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Page 1 of 9

CHAPTER 6



The deflection (and hence current) is
larger when the magnet is pushed
towards or pulled away from the coil
faster
...


ELECTROMAGNETIC INDUCTION
INTRODUCTION




experiments on electric current by
Oersted, Ampere etc established the
interrelationship between electricity and
magnetism
...


Electromagnetic induction


Conclusion


The relative motion between the magnet
and the coil is responsible for generation
(induction) of electric current in the coil
...


The Experiments of Faraday and Henry
Experiment I








When the North-pole of a bar magnet is
pushed towards the coil, the
galvanometer deflects
...

When the magnet is pulled away from the
coil, the galvanometer shows deflection in
the opposite direction
...


Page 2 of 9



The bar magnet is replaced by a
second coil C2 connected to a
battery
...


Conclusion –


The relative motion between the coils
induces the electric current
...

If the key is held pressed continuously,
there is no deflection in the
galvanometer
...

The deflection increases dramatically
when an iron rod is inserted into the coils
along their axis
...




Mathematically



If there are N turns



The negative sign indicates the direction
of emf
...
A = BA cosθ




The polarity of induced emf is such that it
tends to produce a current which
opposes the change in magnetic flux that
produced it
...
m
...


If the magnetic field has different
magnitudes and directions at various
parts of a surface then the magnetic flux
through the surface is given by
Polarity of a current carrying loop



anticlockwise current
Clockwise current

north pole
...

In electromagnetic induction the mechanical
energy is converted in to electrical energy
...

This violates the law of conservation of energy
and hence cannot happen
...
The energy
spent by the person is dissipated by Joule
heating produced by the induced current
...


Eddy Currents


Ways to increase the induced emf




By increasing the number of turns, N
...

The magnetic flux can be varied by
 Changing magnetic field, B
 Changing area, A
...

 Rotating the coil in a magnetic
field
...







Motional Electromotive Force


The emf induced by the motion of a
conductor in a magnetic field is called
motional emf
...

Eddy currents flow in closed loops within
conductors, in planes perpendicular to the
magnetic field
...

The direction of eddy currents is given by
Lenz’s law
...


Reason :






As the plates moves the magnetic flux
associated with it changes and eddy
currents are induced on its surface
...

Hence the plate comes to rest
...

The pendulum plate with holes or slots
reduces electromagnetic damping and the
plate swings more freely
...

The direction of the induced currents is as
per Lenz’s law and hence the disc is
thrown up into air
...


The eddy currents dissipate energy in the
form of heat
...

Eddy currents are undesirable, in most of
the electrical devices like transformer,
induction coil, choke coil etc
...


Applications of Eddy currents










Magnetic braking in trains
Electromagnetic damping in
galvanometers
...

When the electromagnets are
activated, the eddy currents induced

Page 6 of 9



in the rails oppose the motion of the
train
...


Electromagnetic damping in galvanometers




Certain galvanometers have a fixed core
made of nonmagnetic metallic material
...


Speedometer







Induction furnace


induced in the metal, and this produces a
magnetic field of its own
...




In the speedometer an aluminum drum
rotates according to the speed of the
vehicle
...

As the vehicle moves the magnet rotates,
the eddy currents are produced in the
aluminum drum
...

The pointer of the speedometer moves
according to the rotation of the drum
...

The eddy currents generated in the metals
produce high temperatures sufficient to
melt it
...




Electric currents are induced in the disc by
magnetic fields produced by sinusoidally
varying currents in a coil
...

If a piece of electrically conductive metal
is close to the coil, eddy currents will be

www
...
com






Inductance is the property of a coil by
which a change in current through it
induces an e m f in both the conductor
itself and in any nearby coil by mutual
inductance
...

ΦB α I
...

The product of magnetic flux and number
of turns of a coil is called flux linkage
...

Inductance depends only on the geometry
of the coil and intrinsic material
properties
...

The dimensions of inductance are
[M L2 T-2 A-2]
...

The two types of inductance are
1) Mutual inductance 2) Self inductance



Mutual induction


Also flux linkage with solenoid S2 when a
current I1 is passed through the solenoid
S1 is



When current through a coil changes an
e
...
f
...

This is called mutual induction
...




Comparing two equations

General equation of mutual inductance


We have

Page 8 of 9





Thus



Therefore the mutual inductance is



The mutual inductance of a pair of coils,
solenoids, etc
...


Where constant of proportionality L is
called self-inductance of the coil
...


Equation of self inductance


The magnetic field due to a current I
flowing in the solenoid is B = μ0n I
...




The self-induced emf is also called the
back emf as it opposes any change in the
current in a circuit
...

It is the electromagnetic analogue of mass
in mechanics
...


Self-inducction




NφB= L I

When the current through a coil changes,
an e
...
f
...
This is called self
induction
...




Relation connecting self inductance and induced
emf


We have

Page 9 of 9







When the current is varied, the flux linked
with the coil also changes and an emf is
induced in the coil
...


Energy stored in an inductor




The work to be done against the back emf
in an inductor is stored as magnetic
potential energy
...


AC Generator







But



Therefore



Total amount of work done in establishing
the current I is,

Principle/Theory


A
...
generator works on the principle of
electro-magnetic induction
...

When the coil is rotated with a constant
angular speed ω, the angle θ between the
magnetic field vector B and the area vector A
of the coil at any instant t is θ = ωt
The flux at any time t is








An ac generator converts mechanical
energy into electrical energy
...

Modern day generators produce electric
power as high as 500 MW
...

In certain countries such as USA, it is 60
Hz
...


Page 10 of
9



If we denote NBAω as ε0, then

ε = ε0 sin ωt




ε = ε0 sin ωt


The ends of the coil are connected to
external circuit by means of slip rings and
brushes
...


The direction of the current changes
periodically and therefore the current is
called alternating current (ac)
...


Construction


An AC Generator consists of a coil
mounted on a rotor shaft
...




The coil (called armature) is mechanically
rotated in the uniform magnetic field by
some external means
...


Hydro-electric generators
...


Thermal generators



Water is heated to produce steam using
coal or other sources
...


Nuclear power generators


Nuclear fuel is used to heat water to
produce steam
...




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