Electromagnetic Induction and

Faraday’s Law

Contents
1. Induced EMF
2. Faraday’s Law of Induction; Lenz’s Law
3. EMF Induced in a Moving Conductor
4. Changing Magnetic Flux Produces an Electric Field
5. Electric Generators
6. Transformers and Transmission of Power
7. Information Storage: Magnetic and Semiconductor; Tape, Hard Drive,
RAM
8. Applications of Induction: Microphone
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Faraday’s Law of Induction
 Faraday’s Law of Induction
• At the instant the switch is closed or opened, the
galvanometer needle deflects in one direction and then
returns to zero.
• when the switch is closed, the current in the primary
circuit produces a magnetic field that penetrates the
secondary circuit.
 Faraday’s Law of Induction
• the magnetic field produced by the current in the primary
circuit changes from zero to some value over some finite
time, and this changing field induces a current in the
secondary circuit.
• an electric current can be induced in a circuit (the
secondary circuit in our setup) by a changing magnetic
field.

• Finally, the galvanometer reads zero when there is either a

steady current or no current in the primary circuit.
1. - Induced Electromotive force

Figure 1: Faraday’s experiment to induce an emf.

-Electromagnetic Induction: is the process to produce a voltage in a

conductor either by changing the conductor or the flux or both.
-From experiment Faraday’s summarized that:
1- Whenever the magnetic flux linked with an electric circuit is
altered, an emf is induced in the circuit.
2- An emf is produced when magnet is moved or removed as in figure
1 a and b.
3- No emf produced while magnet is stationary, as in figure 1 c.
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2. Faraday’s Law of Induction; Lenz’s Law
- Faraday investigated quantitatively what factors influence the
magnitude of the emf induced
- The induced emf increasing with more rapidly magnetic field
changes.
- The induced emf depends on the area of the circuit loop (and the
angle it makes with).
- The emf is proportional to the rate of change of the magnetic flux,
passing through the circuit or loop of area A.

Figure 2. Magnetic fluxDr.

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is Zeinab
proportional to the number of lines of that
Abd El-Wahab
pass through the loops of a coil (here with 3 loops).
2. Faraday’s Law of Induction; Lenz’s Law
Statement of Faraday’s law of induction: The emf induced in
a circuit is equal to the rate of change of magnetic flux
through the circuit.
∆𝜑𝐵
𝜀= − , 𝜑B=BAcos
∆𝑡
- If the circuit contains N loops that are closely wrapped so the same
flux passes through each, the emf. induced in each loop add together,
so the total emf is ∆𝜑𝐵
𝜀 = −𝑁
∆𝑡
The minus sign gives the direction of the induced emf:

- It is important to note that an emf is induced whenever there is a

change in flux through the coil, and we now consider some more
possibilities.
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2. Faraday’s Law of Induction; Lenz’s Law

- Lenz’s law states that a current produced by an induced emf

moves in a direction so that the magnetic field created by that
current opposes the original change in flux.
Lenz’s law states : An induced emf is always in a direction that
opposes the original change in flux that caused it.
∆𝜑𝐵
𝜀= − , 𝜑B=BAcos
∆𝑡

ⅆ
𝜀=− 𝐵𝐴 cos 𝜕
ⅆ𝑡
Note/ The emf can be induced in three ways:
(1) by changing magnetic field B;
(2) by changing the area, A of the loop in the field;
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by changing the loop’s orientation with respect to the field.
2. Faraday’s Law of Induction; Lenz’s Law

Fig.3 A current can be induced by changing the coil’s area, even

though B doesn’t change. Here the area A is reduced by pulling on
the sides of the coil: the flux through the coil is reduced as we go from
(a) to (b).

Fig. 4 A current can be induced by rotating a coil in a magnetic field.

The flux through the coil changes from (a) 𝜽 = 𝟎, 𝝋 = 𝒎𝒂𝒙𝒊𝒎𝒖𝒎
to (b) 𝜽 = 𝟗𝟎 , 𝝋 = 𝒎𝒊𝒏𝒖𝒎𝒖𝒎
2. Faraday’s Law of Induction; Lenz’s Law

Problem Solving: Lenz’s Law

1. Determine whether the magnetic flux is increasing, decreasing, or
unchanged.
2. The magnetic field due to the induced current points in the
opposite direction to the original field if the flux is increasing; in
the same direction if it is decreasing; and is zero if the flux is not
changing.
3. Use the right-hand rule to determine the direction of the current.
4. Remember that the external field and the field due to the induced
current are different.

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Q 1: A loop of wire in a magnetic field.
A square loop of wire of side L=5.0 cm is in a uniform magnetic field
B=0.16 Tesla. What is the magnetic flux in the loop (a) when is
perpendicular to the face of the loop and (b) when is at an angle of
30°to the area of the loop? (c) What is the magnitude of the average
current in the loop if it has a resistance 0.012 ohm and it is rotated
from position (b) to position (a) in 0.14s.
Sol. The area of the coil is L2=5x5x10-4=25x10-4 m2
(a) is perpendicular to the coil’s face, so
B=B.A.cos=BA.cos0˚=B.A(1)=0.16x25x10-4 =4 x10-4 Webr
(b) The angle is 30° and , so
B=BAcos=BAcos30=0.16x25x10-4cos 30=3.4x10-4 Webr
∅𝒊 = ∅𝒃 = 𝟑. 𝟒 × 𝟏𝟎−𝟒 , ∅𝒇 = ∅𝒂 = 𝟒 × 𝟏𝟎−𝟒 , 𝒔𝒐 ∆∅ flux is increasing
֜ 𝒊𝒏𝒅𝒖𝒄𝒆𝒅 𝒆𝒎𝒇 𝒊𝒏 𝒐𝒑𝒑𝒐𝒔𝒊𝒕𝒆 𝒅𝒊𝒓𝒆𝒄𝒕𝒊𝒐𝒏 𝒐𝒇 𝒕𝒉𝒆 𝒐𝒓𝒊𝒈𝒊𝒏𝒂𝒍 𝒇𝒊𝒆𝒍𝒅 ( - sign)
∆𝜑𝐵 (∅𝑎 −∅𝑏 ) −(4×10−4 − 3.4×10−4 )
𝒄 𝜀=− =- = = - 4.3x10-4 volt
∆𝑡 ∆𝑡 0.14
𝜀 (4.3x10−4 )
Then the magnitude I →≫ I = = 0.012 = 35.8x10-3 A= 35.8 mA
𝑅
3. EMF Induced in a Moving Conductor
- Another way to induce an emf. is shown in (figure. 5) :

Figure 5. (a) A conducting rod is moved to the right on a conductor in a

uniform magnetic field that points out of the page. The induced current
is clockwise. (b) Upward force on an electron in the metal rod (moving
to the right) due to pointing out of the page; hence electrons can collect
at the top of the rod, leaving + charges to the bottom.
 3. EMF Induced in a Moving Conductor
- If the rod is made to move at a speed v to the right, it travels a
distance (dx=vdt) in a time t.

- Therefore, the area of the loop increases by an amount dx, (A=vLdt)

- By Faraday’s law there is an induced emf whose magnitude is given by:

∆𝜑 −𝐵𝐿∆𝑥 −𝐵𝐿𝑣∆𝑡
𝜀= − = = =-BLv
∆𝑡 ∆𝑡 ∆𝑡

-The induced current is clockwise (to counter the increasing

flux).
3. EMF Induced in a Moving Conductor
Q 2: Does a moving airplane develop a large emf? In 1000 km/h a
region where the Earth’s magnetic field is about 5x10-5 T and is nearly
vertical. What is the potential difference induced between the wing
tips that are 70 m apart?

-sol. B= 5x10-5 T, L=70 m, v=(1000x1000)/(60x60)=277.7 m/sec

𝜀 =-BLv,

𝜀 =(5x10-5x70x277.7)=0.97=1 volt Don’t worry

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4.Changing Magnetic Flux Produces an Electric Field

- From all the previous discussions now we know well : a changing

magnetic flux produces an electric field.
-This result applies not only to wires and other conductors, but is a
general result that applies to any region in space.
- Indeed, an electric field will be produced at any point in space
where there is a changing magnetic field.

𝑬 = 𝑭/𝒒 𝑭 = 𝒒𝒗𝑩

𝑞𝑣𝐵
𝐸= =vB
𝑞

We will study some applications about this applications.

5. Electric Generator

- A generator is a device which transforms

mechanical energy into electric energy
(figure 6)

- A generator consists of many loops of wire

(only one is shown) wound on an armature
that can rotate in a magnetic field.
- The axle is turned by some mechanical
means (falling water, steam turbine, car Figure 6. An ac generator
motor belt), and an emf is induced in the
rotating coil.
- An electric current is thus the output of a
generator.

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5. Electric Generator

The magnetic Flux equation for the electronic Generator is :

𝝋 = 𝑩𝑨𝒄𝒐𝒔𝜽 = 𝑨𝑩𝒄𝒐𝒔 𝝎𝒕

𝒅𝝋 𝒅(𝑨𝑩𝒄𝒐𝒔𝝎𝒕)
, 𝒉𝒆𝒏𝒄𝒆 𝜺 = −𝑵 𝜺 = −𝑵
𝒅𝒕 𝒅𝒕
𝒅(𝑨𝑩𝒄𝒐𝒔𝝎𝒕)
𝒕𝒉𝒆𝒏 𝜺 = −𝑵
𝒅𝒕

When θ = 900  =  max

𝜺 = 𝑵𝑩𝑨𝒘𝒔𝒊𝒏 𝒘t 𝜺 = 𝑵𝑩𝑨𝒘
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6. Transformers and Transmission of Power
- A transformer is a device for increasing or decreasing an ac voltage.
Transformers are found everywhere.(see figure 8)
-

- Figure. 8 Transformer
-Transformer has no internal moving parts, and it transfers
energy from one circuit to another by electromagnetic induction.
From Faraday’s law, the voltage or emf induced in the secondary coil
is:
𝑑𝜑
𝑉𝑠 = −𝑁𝑠
𝑑𝑡
Where N
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6. Transformers and Transmission of Power

- The input primary voltage, is related to the rate at which the

flux changes through it,
ⅆ𝜑
𝑉𝑝 = −𝑁𝑝
ⅆ𝑡

We divide these two equations, assuming little or no flux is lost, to

find the transformer equation
𝑉𝑠 𝑁𝑆
=
𝑉 𝑃 𝑁𝑃

-This transformer equation tells how the secondary (output)

voltage is related to the primary (input) voltage; and in
- If Np>Ns, we have a step-down transformer
- If Np<Ns, we have a step-up transformer

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 Figure 9 The transmission of electric power from power plants to homes
makes use of transformers at various stages.

11/5/2024 Dr. Zeinab Abd El-Wahab

Q3: A Cell phone charger. The charger for a cell phone contains a
transformer that reduces 120-V (or 240-V) ac to 5.0-V ac to charge
the 3.7-V battery. (It also contains diodes to change the 5.0-V ac to
5.0-V dc.) Suppose the secondary coil contains 30 turns and the
charger supplies 700mA. Calculate (a) the number of turns in the
primary coil, (b) the current in the primary, and (c) the power
transformed.
-Sol.
-the number of turns in the secondary coil is
𝑁𝑆𝑉𝑃 30𝑥120
𝑁𝑃 = 𝑉𝑆
= 5
=720 turns
- The current in the primary coil
𝐼𝑆𝑁𝑆 30x0.7
𝐼𝑃 = = =29x10-3 A
N𝑃 720
- The power in the secondary coil
- 𝑃 = 𝐼𝑆𝑉𝑆 =0.7x5=3.5 watt

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7.Information Storage: Magnetic and Semiconductor; Tape, Hard
Drive

Magnetic Storage: Read/Write on Tape and Disks

Figure 10 (a) Photo of a hard drive showing several platters and read
write heads that can quickly move from the edge of the disk to the
center.(b) Read Write (playback recording) head for disk or tape.
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8. Applications of Induction: Microphone

Microphone : operate on the principle of induction. A small coil

connected to a membrane is suspended close to a small permanent
magnet. The coil moves in the magnetic field when sound waves
strike the membrane, and this motion induces an emf in the moving.

membrane Small coil of wire

Figure. 11 - Diagram of a microphone that works by

induction
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