Download Problem Set 5 Due: see website for due date

Problem Set 5
Due: see website for due date
Chapter 22: Electromagnetic Induction
Questions: 2, 4, 7, 9
Problems: 2, 4, 16, 20, 27, 37, 38, 73
Q22.2: You have three light bulbs; bulb A has a resistance of
240 Ω, bulb B has a resistance of 192 Ω, and bulb C has a
resistance of 144 Ω. Each of these bulbs is used for the same
amount of time in a setup like the one in the drawing. In each
case the speed of the rod and the magnetic field strength are
the same. Rank the setups in descending order, according to
how much work the hand in the drawing must do (largest
amount of work first).
(a) A, B, C (b) A, C, B (c) B, C, A (d) B, A, C (e) C, B, A
Q22.4: The drawing shows a cube. The dashed lines in the drawing are
perpendicular to faces 1, 2, and 3 of the cube. Magnetic fields are
oriented with respect to these faces as shown, and each of the three
fields B1, B2, and B3 has the same magnitude. Note that B2 is parallel
to face 2 of the cube. Rank the magnetic fluxes that pass through the
faces 1, 2, and 3 of the cube in decreasing order (largest first).
(a) Φ1, Φ2, Φ3 (b) Φ1, Φ3, Φ2 (c) Φ2, Φ1, Φ3 (d) Φ2, Φ3, Φ1 (e) Φ3, Φ2, Φ1
Q22.7: The drawing shows three flat coils, one square and two rectangular, that are
each being pushed into a region where there is a uniform magnetic field directed into the
page. Outside of this region the magnetic field is zero. In each case the magnetic field
within the region has the same magnitude, and the coil is being pushed at the same
velocity v. Each coil begins with one side just at the edge of the field region. Consider
the magnitude of the average
emf induced as each coil is
pushed from the starting position
shown in the drawing until the
coil is just completely within the
field region. Rank the
magnitudes of the average emfs
in descending order (largest first).
(a) ξA, ξB, ξC (b) ξA, ξC, ξB (c) ξB, ξA and ξC (a tie) (d) ξC, ξA and ξB (a tie)
Q22.9: The drawing shows a top view of two circular coils of conducting
wire lying on a flat surface. The centers of the coils coincide. In the
larger coil there are a switch and a battery. The smaller coil contains no
switch and no battery. Describe the induced current that appears in the
smaller coil when the switch in the larger coil is closed. (a) It flows
counterclockwise forever after the switch is closed. (b) It flows clockwise
forever after the switch is closed. (c) It flows counterclockwise, but only
for a short period just after the switch is closed. (d) It flows clockwise, but only for a short
period just after the switch is closed.
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P22.4: The drawing shows a type of flow meter that can be used to measure the speed
of blood in situations when a blood vessel is sufficiently exposed (e.g., during surgery).
Blood is conductive enough that it can be treated as
a moving conductor. When it flows perpendicularly
with respect to a magnetic field, as in the drawing,
electrodes can be used to measure the small voltage
that develops across the vessel. Suppose that the
speed of the blood is 0.30 m/s and the diameter of
the vessel is 5.6 mm. In a 0.60-T magnetic field what
is the magnitude of the voltage that is measured with
the electrodes in the drawing?
Answer: 0.001 V
P22.6: Two circuits contain an emf produced by a moving metal rod, like that shown in
Figure 22.4b. The speed of the rod is the same in each circuit, but the bulb in circuit 1
has one-half the resistance of the bulb in circuit 2. The circuits are
otherwise identical. The resistance of the light bulb in circuit 1 is 55
Ω, and that in circuit 2 is 110 Ω. Determine (a) the ratio ξ1/ ξ2 of the
emfs and (b) the ratio I1/ I2 of the currents in the circuits. (c) If the
speed of the rod in circuit 1 were twice that in circuit 2, what would
be the ratio P1/P2 of the powers in the circuits?
Answer: 1, 2, 8
22.16: A square loop of wire consisting of a single turn is perpendicular to a uniform
magnetic field. The square loop is then re-formed into a circular loop, which also
consists of a single turn and is also perpendicular to the same magnetic field. The
magnetic flux that passes through the square loop is 7.0×10-3 Wb. What is the flux that
passes through the circular loop? Answer: 0.0089 Wb
P22.20: Magnetic resonance imaging (MRI) is a medical technique for producing
pictures of the interior of the body. The patient is placed within a strong magnetic field.
One safety concern is what would happen to the positively and negatively charged
particles in the body flu- ids if an equipment failure caused the magnetic field to be shut
off suddenly. An induced emf could cause these particles to flow, producing an electric
current within the body. Suppose the largest surface of the body through which flux
passes has an area of 0.032 m2 and a normal that is parallel to a magnetic field of 1.5 T.
Determine the smallest time period during which the field can be allowed to vanish if the
magnitude of the average induced emf is to be kept less than 0.010 V.
Answer: 4.8 s
P22.27: A 1.1-m-diameter MRI solenoid with a length of 2.4 m has a magnetic field of 1.5
T along it axis. If the current is turned off in a time of 1.2 s, what is the induced emf in one
turn of the solenoid’s windings?
Answer: 0.0036 V, 0.002 m2/s
P22.37: A circular loop of wire rests on a table. A long, straight wire lies on this loop,
directly over its center, as the drawing illustrates. The current I
in the straight wire is decreasing. In what direction is the
induced current, if any, in the loop? Give your reasoning.
Answer: no induced current
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P22.38: The drawing shows a bar magnet falling through a metal
ring. In part a the ring is solid all the way around, but in part b it
has been cut through. (a) Explain why the motion of the magnet in
part a is retarded when the magnet is above the ring and below
the ring as well. Draw any induced currents that appear in the ring.
(b) Explain why the motion of the magnet is unaffected by the ring
in part b.
Answer: no answer
P22.73: Review Conceptual Example 9 as an aid in
understanding this problem. A long, straight wire lies on a table
and carries a current I. As the drawing shows, a small circular
loop of wire is pushed across the top of the table from position 1
to position 2. Determine the direction of the induced current,
clockwise or counterclockwise, as the loop moves past (a)
position 1 and (b) position 2. Justify your answers.
Answer: clockwise, clockwise
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