall 2010
Exam 4
Permeability of free space
Name:
μ0 = 4π×10-7 T-m/A
PART 1 ( 52 points total. 4 points each.)
Circle the correct answer for the next 13 questions
1. A 2.0mm short wire is situated at the origin of a rectangular coordinate system and carries 3.0A current in
the direction of the z-axis. Find the magnetic field it creates at the point (0,-1,1) where the coordinates are
measured in meters.
(a) 0.37(nT ) ˆj
(b) 0.21(nT )iˆ
(c)  0.37(nT )iˆ
(d)  0.21(nT ) ˆj
2. The diagram below shows an infinitely long wire carrying a 6.0A current into the paper and a point P
directly above it at 4.0cm away. Find the magnitude and direction of the magnetic field at the point P.
P
(a)
(b)
(c)
(d)
20T to the right
20T to the left
30T to the right
30T to the left
3. A small current loop is placed at the point P of the previous problem. Its magnetic moment points to the left.
Describe what will happen to the current loop.
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4. A current loop consists of two concentric semi-circular sections and two straight sections. The radii of the
semicircles are 5.0cm and 10cm respectively. Find the magnitude and direction of the magnetic field at the
center if the current in the loop is 5.0A clockwise.

(a)
(b)
(c)
(d)
6.3T out of the paper
6.3T into the paper
9.6T out of the paper
9.6T into the paper
5. A 10cm long solenoid has 800 turns of wire and a circular cross-section of radius 10cm. How large should
the current be to produce a magnetic field of 500G at its center, assuming end effect can be neglected.
(a)
(b)
(c)
(d)
2.0A
3.0A
4.0A
5.0A
6. Three infinitely long wires carrying currents as shown. The value of the integral
the direction indicated is:
1A
8A
5A
(a) 8  10 7 T  m
(b)  8  10 7 T  m
(c) 12  10 7 T  m
(d)  12  10 7 T  m
2
 
B
  d  around the loop in
7. A toroid has circular cross-section whose center is 15.0cm from the central axis. There are on it 500 turns of
wire carrying a 4.00A current. Find the magnetic field at the center of each cross-section.
(a)
(b)
(c)
(d)
4.23mT
3.59mT
2.67mT
1.84mT
8. The number density of atoms in a certain substance is 5.00  10 28 m 3 . Each atom has a magnetic moment
equal to one Bohr magneton, which is 9.27×10-24 J/T. If all the magnetic moments are aligned in a sample of
this substance, how large is the magnetic field in the sample?
(a) 0.58T
(b) 0.36T
(c) 1.25T
(d) 0.73T
9. The thick arrow indicates the direction of the magnetic moment created when an external field Bapp is
applied to a material specimen. Which of the following statements is correct?
Bapp
(a)
(b)
(c)
(d)
the material is paramagnetic and the magnetic field inside the specimen is less than Bapp
the material is paramagnetic and the magnetic field inside the specimen is greater than Bapp
the material is diamagnetic and the magnetic field inside the specimen is less than Bapp
the material is diamagnetic and the magnetic field inside the specimen is greater than Bapp
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10. The diagram shows a circular loop of diameter 3.0m in a region where the magnetic field points out of the
paper. The strength of the magnetic field increases from 1.0T to 3.0T in 4.0s. What is the direction and
magnitude of the induced electric field inside the loop?


B



3.0m
(a)
(b)
(c)
(d)
0.76V / m clockwise
0.76V / m counter clockwise
0.38V / m clockwise
0.38V / m counter clockwise
11. Referring to the previous problem, where now the magnetic field remains steady at 1.0T, and the loop is
flipped through 180°. How long a time should this process take so that the average induced emf during the
time period is equal to that in the previous problem?
(a)
(b)
(c)
(d)
1.0s
2.0s
3.0s
4.0s
12. The magnetic flux through a rotating coil is given by m t   5.0 cos120t  Wb where t is in seconds. Find
the induced emf at t  1 / 240 s
(a) 1.9kV
(b) 2.5kV
(c) 3.3kV
(d) 4.8kV
13. A metallic ring is pulled away from a region where the magnetic field is into the paper as shown. Which is
the direction of the current induced while it is exiting?
(a) clockwise
(b) counter clockwise
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PART B (48 points)
1. Consider a rectangle abcd measuring 4m by 3m where two infinitely long wires occupy two adjacent
corners a and b, carrying currents with magnitude and direction as indicated. Choose a rectangular
coordinate system where the first current is at the point (0,0) on the x-y plane and the second is at (4,0).
(a) ( 5 points) Find the magnitude of the magnetic field at the corner c.
(b) ( 5 points) If a third infinitely long wire carrying 2.0A current running into the paper is placed at the
point c, find the x and y components of the force per meter on this wire due to the magnitude field.
(c) ( 5 points) Find the magnitude and direction of the current in a wire parallel to the z-axis placed at
the point d so that the magnetic field due to it and the wires at a and b is directed toward d.
c
d
3m
10A
9A
a
4m

b
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2.
A wire frame in the form of a right triangle is placed near an infinitely long wire carrying a current I in
the direction shown. Find
(a) ( 5 points ) an expression for the magnetic flux through the triangle in terms of the lengths identified,
choosing the normal to point out of the paper,
(b) ( 5 points ) the magnitude and direction of the average emf induced in the frame if the current reverses
itself in a time T .
h
I
a
b
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3. ( 8 points ) The diagram shows a long thick cylindrical shell of inner radius a and outer radius b and a thin
wire at the axis. A current I runs in the wire into the paper, and a return current of the same magnitude runs
in the shell with uniform distribution. Find the magnitude of the magnetic field for points at a distance r
from the axis for r  a , a  r  b and b  r .

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4. A perfectly conducting rod of length 0.5m and mass 2.5kg lies on a pair of smooth railings connected to a
10-Ω resistor. The whole assembly is in a uniform magnetic field 2.0T point pointing into the paper. At
t=0, the rod is given a push so that it travels at 8.0m/s to the right.
(a) ( 5 points ) What is the induced emf and the current at t=0?
(b) ( 5 points ) What is the magnetic force on the rod at t=0?
(c) ( 5 points ) How long does it take for the velocity of the rod to be reduced to 5.0m/s?
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