Download Circular Motion HW-1

AP Physics 2
Electromagnetic Induction HW
due___________
Conceptual Questions
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An airplane flies horizontally toward the north pole. Is the induced emf from wing tip to wing tip greater when
the plane is at the equator or when it is at the latitude of New York? Explain.
Explain the difference between a magnetic field and a magnetic flux.
You hold a circular loop of wire at the equator. Consider the magnetic flux through this loop due to the Earth’s
magnetic field. Is this flux greater when the normal to the loop points north or when it points vertically upward?
Explain.
You hold a circular loop of wire at the north pole. Consider the magnetic flux through this loop due to the
Earth’s magnetic field. Is this flux greater when the normal to the loop points horizontally or when it points
vertically downward? Explain.
Figure 1 shows two metal disks of the same size and material oscillating in and out of a region with a magnetic
field. One disk is solid; the other has a series of slots. Is the retarding effect of eddy currents on the solid disk
greater than, less than, or equal to the retarding effect on the slotted disk? Explain.
Consider the solid disk in Figure 1. When this disk has swung to the right as far as it can go, is the induced
current in it a maximum or a minimum? Explain.
Figure 1
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Figure 2
As the solid metal disk in Figure 1 swings to the right, from the region with no field into the region with a finite
magnetic field, does the induced current in the disk circulate clockwise or counterclockwise? Explain.
A metal ring with a break in its perimeter is dropped from a field-free region of space into a region with a
magnetic field. What effect does the magnetic field have on the ring?
Figure 2 shows a vertical iron rod with a wire coil of many turns wrapped around its base. A metal ring slides
over the rod and rests on the wire coil. Initially the switch connecting the coil to a battery is open, but when it is
closed the ring flies into the air. Explain why this happens.
Referring to Question 9, suppose the metal ring has a break in its circumference. Describe what happens when
the switch is closed in this case.
In a common classroom demonstration, a magnet is dropped down a long, vertical copper tube. The magnet
moves very slowly as it moves through the tube, taking several seconds to reach the bottom. Explain this
behavior.
Problems
Magnetic Flux
1. A 0.055-T magnetic field passes through a circular ring of radius 2.1 cm at an angle of 12° with the normal.
Find the magnitude of the magnetic flux through the ring.
2. Find the magnitude of the magnetic flux through the floor of a house that measures 22 m by 18 m. Assume that
the Earth’s magnetic field at the location of the house has a horizontal component of 2.6  105 T pointing
north, and a downward vertical component of 4.2  105 T.
3. At a certain location, the Earth’s magnetic field has a magnitude of 5.9  105 T and points in a direction that is
70° below the horizontal. Find the magnitude of the magnetic flux through the top of a desk at this location that
measures 110 cm by 62 cm.
Faraday’s Law of Induction
4. A 0.25-T magnetic field is perpendicular to a circular loop of wire with 50 turns and a radius of 15 cm. If the
magnetic field is reduced to zero in 0.12 s, what is the magnitude of the induced emf?
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shows the magnetic flux through a coil as a function of time. At what times shown in this plot do (a)
the magnetic flux and (b) the induced emf have the greatest magnitude?
Figure 3
Figure 3
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Figure 4
shows the magnetic flux through a single-loop coil as a function of time. What is the induced emf in the
coil at (a) t  0.05 s, (b) t  0.15 s, and (c) t  0.5 s ?
A single conducting loop of wire has an area of 7.4  102 m2 and a resistance of 110 . Perpendicular to the
plane of the loop is a magnetic field of strength 0.18 T. At what rate (in T/s) must this field change if the
induced current in the loop is to be 0.22 A?
An emf is induced in a conducting loop of wire 1.12 m long as its shape is changed from square to circular.
Find the average magnitude of the induced emf if the change in shape occurs in 4.25 s, and the local 0.105-T
magnetic field is perpendicular to the plane of the loop.
A magnetic field increases from 0 to 0.20 T in 1.5 s. How many turns of wire are needed in a circular coil 12
cm in diameter to produce an induced emf of 6.0 V?
Figure 4
Lenz’s Law
10. A bar magnet with its north pole pointing downward is falling toward the center of a horizontal, conducting
ring. As viewed from above, is the direction of the induced current in the ring clockwise or counterclockwise?
Explain.
11. A loop of wire is dropped and allowed to fall between the poles of a horseshoe magnet, as shown in Figure 5.
State whether the induced current in the loop is clockwise or counterclockwise when (a) the loop is above the
magnet and (b) the loop is below the magnet.
12. Suppose we change the situation shown in Figure 5 as follows: Instead of allowing the loop to fall on its own,
we attach a string to it and lower it with constant speed along the path indicated by the dashed line. Is the
tension in the string greater than, less than, or equal to the weight of the loop? Give specific answers for times
when (a) the loop is above the magnet and (b) the loop is below the magnet. Explain in each case.
13. Rather than letting the loop fall downward in Figure 5, suppose we attach a string to it and raise it upward with
constant speed along the path indicated by the dashed line. Is the tension in the string greater than, less than, or
equal to the weight of the loop? Give specific answers for times when (a) the loop is below the magnet and (b)
the loop is above the magnet. Explain in each case.
Figure 5
Figure 6
shows a current-carrying wire and a circuit containing a resistor R. (a) If the current in the wire is
constant, is the induced current in the circuit clockwise, counterclockwise, or zero? Explain. (b) If the current in
the wire increases, is the induced current in the circuit clockwise, counterclockwise, or zero? Explain.
15. Consider the physical system shown in Figure 6. If the current in the wire changes direction, is the induced
current in the circuit clockwise, counterclockwise, or zero? Explain.
14. Figure 6
shows a circuit containing a resistor and an uncharged capacitor. Pointing into the plane of the circuit is
a uniform magnetic field B. If the magnetic field increases in magnitude with time, which plate of the capacitor
(top or bottom) becomes positively charged? Explain.
17. Referring to Problem 16, which plate of the capacitor (top or bottom) becomes positively charged if the
magnetic field reverses direction?
18. A long, straight, current-carrying wire passes through the center of a circular coil. The wire is perpendicular to
the plane of the coil. (a) If the current in the wire is constant, is the induced emf in the coil zero or nonzero?
Explain. (b) If the current in the wire increases, is the induced emf in the coil zero or nonzero? Explain. (c)
Does your answer to part (b) change if the wire no longer passes through the center of the coil but is still
perpendicular to its plane? Explain.
16. Figure 7
Figure 7
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Figure 8
A wire with a current I is placed under a clear sheet of plastic, as shown in Figure 8. Three loops of wire, A, B,
and C, are placed on the sheet of plastic at the indicated locations. If the current in the wire is increased,
indicate whether the induced emf in each of the loops is clockwise, counterclockwise, or zero. Explain your
answer for each loop.
Answers
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 = 7.5 x 105 Wb
 = 1.7 x 102 Wb
 = 4 x 105 Wb
 = 7.4 V
(a) The magnetic flux has its greatest magnitude at t = 0 s, 0.2 s, 0.4 s, and 0.6 s .
(b) The magnitude of the induced emf is greatest when the magnitude of the slope of the plot is greatest, which
occurs at t = 0.1 s, 0.3 s, and 0.5 s .
(a)  = 0.1 kV (b)  = 0, because the rate of flux change is zero. (c)  = 0.04 kV
B/t = 3.3 x 102 T/s
 = 5.29 x 104 V
N = 4000 turns
Remaining problems (#’s 10 - 19) are conceptual rather than
numerical; answers may be found online as an extension of
this file, and they will be discussed in class.
10. The current in the loop flows counterclockwise as viewed from above…explain.
11. (a) The current in the loop will oppose the increasing field by flowing clockwise …explain.
(b) The current in the loop will oppose the decreasing field by flowing counterclockwise …explain.
12. The current in the loop opposes the loop’s change in position.
(a) The loop resists moving downward toward the magnet. (The poles of the loop’s field line up with the magnet poles northto-north and south-to-south, causing repulsion.) So the string tension is less than the loop’s weight.
(b) The loop resists moving downward away from the magnet. (The poles of the loop’s field line up with the magnet poles
north-to-south and south-to-north, causing attraction.) So the string tension is again less than the loop’s weight.
13. The current in the loop opposes the loop’s change in position.
(a) The loop resists moving upward toward the magnet. (The poles of the loop’s field line up with the magnet poles north-tonorth and south-to-south, causing repulsion.) So the string tension is greater than the loop’s weight.
(b) The loop resists moving upward away from the magnet. (The poles of the loop’s field line up with the magnet poles
north-to-south and south-to-north, causing attraction.) So the string tension is again greater than the loop’s weight.
14. (a) Since the current in the wire is constant, the magnetic field through the circuit does not vary with time, so the
induced current is zero .
(b) Since the current in the wire is increasing, the magnetic field through the circuit is increasing. And, since the
magnetic field is directed out of the page, the induced current in the circuit will induce a magnetic field into
the page. So, the current in the circuit flows clockwise .
15. If the current in the wire changes direction, the direction of the magnetic field is reversed, changing its direction
from out of the page to into the page. According to Lenz’s law, the current induced in the circuit will oppose this
change by flowing counterclockwise , generating a field which is directed out of the page.
16. Since the field is increasing and is directed into the page, the current in the circuit will flow counterclockwise to
generate a field directed out of the page to oppose it. So, the bottom plate will become positively charged.
17. If the magnetic field changes direction, the current in the circuit will flow clockwise to generate a field to
oppose the change. So, the top plate will become positively charged.
18. (a) The induced emf is zero because the magnetic field is parallel to the plane of the loop.
(b) The induced emf is still zero because, although the field is varying in time, it is still parallel to the plane of
the loop, so there is no time-varying flux through the loop to generate an emf.
(c) The answer to part (b) does not change because the field is still parallel to the plane of the loop.
19. The increasing current in the wire generates an increasing magnetic field which is directed out of the page above
the wire and into the page below.
Loop A: The induced emf is clockwise . The field generated is into the page and opposes the outwardly
directed field generated by the current in the wire.
Loop B: Although the field through the loop is varying with time, the net flux through the plane of the loop is
zero, so the induced emf is zero .
Loop C: The induced emf is counterclockwise . The field generated is out of the page and opposes the
inwardly directed field generated by the current in the wire.