NAME:__________________________________________
GRADE/SECTION:______________________________
12
GENERAL PHYSICS 2
Semester II – Week 8
Magnetic Induction
CONTEXTUALIZED LEARNING ACTIVITY SHEETS
SCHOOLS DIVISION OF PUERTO PRINCESA CITY
General Physics II – Grade 12
Contextualized Learning Activity Sheets (CLAS)
Semester II - Week 8: Magnetic Induction
First Edition, 2020
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Lesson 1
Magnetic Induction
MELC: Identify the factors that affect the magnitude of the induced emf and the magnitude
and direction of the induced current (Faraday’s Law) (STEM_GP12EM-IVa-1).
Compare and contrast electrostatic electric field and non-electrostatic/induced electric
field (STEM_GP12EM-IVa-3).
Calculate the induced emf in a closed loop due to a time-varying magnetic flux using
Faraday’s Law (STEM_GP12EM-IVa-4).
Describe the direction of the induced electric field, magnetic field, and current on a
conducting/nonconducting loop using Lenz’s Law (STEM_GP12EM-IVa-5).
Compare and contrast alternating current (AC) and direct current (DC)
(STEM_GP12EM-IVb-6).
Characterize the properties (stored energy and time-dependence of charges, currents,
and voltages) of an LC circuit (STEM_GP12EM-IVb-8).
Objectives:
1. Cite the factors that affect the magnitude of the induced emf and induced current.
2. Differentiate electrostatic electric field and induced electric field.
3. Determine the induced emf in some physics problems using Faraday’s law.
4. Explain the direction of the induced electric field, magnetic field, and current using
Lenz’s law.
5. Differentiate alternating current and direct current.
6. Distinguish the properties of an LC circuit.
Let’s Try
Directions: Read each question carefully. Write the letter of the correct answer on the space
provided before the number.
______ 1. The north pole of a magnet approaches a coil that causes its magnetic flux to
increase. Given this scenario, what will be the direction of the induced current?
A. Clockwise
C. Down
B. Counter-clockwise
D. Up
______ 2. A wire loop is being pulled through a uniform magnetic field. What is the direction
of the induced current?
A. Clockwise
C. Down
B. Counter-clockwise
D. No induced-current
______ 3. When a double loop of wire is used, the kick on the millivoltmeter is twice as large
as before. A triple loop induces three times the emf and so on. Which of the
following can be deduced from this statement?
A. The emf is proportional to the number of turns in a coil.
B. The speed at which the conductor moves increases the current.
C. The induced emf is directly proportional to the current in the system.
D. The coil brought changes in magnetic field, thus changes the emf and
current.
3
______ 4. How does an alternating current differ from a direct current?
A. AC is a current that changes while DC is steady.
B. AC is unidirectional on the other hand DC is bidirectional.
C. AC has no polarity but DC has positive and negative polarity.
D. AC contains a single path on the other hand DC contains back and forth
movement of the electron.
______ 5. In an LC Circuit, the charge on the capacitor and the current on the inductor
varies sinusoidally with time. If there are no energy losses, what will happen to the
charges in the capacitor?
A. It decreases the voltage.
B. It increases the current.
C. It oscillates back and forth indefinitely.
D. It travels in unidirectional along with the path in the circuit.
______ 6. A varying magnetic field linking a loop or coil causes an emf within the conductor
– an induced current. This induced current is the displacement of charges of an
electric force due to the existence of ____________.
A. Electrostatic electric field
C. Nonelectrostatic electric field
B. Magnetic Force
D. All of these
______ 7. How will you differentiate an electrostatic electric field from nonelectrostatic or
induced electric field?
A. Electrostatic electric field is nonconservative while nonelectrostatic field is
conservative.
B. Electrostatic electric field does net work on moving charge but
nonelectrostatic electric field does no work.
C. Electrostatic electric field is determined via Faraday’s law on the other hand
Coulomb’s law applies in induced electric field.
D. An electrostatic electric field is produced by static distribution of charge
while induced electric field is produced by a changing magnetic field.
______ 8. Which of the following are factors that affect the magnitude and direction of
induced current?
I. Mass of the load
II. Length of the conductor
III. Strength of the magnetic field
IV. Number of the loops in the coil
A. I and II
C. I,II, and III
B. II and IV
D. II, III, and IV
______ 9. A bar magnet approaches a single coil of area 1.73 x 10-2 m2 and makes the
average value of B cos θ to decrease from 0.38 T to 0.079 T in 0.17 seconds. What
is the magnitude of the induced emf?
A. 0.056 V
C. 0.14 V
B. 0.031 V
D. 1.17 V
______ 10. (Refer to situation no. 9). What will be the induced emf if there are 127 loops in
the coil?
A. 7.11 V
C. 17.78 V
B. 3.94 V
D. 148.59 V
4
Let’s Explore and Discover
Unlocking of Difficulties
 Electromagnetism - A
branch of Physics that
deals
with
the
electromagnetic
force
that occurs between
electrically
charged
particles.
 Induction - Generation
of an electric current by
a varying magnetic field.
Michael Faraday is best known
for
his
contribution
to
electromagnetism. Being born
in poor family and only
receiving
a
basic
formal
education did not limit him to
excel in the field of Science. He
was the first scientist to
produce an electric current
from a magnetic field and
invented the first electric motor
and dynamo. His experiments
significantly paved the way for
our
understanding
of
electromagnetism.
Have you experienced going to the supermarket
and noticed that you are cashless and pay using a card?
Or have you witnessed someone withdrawing cash using
an Automated Teller Machine (ATM)? Have you asked how
swiping or scanning the card can deduct money? Have
you wondered how it works? The answer to these
questions lies on the idea of “electromagnetic induction”
and thanks to Michael Faraday for his great contribution
to this field.
Michael Faraday (1791 - 1867)
(Source: roberthuffstutter , MICHAEL FARADAY,
https://creativecommons.org/licenses/by-nc/2.0/.
licensed with CC BY-NC 2.0.)
After Hans Christian Oersted demonstrated that electric currents can produce
magnetic fields, another physicist in the person of Michael Faraday established a law where
electromotive force (emf) is produced from the interaction of magnetic field and electric
current (electromagnetic induction). This law is known as Faraday’s law. Several factors can
affect the emf induced by magnetic flux such as the change in the magnetic flux, since emf
depends on the loop’s area and angle. Also, the emf is greatest when the change in time is
smallest, thus the speed at which the conductor moves is also considered. In addition, the
number of turns in a coil is also a factor that can affect the induced emf. Based on that,
the following relationships are formulated:
1. Emf is directly proportional to the change in magnetic flux.
2. Emf is inversely proportional to the change in time.
3. Emf is directly proportional to the number of turns of a coil.
5
Furthermore, Faraday’s law also implies that a changing magnetic field induces an
emf when it interacts in an electric circuit, therefore work is done on the conduction of
electrons in the wire. The source of this work is the electric field that is induced in the wires.
It is important to note the difference between the electrostatic electric field and
nonelectrostatic or induced electric field. Electrostatic electric field is determined by
Coulomb’s law, it is conservative and does no work over a closed path, on the other hand,
induced electric field is nonconservative since it does net work in moving a charge over a
closed path.
In formula, Faraday’s law of magnetic induction is given by:
٤
= induced voltage (electromotive force)
N = number of turns
∆Φ = change in magnetic flux
∆t = change in time
The unit for emf is volts (V) and the negative sign (-) indicates that the emf creates a
current (I) and magnetic field (B) that oppose the change in flux (∆Φ). This principle is known
as Lenz’s law after the Russian physicist Heinrich Lenz. Lenz’s law is used to predict the
direction of an emf induced in a loop or coil of wire by the changing magnetic field.
(Source: Keministi , “Lenz law demonstration.png" http://creativecommons.org
/publicdomain/zero/1.0/deed.en , marked under CC0 1.0. ).
6
To use Lenz’s law to determine the directions of the induced magnetic fields,
currents, and emfs, follow this problem-solving strategy:
1. Make a sketch of the situation for visualizing and recording directions.
2. Determine the direction of the magnetic field B.
3. Determine whether the flux is increasing or decreasing.
4. Now determine the direction of the induced magnetic field B. It opposes the
change in flux by adding or subtracting from the original field.
5. Use Right Hand Rule-2 to determine the direction of the induced current I that is
responsible for the induced magnetic field B.
6. The direction (or polarity) of the induced emf will now drive a current in this
direction and can be represented as current emerging from the positive terminal
of the emf and returning to its negative terminal.
(Source: “Faraday’s Law of Induction: Lenz’s Law,” Lumen Boundless Physics,
accessed March 24, 2021, https://courses.lumenlearning.com/austinccphysics2/chapter/23-2-faradays-law-of-induction-lenzs-law/.)
The changing magnetic flux through the coil induces an emf, thus producing a
current. The induced current produces its own magnetic field. If the number of field lines
or magnetic field increases, the magnetic flux also increases. Following the Lenz’s law, the
induced emf creates its own current and magnetic field that opposes the change in magnetic
flux. When there is no change in magnetic flux, there will be no emf or current that is
induced in the loop.
Thought to Ponder: Induced emf occurs when there’s a change in the magnetic flux. If the
flux in the circuit has a constant value, there is no induced emf.
Sample Problem 1.a. Study the illustrations below. In which direction is the current induced
on the loop directed?
In figure A, the magnetic field lines point out from the North pole of the magnet, the
magnetic flux in the loop increases due to the increasing number of magnetic field lines. To
oppose this change, the current in the loop will be induced in the counter-clockwise direction
with respect to the bar magnet. In figure B, the approaching South pole will induce a current
that is in clockwise with respect to the direction bar magnet. The flux in the loop increases
because of the increase in the number of field lines. Using Lenz’s law, the magnetic field
line induced by the current is directed from the front to the back.
7
Sample problem 1.b. A bar magnet approaches a single coil with a radius of 7.42 cm and
the average value of B cos θ increases from 0.079 Tesla (T) to 0.38 T in 0.17 s. Find a.) The
rate of change in the flux in Weber per second (Wb/s). (b.) The emf and current in Amperes
(A) induced if the coil has a total resistance of 100 Ohms (Ω). (c.) The emf induced if the coil
contains 50 loops (d.) the direction of the induced current and magnetic field.
Follow these steps in solving problems:
1st : Write all of the given data needed in the solution.
2nd:
Write the unknown or the information the problem is seeking to solve.
rd
3 :
Write the formula and perform a derivation if necessary.
4th:
Calculate.
5th:
Write your final answer.
6th:
Formulate a conclusion.
Illustration
Given:
Unknown:
Radius of the coil
Average value of initial B cos θ
Average value of final B cos θ
Change in time
Total resistance
r = 7.42 cm = 0.0742 m
B cos θi = 0.079 T
B cos θf = 0.38 T
∆T = 0.17 s
R =100 Ω
Formula:
a.) The rate of change in the flux
b.) The emf and current induced
c.) The emf induced if the coil contains 50 loops
d.) The direction of the induced current and magnetic field
Faraday’s and Lenz’s laws
Calculate:
a.) Magnetic flux Φ = ABcosθ
Area of the coil = Πr2
= 3.1415(0.0742m)2
A = 0.0173 m2
∆Φ = A B cos θf - A B cos θi
= A (0. 38 T - 0.079 T)
= A (0.301 T)
= (0.0173 m2) (0.301 T)
∆Φ = 5.21 x 10-3 Wb
Rate of change in the flux = ∆Φ
∆T
= 5.21 x 10-3 Wb
0.17 s
Rate of change in the flux = 0.031 Wb/s
8
b.)
= - 1 (0.031 Wb/s)
٤ = - 0.031 V
c.)
= - 50 (0.031 Wb/s)
= - 1.55 V
Answer:
a.) 0.031 Wb/s
b.) ٤ = - 0.031 V , I = 3.1 x 10-4 A
c.) - 1.55 V
d.) Following the Lenz’s law, the magnetic field lines point out from the
north pole of the magnet, the magnetic flux in the loop increases. To oppose
this change, the current in the loop will be induced in the counter-clockwise
direction with respect to the bar magnet and the induced magnetic field
will be on the opposite direction of the magnetic field, and that is from back
to front.
Conclusion: a.) The rate of change in the flux is 0.031 Wb/s.
b.) The emf induced has the value of 0.031 V.
c.) The emf induced if the coil contains 50 loops is 1.55 V.
d.) The direction of the induced current is counter clockwise and the
induced magnetic field is from the back to the front.
Alternating Current and Direct Current
Direct current (DC) and alternating current (AC) both describe the types of current
flow in a circuit. Direct current refers to the flow of electric charge in only one direction and
the source voltage is constant, thus the magnitude does not change, on the other hand,
alternating current reverses the direction of the flow of the electric charge. The electric
charge can move either forward or backward, also the magnitude and polarity change along
with time. Further comparison of AC and DC is stated in the following table.
Basis
Definition
Alternating current
The direction of the current reverses
periodically.
Causes of flow of
electrons
Rotating a coil in a uniform magnetic
field or rotating a uniform magnetic
field within a stationary coil
50 or 60 Hertz depends on the country
Bidirectional
Frequency
Direction of flow of
electrons.
Power factor
Lies between 0 and 1
Direct current
The direction of the
current remains the
same.
Constant magnetic field
across the wire
Zero
Unidirectional
Always 1
9
Polarity
Obtained from
It has polarity (+, -)
Alternators
Type of load
Their load is resistive, inductive, or
capacitive.
It is represented by irregular waves like
triangular wave, square wave, square
tooth wave, and sine wave.
Can be transmitted over long distance
with some losses.
Graphical
representation
Transmission
Convertible
Easily converted into direct current
Substation
Few substation is required for
generation and transmission.
Passive parameter
Hazardous
Application
Impedance
Dangerous
Factories, Industries, and for domestic
purposes
Do not have polarity
Generators, battery, and
solar cell, etc.
Their load is usually
resistive in nature.
It is represented by the
straight line.
It can be transmitted
over very long distance
with negligible losses.
Easily converted into
alternating current
More substations are
required for generation
and transmission.
Resistance
Very dangerous
Electroplating,
Electrolysis, Electronic,
Equipment etc.
(Source: “Difference Between Alternating Current (AC) and Direct Current (DC),” Circuitglobe.com,
accessed March 28, 2021, https://circuitglobe.com/difference-between-alternating
current-ac-and-direct-current-dc.Html#KeyDifferences)
LC Circuit
An LC circuit (inductor- capacitor circuit) is a closed loop that contains only two
elements, a capacitor and an inductor. The inductor stores energy in its magnetic field while
energy is stored in its electric field for the capacitor. The LC circuit shifts the energy stored
in the circuit between the electric and magnetic field, thus it can oscillate even without a
source of emf.
If the capacitor of an LC circuit contains a charge before the switch is closed, all of
the energy in the circuit will be stored in the capacitor’s electric field. The energy in the
capacitor is given by:
Where U is energy in the capacitor, q is the charge,
and C is the capacitance of the capacitor.
The capacitor begins to discharge the energy when the switch is closed, therefore
producing a current in the circuit. The produced current will create a magnetic field in the
inductor. This process will lead to the transfer of energy from the capacitor (electric field
will diminish) to the inductor where its magnetic field increases. The current is at its
maximum level value (Io) when the capacitor is completely discharged, all the energy is
stored in the magnetic field of the inductor and the energy in the inductor is UL= ½ LIo2.
(UL – energy in the inductor, L- inductance and Io- maximum current). Due to the absence
of resistance in the circuit, there is no loss of energy, therefore, the maximum energy stored
in the capacitor is equal to the maximum energy stored in the inductor is:
10
When the capacitor charge q at time t and the current is I at time t, the total energy
in the circuit is:
Because there is no energy dissipation, it can be written as:
After reaching the maximum current (Io), the capacitor will be recharged due to the
continuous transport charge between the capacitor’s plates by the current. Current will
continue to flow even though the capacitor is discharged because the inductor resists a
change in current, this will result for the capacitor to change with opposite polarity. The
capacitor’s electric field increases while the inductor’s magnetic field diminishes. As a
result, the energy from the inductor is transferred back to the capacitor. Following the law
of conservation of energy, the capacitor will re-acquire its maximum charge however its
plates will be charged opposite to their initial charge. When the capacitor is completely
charged, it will transfer its energy again to the inductor until it becomes fully discharged.
Then again, the energy flows back to the capacitor, and the initial state of the circuit is
restored.
(Source: Chetvorno ,Tuned circuit animation 3.gif,http://creativecommons.
.org/publicdomain/zero/1.0/deed.en Marked under CCO 1.0)
11
Let’s Practice
Directions: Solve the word problem below. Write your answer on the space provided.
A bar magnet approaches a coil with a radius of 124 mm and the average value of B
cos θ increase from 0.0043 T to 0.17 T in 0.01 s. Find the a.) emf induced in the coil;
and b.) the induced emf if the coil contains 100 loops.
Given:
Unknown:
Formula:
Calculate:
Answer:
Conclusion:
Directions: Study the figure below and answer the given question.
In which direction is the induced current and magnetic field
directed? Support your answer.
_________________________________________________________________________________________
_________________________________________________________________________________________
_________________________________________________________________________________________
_________________________________________________________________________________________
_________________________________________________________________________________________
_________________________________________________________________________________________
_________________________________________________________________________________________
12
Let’s Do More
Directions: Using the venn
diagram below, compare and
contrast alternating current
(AC) and direct current (DC).
Give at least 5 differences.
Directions: Solve the word problem below. Write your answer on the
space provided. Use additional sheet of paper if necessary.
A magnet is approaching a square coil of wire with a length of 3.56 cm that contains
77 loops. The average value of Bcosθ decreases from 0.54 T to 0.0032 T in 0.13 s.
What is the magnitude of the induced emf? How about the magnitude of induced
current if the coil has a resistance of 75 Ω?
Given:
Unknown:
Formula:
Calculate:
Answer:
Conclusion:
13
Let’s Sum Up
Directions: Identify whether the following statements about magnetic induction is true or
false. Write T if the statement is correct and F if it is incorrect. Write your answer on the
space provided before each number.
________ 1. Emf is inversely proportional to the change in magnetic flux.
________ 2. The number of loop in a coil is a factor that affects the magnitude of the
induced emf, thus if the number of the loop in a coil increases, the emf also
increases.
________ 3. An electrostatic electric field is conservative and does no work in a closed
path while an induced electric field is nonconservative.
________ 4. Induced electric field is determined by using Coulomb’s law on the other
hand an electrostatic electric field follows Faraday’s law.
________ 5. Since magnetic flux affects the induced emf, area, and angle are also factors
that need to be considered.
Directions: Answer the following questions on the space provided after each item.
1. What are the factors that can affect the magnitude of the induced emf and current? Cite
3 and briefly explain each.
_______________________________________________________________________________________
_______________________________________________________________________________________
_______________________________________________________________________________________
_______________________________________________________________________________________
2. How will you differentiate an electrostatic electric field and an induced electric field?
_______________________________________________________________________________________
_______________________________________________________________________________________
_______________________________________________________________________________________
_______________________________________________________________________________________
3. What are the properties of an LC circuit? How will you distinguish these properties from
one another?
_______________________________________________________________________________________
_______________________________________________________________________________________
_______________________________________________________________________________________
_______________________________________________________________________________________
4. What does Faraday’s law suggest about magnetic induction? How about Lenz’s law?
Briefly explain the idea regarding the two laws.
_______________________________________________________________________________________
_______________________________________________________________________________________
_______________________________________________________________________________________
_______________________________________________________________________________________
_______________________________________________________________________________________
14
_______________________________________________________________________________________
_______________________________________________________________________________________
Let’s Assess
Directions: Read each question carefully. Write the letter of your answer on the space
provided before the number.
______ 1.Which of the following are factors that affect the magnitude and direction of
induced current?
I. Mass of the load
II. Length of the conductor
III. Strength of the magnetic field
IV. Number of the loops in the coil
A. I and II
C. I,II, and III
B. II and IV
D. II, III, and IV
______ 2. When a double loop of wire is used, the kick on the millivoltmeter is twice as large
as before. A triple loop induces three times the emf and so on. Which of the
following can be deduced from this statement?
A. The emf is proportional to the number of turns in a coil.
B. The speed at which the conductor moves increases the current.
C. The induced emf is directly proportional to the current in the system.
D. The coil brought changes in magnetic field, thus changes the emf and
current.
______ 3. A varying magnetic field linking a loop or coil causes an emf within the conductor
– an induced current. This induced current is the displacement of charges of an
electric force due to the existence of ____________.
A. Electrostatic electric field
C. Nonelectrostatic electric field
B. Magnetic Force
D. All of these
______ 4. How will you differentiate an electrostatic electric field from nonelectrostatic or
induced electric field?
A. Electrostatic electric field is nonconservative while nonelectrostatic field is
conservative.
B. Electrostatic electric field does net work on moving charge but
nonelectrostatic electric field does no work.
C. Electrostatic electric field is determined via Faraday’s law on the other hand
Coulomb’s law applies in induced electric field.
D. An electrostatic electric field is produced by static distribution of charge
while induced electric field is produced by a changing magnetic field.
______ 5. A bar magnet approaches a single coil of area 1.73 x 10-2 m2 and makes the
average value of B cos θ to decrease from 0.38 T to 0.079 T in 0.17 seconds. What
is the magnitude of the induced emf?
A. 0.056 V
C. 0.14 V
B. 0.031 V
D. 1.17 V
______ 6. (Refer to situation no. 5.) What will be the induced emf if there are 127 loops in
the coil?
A. 7.11 V
C. 17.78 V
B. 3.94 V
D. 148.59 V
15
______ 7. The north pole of a magnet approaches a coil that causes its magnetic flux to
increase. Given this scenario, what will be the direction of the induced current?
A. Clockwise
C. Down
B. Counter-clockwise
D. Up
______ 8. A wire loop is being pulled through a uniform magnetic field. What is the direction
of the induced current?
A. Clockwise
C. Down
B. Counter-clockwise
D. No induced-current
______ 9. How does an alternating current differ from a direct current?
A. AC is a current that changes while DC is steady.
B. AC is unidirectional on the other hand DC is bidirectional.
C. AC has no polarity but DC has positive and negative polarity.
D. AC contains a single path on the other hand DC contains back and forth
movement of the electron.
______ 10. In an LC Circuit, the charge on the capacitor and the current on the inductor
varies sinusoidally with time. If there are no energy losses, what will happen to the
charges in the capacitor?
A. It decreases the voltage.
B. It increases the current.
C. It oscillates back and forth indefinitely.
D. It travels in unidirectional along with the path in the circuit.
16
Answer Key
Let’s Try
1. B 2. D 3. A 4. A 5. C
6. C 7. D 8. C 9.B 10. B
Let’s Practice
Activity 1
Activity 2
1.a. Emf = -0.80 V
I - clockwise with respect to
1.b. Emf = -80 V
the magnet
B – front to the back
Let’s Do More
Activity 1
Answers may vary. Refer to the table on page 10
1. F
4. F
Let’s Sum Up
Activity 1
Activity 2
2. T
3.T
Answers may
5. T
vary
Activity 2
Emf = 0.404 V
I = 5.39 x 10-3 A
Let’s Assess
1. C
6. B
2. A
7. B
3. C
8. D
4. D
9. A
5. B
10.C
References
Websites
Circuit Globe. “Difference Between Alternating Current (AC) and Direct Current (DC).” Accessed
March 28,2021. https://circuitglobe.com/difference-between-alternating-current-ac-anddirect-current-dc.html.
Lumen Boundless Physics. “Faraday’s Law of Induction: Lenz’s Law.” Accessed March 24, 2021.
https://courses.lumenlearning.com/austincc-physics2/chapter/23-2-faradays-law-ofinduction-lenzs-law/.
17
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Teacher’s Name and Signature:
Parent’s / Guardian’s Name and
Signature:
Date Received:
Date Returned:
18
YES
NO