Electromagnetic Inductio

What Is Electromagnetic Induction?

Electromagnetic Induction was discovered by Michael
Faraday in 1831, and James Clerk Maxwell
mathematically described it as Faraday’s law of induction.
Electromagnetic Induction is a current produced because
of voltage production (electromotive force) due to a
changing magnetic field. This either happens when a
conductor is placed in a moving magnetic field (when
using an AC power source) or when a conductor is
constantly moving in a stationary magnetic field. As per
the setup given below, Michael Faraday arranged a
conducting wire attached to a device to measure the
voltage across the circuit. When a bar magnet is moved
through the coiling, the voltage detector measures the
voltage in the circuit.
Through his experiment, he discovered that there are certain
factors that influence this voltage production. They are:

1. Number of Coils: The induced voltage is directly

proportional to the number of turns/coils of the wire.
Greater the number of turns, greater is voltage
produced
2. Changing Magnetic Field: Changing magnetic field
affects the induced voltage. This can be done by
either moving the magnetic field around the
conductor or moving the conductor in the magnetic
field.
Inductance- Self Inductance and
Mutual Inducation

We are aware that whenever an electric current flows

through a conductor, a magnetic field surrounding it is
produced. A varying current results in a varying magnetic
field. Due to this, the magnetic flux varies and an
electromotive force is induced in the circuit. Let us learn
about it in more detail in this article.

What is Inductance?

Inductance is the tendency of an electrical conductor to

oppose a change in the electric current flowing through it.
L is used to represent the inductance, and Henry is the SI
unit of inductance. 1 Henry is defined as the amount of
inductance required to produce an emf of 1 volt in a
conductor when the current change in the conductor is at
the rate of 1 Ampere per second.
An electric current flowing through a conductor creates a
magnetic field around it. The strength of the field
depends upon the magnitude of the current. The
generated magnetic field follows any changes in the
current, and from Faraday’s law of induction, we know
that changing the magnetic field induces an
electromotive force in the conductor. Considering this
principle, inductance is defined as the ratio of the
induced voltage to the rate of change of current causing
it. The electronic component designed to add inductance
to a circuit is an inductor.
Factors Affecting Inductance

Following factors affect the inductance in a circuit:

 Number of Wire Turns in the Coil

Inductance is greater when the number of turns of
wire in the coil is greater. More coils of wires indicate
a greater amount of magnetic field force for a given
amount of coil current.
 Coil Area
Inductance is proportional to the coil area. Greater
the coil area, the greater the inductance. Greater coil
area presents less opposition to the formation of
magnetic field flux for a given amount of field force
 Core Material
The greater the magnetic permeability of the core to
which the coil is wrapped around, the greater the
inductance.
 Coil Length
The longer the coil’s length, the lesser the
inductance. The shorter the coil’s length, the greater
the inductance.

Types of Inductance

Inductance is classified into two types as:

  Self Inductance
 Mutual Inductance

What is Self Inductance?

When there is a change in the current or magnetic flux of

the coil, an electromotive force is induced. This
phenomenon is termed Self Inductance. When the current
starts flowing through the coil at any instant, it is found
that, that the magnetic flux becomes directly proportional
to the current passing through the circuit. The relation is
given as:

ϕ=LxI
Where L is termed as the self-inductance of the coil or the
coefficient of self-inductance, the self-inductance
depends on the cross-sectional area, the permeability of
the material, and the number of turns in the coil.
The rate of change of magnetic flux in the coil is given as,
e = -d ϕ/dt = -d(LI)/dt
e = -L dI/dt
Self Inductance Formula

ϕ
L=N
T
Where,
 L is the self inductance in Henries
  N is the number of turns
 Φ is the magnetic flux
 I is the current in amperes
What is Mutual Inductance?

Consider two coils: P – coil (Primary coil) and S – coil

(Secondary coil). A battery and a key are connected to
the P-coil, whereas a galvanometer is connected across
the S-coil. When there is a change in the current or
magnetic flux linked with the two coils, an opposing
electromotive force is produced across each coil, and this
phenomenon is termed Mutual Inductance.
This phenomenon is given by the relation:
Φ=MI
Where M is termed as the mutual inductance of the two
coils or the coefficient of the mutual inductance of the
two coils.
The rate of change of magnetic flux in the coil is given as,
e=-d ϕ/dt = -d(MI)/dt
e=-M dI/dt
Mutual Inductance Formula

M= μ0μrN1N2A
l

Where,
 μ0 is the permeability of free space
 μr is the relative permeability of the soft iron core
  N is the number of turns in coil
 A is the cross-sectional area in m2
 l is the length of the coil in m
Difference between Self and Mutual Inductance
Self inductance Mutual inductance

In self inductance, the In mutual inductance out of

change in the strength of the two coils one coil
current in the coil is opposes change in the
opposed by the coil itself strength of the current
by inducing an e.m.f. flowing in the other coil.

The induced current

The induced current developed in the
opposes the growth of neighboring coil opposes
current in the coil when the the growth of current in
main current in the coil the coil when the main
increases. current in the coil
increases.

The induced current

The induced current developed in the
opposes the decay of neighboring coil opposes
current in the coil when the the decay of the current in
main current in the coil the coil when the main
decreases. current in the coil
decreases.

Examples of Self Inductance and Mutual Inductance

Example 1.
Consider a solenoid with 500 turns which are wound on
an iron core whose relative permeability is 800. 40 cm is
the length of the solenoid, while 3 cm is the radius. The
change in current is from 0 to 3 A. Calculate the average
emf induced for this change in the current for a time of
0.4 seconds.
Solution:
Given:
No.of turns, N = 500 turns
Relative permeability, μr = 800
Length, l = 40 cm = 0.4 m
Radius, r = 3 cm = 0.03 m
Change in current, di = 3 – 0 = 3 A
Change in time, dt = 0.4 sec
Self-inductance is given as
L = μN2Al = μ0μrN2𝜋r2/l
Substituting the values we get
(4)(3.14)(10-7)(800)(5002)(3.14)(3×10-2)2/0.4
L = 1.77 H
Magnitude of induced emf, ε = L di/dt = 1.77×3/0.4
ε = 13.275 V

Electromagnetism
Electromagnetism is a branch of Physics, that deals with
the electromagnetic force that occurs between
electrically charged particles. The electromagnetic force
is one of the four fundamental forces and exhibits
electromagnetic fields such as magnetic fields, electric
fields, and light. It is the basic reason electrons are bound
to the nucleus and are responsible for the complete
structure of the nucleus.
What is Electromagnetic Force?
The electromagnetic force is a type of physical interaction
that occurs between electrically charged particles. It acts
between charged particles and is the combination of all
magnetic and electrical forces. The electromagnetic force
can be attractive or repulsive.
Before the invention of electromagnetism, people or
scientists used to think electricity and magnetism are two
different topics. The view has changed after James Clerk
Maxwell published A Treatise on Electricity and
Magnetism in the year 1873. The publication states that
the interaction of positive and negative charges are
mediated by one force. This observation laid a foundation
for Electromagnetism. Later many scientists like Michael
Faraday, Oliver Heaviside, and Heinrich Hertz contributed
their ideas in electromagnetism.

What is Electromagnetism?

Electromagnetism is a process where a magnetic field is

created by introducing the current in the conductor.
When a conductor is electrically charged it generates
magnetic lines. For example, if current i.e., positive
charges move in a wire, it produces the magnetic field
along the wire, and the direction of magnetic lines and
force can be determined using Right-hand Rule. Refer to
the image for a detailed explanation.
Explanation of Electromagnetism with an
Example

Permanent Magnetic speakers commonly used in TV’s

and Radios are perfect examples of Electromagnetic
devices. Let’s see the operation of these devices which
are based on the principle of electromagnetism. See the
picture below.
In order to convert electrical waves into audible sound,
the speakers are designed. A metal coil is attached to a
permanent magnet and when current passes through the
coil it generates a magnetic field. The newly formed
magnetic field is repelled by the permanent magnetic
field resulting in the vibrations. These vibrations are
amplified by the cone-like structure causing the sound.
This is how speakers work based on electromagnetism.
Electromagnetic Induction
We have seen what happens when a conductor is
electrically charged. Now, let’s see what happens if we
place a conductor in between the magnetic field.
When a conductor is placed or moved through the
magnetic field it generates voltage i.e., electricity. This
principle is called Electromagnetic Induction. The
voltages generated will be based on the speed of the
conductor moving through the magnetic field. Faster the
speed of the conductor, the greater the induced
electricity or voltage.
Faraday’s Law
According to Faraday’s Law, the relative motion between
the magnetic field and conductor, the flux linkage
changes and this change in flux induces a voltage across
the coil.
Explanation with an example
DC Generator works on the principle of Faraday’s Law of
Electromagnetic Induction. It is a system that converts
mechanical energy into electrical energy.
In the above figure, A rectangular conductor width sides
are placed in between a magnetic field. When the
rectangular conductor rotates in between magnetics, it
cuts the magnetic field thereby causing the
Electromagnetic field (e m f).

Properties of the Electromagnetic Wave

A few properties of electromagnetic
waves are:
 Electromagnetic waves are propagated by oscillating
electric and magnetic waves at right angles to each
other.
 They exhibit the properties of interference and
diffraction.
 They travel at a speed of 3 × 108m/s in a vacuum.
 They are transverse waves.
 The relationship between the wavelength (λ) and
frequency (c) of an electromagnetic wave is given as
follows:
c=vλ
Applications of Electromagnetism
A few applications of electromagnetism are:
 Electromagnetism serves as a fundamental working
principle for many of the home appliances in
household applications.
 The Maglev trains or high-speed trains work on the
principle of electromagnetism.
 Electromagnetic radiations are used in the
communication system to transfer data from the
source to the receiver.
 In industries, starting from small instruments to large
power equipment, electromagnetism is used at least
at one stage of their work.

Magnetic induction Formula

Magnetic induction was discovered by Michael Faraday in

1831. Later Maxwell described it mathematically and it
came to be known as Faraday’s law of induction. Faraday
had performed three experiments to understand
electromagnetic induction. Then Faraday’s law became
crucial to understand induction which now has several
practical applications like in generators, transformers,
etc. In this session, let us know more about
electromagnetic induction class 12 formulas.
Law of Magnetic Induction

Magnetic induction, also called electromagnetic induction

refers to the production of voltage (or EMF) across an
electrical conductor placed inside a varying magnetic
field. According to Faraday’s law, for a closed circuit, the
induced electromotive force is equal to the rate of change
of the magnetic flux enclosed by the circuit. To know
more about magnetic induction, visit electromagnetic
induction. Now, let us know more about electromagnetic
induction class 12 formulas.

Formula For Magnetic Induction

From Faraday’s law, the EMF induced in a closed circuit is
given by –

Here, is the magnetic flux, t is the time and is the EMF

induced.
Note:

Where, B = magnetic field and “ds” is a very small area.

In a coil of wire with N turns, the EMF will be-

Later, according to Lenz law, Faraday’s equation was

modified accordingly which is now given by-

Now, this equation determines the direction of induced

current and follows the law of conservation of energy.
For a moving conductor, the EMF is given by:

Where, l = length of the conductor, v = velocity of the

conductor and θ is the angle between the magnetic field
and the direction of motion.
An example related to the magnetic induction is given
below for better understanding.