Electromagnetic Induction Chapter Questions
1. What is the Electromagnetic Force (EMF)? What are the units of EMF?
2. The discovery of electric currents generating a magnetic field led physicists to look for
what other phenomenon?
3. What did Michael Faraday’s experiment demonstrate?
4. When is the magnetic flux through a surface at its maximum value? Where is it at its
minimum value?
5. Using Faraday’s Law of Induction, explain how a constant magnetic field can still
generate an EMF in a closed loop.
6. What is Lenz’s Law?
7. When determining the direction of the induced EMF in a loop, is the magnetic field
outside the loop considered?
8. Why is it important to turn off power to an appliance before you unplug it?
9. Lenz’s Law specifies the direction of the induced current due to a bar sliding on metal
rails due to an external force within a magnetic field. What major Conservation Law can
also be used to determine the current’s direction?
10. If a changing electric field creates a changing magnetic field, and a changing magnetic
field creates a changing electric field, is it possible for these two fields to be stuck in an
infinite loop where they constantly change into one another? Why or why not?
11. Is there an induced magnetic field during electromagnetic induction?
12. What are some real world applications of electromagnetic induction? How is this
phenomenon used to improve situations in everyday life? You will probably need to
research this on the web.
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Chapter Problems
Magnetic Flux
Class Work
1. A wire loop with an area of 0.0050 m2 is oriented perpendicular to a uniform
magnetic field of 1.3 T. What is the magnetic flux through the loop?
2. A 0.20 m wide and 0.60 m long rectangular loop of wire is oriented perpendicular to
a uniform magnetic field of 0.30 T. What is the magnetic flux through the loop?
3. The magnetic flux through a rectangular loop, with an area of 0.0080 m2 is 0.40 Wb.
How strong is the magnetic field?
Homework
4. A loop of wire, 4.2 cm in diameter, is oriented perpendicular to a uniform magnetic
field of 0.60 T. What is the magnetic flux in the loop?
5. A 0.40 m wide and 0.80 m long rectangular loop of wire is oriented perpendicular to
a uniform magnetic field of 0.50 T. What is the magnetic flux through the loop?
6. The magnetic flux through a loop of wire, 15 cm in diameter, is 3.0 Wb. What is the
strength of the magnetic field?
Faraday’s Law of Induction
Class Work
7. The magnetic flux through a loop of wire changes from zero to 12 Wb in 0.30 s. What
is the induced emf in the loop?
8. What is the rate of change of magnetic flux through a coil of wire with 100 turns if
the induced emf is 12 V?
9. The magnetic flux through a coil of wire changes uniformly from 2.0 Wb to 4.8 Wb in
0.20 s and induces an emf of 14 V. How many loops are in the coil?
10. A wire loop with a radius of 9.0 cm is initially parallel to a uniform magnetic field
2.6 T. The loop’s orientation is then changed so that it is perpendicular to the field in
0.12 s. What is the induced emf in the loop?
11. A circular loop is made of a flexible wire. The loop is perpendicular to a uniform
magnetic field with a magnitude of 3.5 T. The area of the loop is changed from
0.0050 m2 to 0.0080 m2 in 0.15 s. What is the induced emf in the loop?
Homework
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12. The magnetic flux through a coil of wire with 100 turns changes from 5.0 Wb to
45 Wb in 0.25 s? What is the induced emf in the coil?
13. A coil with 200 turns is oriented perpendicular to a changing magnetic field. An
induced emf of 30.0 V is caused by the change in magnetic field. What is the rate of
change of magnetic flux through the coil?
14. The magnetic flux through a coil of wire changes uniformly from 5.2x10-2 Wb to zero
in 0.13 s and induces an emf of 4.0 V. How many loops are in the coil?
15. A rectangular loop of wire with an area of 0.048 m2 is perpendicular to a magnetic
field. The magnitude of the field changes uniformly from 0.24 T to 1.67 T in 0.25 s.
What is the induced emf in the loop?
16. A rectangular loop is made of a flexible wire. The loop is perpendicular to a uniform
magnetic field with a magnitude of 4.5 T. The area of the loop is changed from 0.010
m2 to 0.0080 m2 in 0.15 s. What is the induced emf in the loop?
Lenz’s Law
Class Work
17. A loop is placed in a uniform magnetic field. Determine the direction of the induced
current in the loop, when a) the original field, B, increases, b) the original field, B,
decreases.
18. Two loops of wire are moving in
the vicinity of a very long wire
carrying a steady current. Find
the direction of the induced
current in each loop.
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19. A circular loop lies on a horizontal table. A
student holds a bar magnet with the north pole
pointing down. Find the direction of the induced
current when a) the bar magnet is stationary; b)
the bar magnet is dropped into the loop.
20. A rectangular loop of wire, whose axis is oriented horizontally, is
rotating a quarter turn in clockwise direction, as shown above. What
is the induced current in the loop as it rotates from a vertical to
horizontal orientation?
21. A permanent magnet is pushed into a
stationary ring that is suspended from a
vertical string. What happens to the ring?
How can we use Lenz’s Law to explain this
experiment?
22. A bar magnet is pushed into a coil. Is
VB – VA positive, negative or zero?
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Homework
23. A rectangular loop is pushed into a
uniform magnetic field. Find the direction
of the induced current.
24. A circular loop is removed from a uniform
magnetic field. Find the direction of the
induced current in the loop.
25. A loop of wire is placed stationary near a straight
wire with an increasing current. What is the
direction of the induced current in the loop?
26. A straight wire is moving to the right between two magnets facing
each other. What is the direction of the induced current in the wire?
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27. Two coaxial rings are connected to a circuit
shown above. Ring B is connected in series to a
battery, switch and rheostat. After the switch is
closed a steady current flows through the circuit.
Find the direction of the induced current in ring
A when a) the rheostat rider is moved to the
right (R increases, so I decreases); b) the
rheostat rider is moved to the left (I increases).
28. A constant force is applied to a metal rod that is
placed on two parallel conducting rails. The rod then
slides to the right at a constant speed, perpendicular
to a constant magnetic field. Find the direction of the
induced current in the resistor.
EMF induced in a moving conductor
Class Work
29. A 15 cm wire moves at a constant speed of 16 m/s perpendicular to a uniform
magnetic field of 0.80 T. What is the induced emf in the wire?
30. When a 36 cm wire moves at constant speed in a 3.4 T magnetic field the induced
emf is 16 V. What is the speed of the wire?
31. How strong must a magnetic field be in order to induce a 6.0 V emf in a 0.32 m wire
that is moving at a constant speed of 17 m/s, perpendicular to the field?
Homework
32. A 48 cm wire moves at a constant speed of 25 m/s perpendicular to a uniform
magnetic field of 2.2 T. What is the induced emf in the wire?
33. A 1.4 m straight wire moves at constant speed in a 4.9 T magnetic field. What is the
speed of the wire if the induced emf is 24 V?
34. How strong must a magnetic field be in order to induce a 5.0 V emf in a 0.12 m wire
moving at a constant speed of 15 m/s, perpendicular to the field?
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Electromagnetic Induction Applications
Class work
35. The picture shown above depicts the inside of an electric DC motor. In a coherent
paragraph, describe what happens when a current is sent through the loop.
36. What would happen if a coil of wire were to be placed in series with a resistor and
battery?
Homework
37. There are flashlights that can be powered simply by shaking them back and forth.
Using what you know about electromagnetic induction, explain in a coherent
paragraph how you think they work.
38. One description for a generator could be an “anti-motor”. Using what you know
about electromagnetic induction, explain how a hydro-powered generator works.
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General Problems
1. A 0.14 m wide and 0.28 m long wire coil containing 10 loops lies on a horizontal
table top (see the figure above). An upward magnetic field crosses the table top and
the field magnitude increases from zero to the maximum value of 2.6 T in 0.30 s.
a. What is the maximum magnetic flux through the coil?
b. What is the induced emf in the coil?
c. If the net resistance of the coil is 0.60 Ω what is the magnitude of the induced
current in the coil?
d. What is the direction of the induced current in the coil?
e. What is the rate of thermal energy produced by the coil?
2. A circular coil with a radius of 25 cm has 20 turns. The coil
is oriented perpendicularly to a magnetic field whose initial
magnitude is 3.2 T. Suddenly, the magnetic field vanishes in
0.40 s.
a. What is the initial magnetic flux in the coil?
b. What is the induced emf in the coil?
c. If the net resistance of the coil is 6.8 Ω , what is the
magnitude of the induced current in the coil?
d. What is the direction of the induced current in the coil?
e. What is the rate of thermal energy generated by the coil?
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3. A square loop of wire, 0.20 m on each
side, has a resistance of 0.35 Ω. The loop
is moved at constant speed in 0.40 s from
position I where a magnetic field is zero
to position II where a magnetic field is
0.90 T.
a. What is the induced emf in the
loop during this period of time?
b. What is the direction of the induced current in the loop?
c. What is the magnitude of the induced current in the loop?
d. What is the power dissipated in the loop?
e. How much force is required to move the coil from position I to position II?
4. A square loop of wire, 0.40 m on each
side has a resistance of 0.14 Ω. The loop
is moved at constant speed in 0.20 s from
position I where a magnetic field is 1.3 T
to position II where the magnitude of the
magnetic field is zero.
a. What is the induced emf in the
loop during this period of time?
b. What is the direction of the induced current in the loop?
c. What is the magnitude of the induced current in the loop?
d. What is the power dissipated in the loop?
e. How much force is required to move the coil from position I to position II?
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5. A conducting rod with a length of 0.45 m makes a contact with two conducting and
parallel rails. The rails are connected to a 2.5 Ω resistor; ignore the resistance of the
rod and rails. A constant force F moves the rod at a constant speed 4.2 m/s to the
right with no friction between the rod and rails. The apparatus is placed in a
uniform magnetic field 1.8 T that is perpendicular to the rails and the rod.
a. Calculate the induced emf in the rod.
b. Find the direction of the induced current in the resistor.
c. Calculate the magnitude of the induced current in the resistor.
d. Calculate the power dissipated in the resistor during the time when the rod
moves in the field.
e. Calculate the external force necessary to move the rod at constant speed
through the magnetic field.
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6. A 2.0 m conducting rod is connected to a 6.0 V battery by two very light wires. The
rod is moved at a constant speed of 2.8 m/s in a perpendicular magnetic field with a
magnitude of 1.1 T. The total resistance of the circuit is 2.5 Ω. Answer the following
questions:
a. What is the induced emf in the rod while it is moving in the magnetic field?
b. What is the magnitude of the induced current in the rod?
c. What is the direction of the induced current in the rod with respect to the
coordinate system shown on the diagram?
d. What is the magnitude of the current in the rod produced by the battery?
e. What is the direction of the conventional current in the rod due to the battery?
f. What is the magnitude of the net current in the rod?
g. What is the direction of the net current in the rod?
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7. A square loop of wire of sides L has a total resistance of R. The loop is positioned in
a uniform magnetic field B. The field is directed into the
page, perpendicular to the plane of the page, as shown.
a. Calculate the flux through the loop.
The magnetic field strength now increases
uniformly to 3B T in 3 s.
b. Calculate the EMF induced in the loop in the 3s.
c. Calculate the magnitude of the current in the loop.
d. What is the direction of the current? In a short
paragraph, justify your answer by explaining the
concept behind Lenz’s Law and how it applies.
e. Describe a method by which you could induce a current in the loop if the
magnetic field remained constant.
8. Two parallel conducting rails, separated by a
distance L, are connected through a resistance R
as shown to the right. A uniform magnetic field
with a magnitude B points into the page. A
conducting bar slides without friction across the
rails and creates a constant current I.
a. Determine the EMF produced in the
conducting bar.
b. Determine the electric field in the
conducting bar.
c. Determine at what speed the bar must be moved, and in what direction to
induce a counterclockwise current I = 0.5 A as shown.
d. Determine the magnitude and direction of the external force that must be
applied to the bar to keep it moving at this velocity.
e. Calculate the rate at which heat is being produced in the resistor.
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9. A uniform magnetic field with a magnitude 5 T
points out of the page. A conducting bar with a
length 1 m and a mass of 2 kg slides without
friction across the rails, which are connected to a
variable resistor R.
a. Draw a free body diagram of the forces
acting on the bar below:
b. In what direction does the current flow through the bar? Explain your
answer in a short coherent paragraph.
The bar has a constant nonzero acceleration, a, as it moves downwards.
c. Derive an equation that can be used to find the EMF of the circuit as a
function of time.
d. What must be true in order for the bar to have a constant acceleration during
its descent? Explain your answer in a short paragraph.
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A student connected a voltmeter to the circuit and recorded the change in
EMF over time on the table below.
𝜀(V)
t (s)
5
0.48
8
0.83
12
1.18
18
1.81
26
2.58
e.
i.
On the graph below, plot the points from the table and draw a best fit
line through your data.
ii.
Find a.
f. What is the current through the circuit?
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Wt
10. A 0.2 Ω rectangular loop of wire has an area of 0.5 m2
and placed in a region where the magnetic field changes
as shown on the diagram to the right.
a. What is the magnetic flux in the loop at 0.4 s?
b. What is the induced emf for the following times?
i. _______ 0.1 s ii. ________0.3 s iii. ________ 0.5s
c. What is the induced current for the following times? i. _______ 0.1 s ii.
________0.3 s iii. ________ 0.5 s
d. On the diagram below, graph the induced current as a function of time.
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11. Two conducting massless springs each with spring constant
k are suspended from points A and B respectively. The two
springs support a conducting bar of length L and mass m
that is placed inside a constant uniform magnetic field B.
When points A and B are connected to a battery, the bar
lowers into the magnetic field and each spring stretches a
distance x. The diagram to the right shows the circuit after
the battery has been connected.
a. Which point, A or B, is connected to the negative
terminal of the battery? Explain your answer.
b. Given that the total resistance of the circuit is R, derive an equation that can
be used to solve for the EMF of the battery using the variables that have
already been given to you.
A student performs an experiment using batteries of different EMFs in order
to calculate the magnetic field. Her results are shown on the table below.
𝜀
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x
50
2.51
62
2.63
150
3.47
187
3.96
265
4.63
300
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c. Plot the data from the table on the graph below. Orient the graph so that EMF
is a function of x and draw a best fit line through your points.
d. Solve for B
12. A loop of wire with radius r and resistance R sits in a constant magnetic field B
directed at an upward angle 𝜃 with the vertical.
a. What is the flux through the loop?
The magnetic field decreases from B to 0.2 B in 10 s.
b. What direction is the induced current in? Explain your answer.
c. What is the induced EMF in the loop?
d. Find the power dissipated in the loop.
e. What is the net magnetic force on the loop while the field is decreasing?
Explain your answer.
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13.
A wire loop, 1 m by 2 m, of negligible resistance, is in the plane of the page with its left end
in a uniform 1 T magnetic field directed into the page, as shown above. A 5Ω resistor is
connected between points A and B. The field is zero outside the region enclosed by the
dashed lines. The loop is being pulled to the right with a constant velocity of 4 m/s. Make
all determinations for the time that the left end of the loop is still in the field.
a. Determine the potential difference induced between points A and B.
b. On the figure above, show the direction of the current induced in the resistor.
c. Determine the force required to keep the loop moving at 4 m/s.
d. Determine the rate at which work must be done to keep the loop moving at
4 m/s.
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Chapter Questions
1. A potential difference measured in
volts.
2. Whether a changing magnetic field
can generate a current.
3. An EMF would be produced in a
secondary loop when a current
was switched on and off in a
primary loop.
4. Flux is at a maximum when the
magnetic field is parallel to the
Normal to the surface. It is at a
minimum when it is perpendicular
to the Normal.
5. By varying either the angle of the
magnetic field with the Normal to
the surface, or changing the area of
the loop.
6. The direction of induced EMF in a
current loop is such that the
resulting current produces a
magnetic field that opposes the
change of flux through the loop.
7. No, only the area within the loop is
considered.
8. As the plug is pulled out and the
current starts decreasing, the
current supplied by the power
company will increase to produce
a magnetic field to oppose the
decreasing magnetic field –
resulting in a spark.
9. Conservation of Energy.
10. Yes, this is possible, as there is no
physical property to prevent it
from happening. The constantly
changing fields are called
electromagnetic waves, or, as they
are more commonly known, light.
This will be covered in the EM
Waves unit of this course.
11. Yes. The induced magnetic field is
produced by the induced current.
12. Some common applications of
induction are AC current
transformers, inductive charging,
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induction cookers, and induction
motors.
Chapter Problems
1. 6.5 x 10-3 Wb
2. 3.6 x 10-2 Wb
3. 5.0 x 101 T
4. 8.3 x 10-4 Wb
5. 1.6 x 10-1 Wb
6. 1.7 x 102 T
7. 4.0 x 101 V
8. 1.2 x 10-1 Wb/s
9. 1
10. 5.5 x 10-1 V
11. 7.0 x 10-2 V
12. 1.6 x 104 V
13. 1.5 x 10-1 Wb/s
14. 10
15. 2.7 x 10-1 V
16. 6.0 x 10-2 V
17. a) Clockwise b) Clockwise
18. Left loop: Counter-clockwise
Right loop: No change
19. a) None b) Counter-clockwise
20. Clockwise
21. The ring moves away from the
magnet because the induced field
tries to oppose the direction of the
original field (Lenz’s Law).
22. The bar magnet creates an
increasing magnetic field directed
into the loops. The loops will
create a field to oppose this by
carrying a clockwise current;
current flows from b to a, so
VB-VA is positive.
23. Counter-clockwise
24. none
25. Counter-clockwise
26. No induced current.
27. a) Clockwise b) Counter-clockwise
28. Counter-clockwise
29. 1.9 V
30. 1.3 x 101 V
31. 1.1 T
32. 2.6 x 101 V
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33. 3.5 m/s
34. 2.8 T
35. When a current is sent through the
loop, the magnetic force is applied
to opposite ends of the loop in
opposite directions, creating a
torque. When the loop spins, it is
able to power different rotating
devices.
36. The coil would create a current
that is equal and opposite of the
one from the battery.
37. The flashlight consists of a sliding
magnet which moves back and
forth through the center of a coil of
wire, when it is shaken, inducing a
current in the coil which is used to
power a light bulb.
38. A generator must have something
that turns in order to work. A
hydro powered generator would
typically sit at the bottom of a
waterfall. The rushing water
would move turbine blades in the
generator which is attached to a
magnet. The magnet would then
move through a coiled wire,
inducing a current.
General Problems
1. a) 1.0 x 10-1 Wb
b) 3.4 V
c) 5.7A
d) Clockwise
e) 1.9 x101 W
2. a) 6.3 x 10-1 Wb
b) 31 V
c) 4.6 A
d) Clockwise
e) 1.4 x 102 W
3. a) 9.0 x 10-2 V
b) Counter -clockwise
c) 0.26A
d) 0.023W
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e) 0.046N
4. a) 1.0 V
b) Counter-clockwise
c) 7.4A
d) 7.4 W
e) 3.7 N
5. a) 3.4V
b) Clockwise
c) 1.4 A
d) 4.8 W
e) 1.1N
6. a) 6.2 V
b) 2.5A
c) +y direction
d) 2.4 A
e) –y direction
f) 0.1A
g) +y direction
7.
a)
b)
c)
d)
𝛷 = 𝐵𝐿2
𝜀 = 2𝐵𝐿2 /3
𝐼 = 2𝐵𝐿2 /3𝑅
Lenz’s law states that if an induced
current flows, its direction is
always such that it will oppose the
change which produced it. The
magnetic field is directed into the
page and increasing. Current will
be induced to oppose that change.
If the opposing field is out of the
page, the induced current must be
counterclockwise.
e) Pull the loop out of the field, rotate
the loop about an axis in the plane
of the loop, and change the area of
the loop are all acceptable
responses.
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8.
a)
b)
c)
d)
e)
f) 4.8 A
𝐼𝑅
𝐼𝑅/𝐿
𝐼𝑅/𝐵𝐿 to the right
𝐼𝐿𝐵 to the right
𝐼 2 /𝑅
10.
a) 0.2 Wb
b)
i. -1 V
ii. 0
iii. 2v
c)
i. 5 A
ii. 0
iii. 10A
9.
a)
b) Left or Counterclockwise.
According to Lenz’s law, the
induced magnetic field will oppose
any changes that are being made.
The magnetic field is into the page
and increasing, meaning that the
induced field must be out of the
page resulting in a
counterclockwise current.
c) 𝜀 = 𝐵𝐿𝑎𝑡
d) Because 𝐼𝐿𝐵 − 𝑚𝑔 = 𝑚𝑎, current
must be a constant in order for
acceleration to be a constant. The
resistance must be increasing as
the bar moves downwards in
order to keep current constant.
e)
i. The graph should be of a
straight line whose plotted
points correspond to the
points given in the table.
The best fit line should not
pass through all of the
points.
ii. a = 2 m/s2
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d)
11.
a) Point A is connected to the
negative terminal of the battery. In
order for the springs to have
stretched, the conventional
current must be flowing from right
to left. If point b is connected to
the positive terminal, point A is
connected to the negative terminal.
b) 𝜀 = 𝑅(2𝑘𝑥 − 𝑚𝑔)/𝐿𝐵
c) The graph should be of a straight
line whose plotted points
correspond to the points given in
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the table. The best fit line should
not pass through all of the points.
d) B should be between 4.7 T and 5.3
T
12.
a) 𝛷 = 𝜋𝑟 2 𝐵𝑐𝑜𝑠𝜃
b) Counterclockwise. The vertical
component of the magnetic field is
upwards and decreasing. In order
to oppose this change, the induced
magnetic field must be upwards,
creating a counterclockwise
induced current.
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c) 0.08 B
d) 0.0064BR
e) 0 N. Forces on directly opposing
sides of the loop are in opposite
directions.
13.
a) 4 V
b) The current should be in the
counterclockwise direction
c) 0.8 N
d) 1.8 W
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