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## Electromagnetic Induction

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### Electromagnetic Induction emf is induced in a conductor placed in a magnetic field whenever there is a change in magnetic field. Faraday s work Faraday suggested ... – PowerPoint PPT presentation

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Title: Electromagnetic Induction

1
Electromagnetic Induction
• emf is induced in a conductor placed in a
magnetic field whenever there is a change in
magnetic field.

2
• Faraday suggested that an e.m.f. is induced in a
conductor when
• 1. there is a change in the number of lines
• 2. it cuts across field lines.

3
• As shown in the figure, if the coil moves towards
the magnet from X to Y, the number of magnetic
field lines linking it increases from three to
five alternatively we can say it cuts two lines
in moving from X to Y.
• Hence, an e.m.f. is induced in the coil.

4
• The figure shows two stationary coils A and B.
• When a current flowing in coil A increases or
decreases, the magnetic flux linking coil B
increases and decreases respectively. Hence, an
e.m.f. is induced in coil B.

5
Magnetic flux
• B magnetic flux density (i.e. the number of
magnetic field lines per unit cross-section area)
• A cross-section area,
• magnetic flux linking the area is the product BA
represents the number of field lines linking a
surface of cross-sectional area A.
• ? BA
• If B 1 T and A 1 m2, F is defined to be 1
(Tm2) or weber (Wb).

6
Magnetic flux
• If the surface is not perpendicular to the field
with the normal to the surface making an angle q
to the field, the magnetic flux linking the area
is ? BA cos q.
• If F is the flux through the cross-section area A
of a coil of N turns, the total flux through it,
called the flux-linkage, is NF since the same
flux F links each of the N turns.

7
Example 1
• A circular coil of 20 turns with diameter 10 cm
is placed in a region of uniform magnetic field
of 1.5 T. Find the flux-linkage if the plane of
the coil
• (a) is perpendicular to the field,
• Solution

8
Example 1
• A circular coil of 20 turns with diameter 10 cm
is placed in a region of uniform magnetic field
of 1.5 T. Find the flux-linkage if the plane of
the coil
• (b) is along the field, and
• Solution

9
Example 1
• A circular coil of 20 turns with diameter 10 cm
is placed in a region of uniform magnetic field
of 1.5 T. Find the flux-linkage if the plane of
the coil
• (c) makes an angle of 30o to the field.
• Solution

10
The induced e.m.f. is directly proportional to
the rate of change of flux-linkage or rate of
flux cutting.
• Mathematically, or
.
• It is defined that 1 Wb is magnetic flux that
induces in a one-turn coil an e.m.f. of 1 volt
when the flux is reduced to zero in 1 s.
• By putting e 1 V, dt 1 s and d(NF) 1 Wb, we
have 1 constant x 1/1.
• Hence,

11
Example 2
• (a) Suppose a 5000-turn coil of cross-section
area 5 cm2 is at right angles to a flux density
of 0.2 T, which is then reduced steadily to zero
in 10 s. Find the e.m.f. induced in the coil.
• (b) Find the e.m.f. induced if the normal to the
plane of coil makes an angle of 60o with the
field.
• Solution

12
Lenzs law
13
Lenz's law
Induced I always flows to oppose the movement
which started it.
In both cases, magnet moves against a force.
Work is done during the motion it is
transferred as electrical energy.
14
• Lenzs law is incorporated in the mathematic
expression of Faradays law by including a
negative sign to show that current due to the
induced e.m.f. produces an opposing flux change.
So we have

15
Fleming's right-hand rule
For a wire cutting through a B-field...
motion or force F
magnetic field B
induced current I
16
Example 3
• State the direction of induced current flowing
through coil B observed by the observer when the
current through coil A increases steadily.
• Solution

17
Calculation of e.m.f.
• Consider a conducting rod of length l moving
sideways with constant velocity v through and at
right angles to a uniform magnetic field of flux
density B.
• Area swept out per second by the rod per second
lv
• Flux cut per second Blv
• e.m.f induced rate of flux-cutting flux cut
per second
• e Blv

18
Alternative derivation
• Magnetic force Bqv.
• An electric field is built up due to the
accumulation of charges.
• Electric force qE
• Finally, equilibrium is reached when magnetic
force acting on electrons is balanced by electric
force.
• Hence, qE Bqv ? E Bv
• An e.m.f. e is generated across the conductor
such that
• e El Blv.

19
Example 4
• A metal aircraft of wing span l 32 m is flying
with speed v 190 ms-1 towards the earths
magnetic north pole in a region where the earths
magnetic field BR 4.3 x 10-5 T and the angle of
dip a 65o.
• Calculate the e.m.f. induced across its wing
tips.
• Solution

20
Simple a.c. Generator
• According to the Faradays law of electromagnetic
induction,

http//www.walter-fendt.de/ph11e/generator_e.htm
21
Simple d.c. Generator
22
Back e.m.f. Sparks appear while opening a switch
• There is current flowing in the coil of the
electromagnet in use.
• When the circuit is broken by opening the switch,
the current starts to drop and the flux linkage
through the coil of the electromagnet decreases
suddenly.
• By Faradays law, a large induced e.m.f. would
develop across the coil of the electromagnet so
as to oppose the change.
• Sparks occur due to the discharge across the
small gap of the switch.

23
DC motors
• A d.c. motor consists of a coil on an axle,
carrying a d.c. current in a magnetic field.
• The coil experiences a couple as in a moving-coil
galvanometer which makes it rotate.
• When its plane is perpendicular to the field, a
split-ring commutator reverses the current in the
coil and ensures that the couple continues to act
in the same direction thereby maintaining the
rotation.

24
Back emf in Motors
• When an electric motor is running, its armature
windings are cutting through the magnetic field
of the stator. Thus the motor is acting also as a
generator.
• According to Lenz's Law, the induced voltage in
the armature will oppose the applied voltage in
the stator.
• This induced voltage is called back emf.

25
Back emf and Power
Multiplying by I, then
• So the mechanical power developed in motor

26
Variation of current as a motor is started
• As the coil rotates, the angular speed as well as
the back emf increases and the current decreases
until the motor reaches a steady state.

27
The need for a starting resistance in a motor
• When the motor is first switched on, ? 0.
• The initial current, IoV/R, very large if R is
small.
• When the motor is running, the back emf
increases, so the current decrease to its working
value.
• To prevent the armature burning out under a high
starting current, it is placed in series with a
rheostat, whose resistance is decreases as the
motor gathers speed.

28
Variation of current with the steady angular
speed of the coil in a motor
• The maximum speed of the motor occurs when the
current in the motor is zero.

29
Eddy Current
• An eddy current is a swirling current set up in a
conductor in response to a changing magnetic
field.
• When the magnetic flux linkage through a
conductor changes, an e.m.f. is induced in it.
• If the conductor is a lump of metal. These are
known as Eddy Currents.
• Eddy currents may be quite large because of the
low resistance of the paths they follow.

30
Consider a metallic sheet moving away from a
magnetic field.
• By Lenzs law, eddy currents must flow in a
direction to oppose the motion of the sheet.
• Hence, eddy currents act as an effective brake to
its motion.
• The mechanical work done is converted into
internal energy of the sheet.

31
Applications 1 Smooth Braking Device
• The eddy currents induced in the copper plate
produce a strong braking effect on the plate
which stops oscillating quickly.
• If the copper plate is replaced by one with
slits, the induced eddy currents, which can only
flow within the narrow teeth between the slits,
are greatly reduced. This is because the
resistance of the path which the eddy currents

32
Braking effect in moving-coil galvanometer
• As the core swings in a magnetic field, eddy
currents are induced in it. Since the eddy
currents flow in a direction to oppose the
motion, unwanted oscillations are reduced.

33
• Ideal design of the core is to produce critical
damping in which oscillation is just avoided.

34
Metal Detector
• A pulsing current is applied to the coil, which
then induces a magnetic field shown in blue. When
the magnetic field of the coil moves across
metal, such as the coin in this illustration, the
field induces electric currents (called eddy
currents) in the coin.
• The eddy currents induce their own magnetic
field, shown in red, which generates an opposite
current in the coil, which induces a signal
indicating the presence of metal.
• A metal detector can also be used to detect mines
buried underground.

35
Induction cooker
• The induction cooker uses coils of wire with high
frequency a.c. to produce large eddy currents in
the metal cooking pot placing above. The heating
effect of the eddy current cooks the food.
• Moreover, since eddy current is not induced in
its plastic case which is made up of non-metallic
material, the cooker is not hot to touch.

36
Transformer
• A transformer is a device for stepping up or down
an alternating voltage.
• For an ideal transformer,
• (i.e. zero resistance and no flux leakage)

37
Transformer Energy Losses
• Heat Losses
• Copper losses - Heating effect occurs in the
copper coils by the current in them.
• Eddy current losses - Induced eddy currents flow
in the soft iron core due to the flux changes in
the metal.
• Magnetic Losses
• Hysteresis losses - The core dissipates energy on
repeated magnetization.
• Flux leakage - Some magnetic flux does not pass
through the iron core.

38
Designing a transformer to reduce power losses
• Thick copper wire of low resistance is used to
reduce the heating effect (I2R).
• The iron core is laminated, the high resistance
between the laminations reduces the eddy currents
as well as the heat produced.
• The core is made of very soft iron, which is very
easily magnetized and demagnetized.
• The core is designed for maximum linkage, common
method is to wind the secondary coil on the top
of the primary coil and the iron core must always
form a closed loop of iron.

39
Transmission of Electrical Energy
• Wires must have a low resistance to reduce power
loss.
• Electrical power must be transmitted at low
currents to reduce power loss.
• To carry the same power at low current we must
use a high voltage.
• To step up to a high voltage at the beginning of
a transmission line and to step down to a low
voltage again at the end we need transformers.

40
Direct Current Transmission
• a.c. produces alternating magnetic field which
induces current in nearby wires and so reduce
transmitted power this is absent in d.c.
• It is possible to transmit d.c. at a higher
average voltage than a.c. since for d.c., the rms
value equals the peak and breakdown of
insulation or of air is determined by the peak
voltage.
• Changing voltage with d.c. is more difficult and
expensive.

41
Self Induction
• When a changing current passes through a coil or
solenoid, a changing magnetic flux is produced
inside the coil, and this in turn induces an emf.
• This emf opposes the change in flux and is called
self-induced emf.
• The self-induced emf will be against the current
if it is increasing.
• This phenomenon is called self-induction.

42
Definitions of Self-inductance (1)
• Definition used to find L

The magnetic flux linkage in a coil ? the current
flowing through the coil.
Where L is the constant of proportionality for
the coil. L is numerically equal to the flux
linkage of a circuit when unit current flows
through it.
Unit Wb A-1 or H (henry)
43
Definitions of Self-inductance (2)
• Definition that describes the behaviour of an
inductor in a circuit

L is numerically equal to the emf induced in the
circuit when the current changes at the rate of
1 A in each second.
44
Inductors
• Coils designed to produce large self-induced emfs
are called inductors (or chokes).
• In d.c. circuit, they are used to slow the growth
of current.
• Circuit symbol

or
45
Inductance of a Solenoid
• Since the magnetic flux density due to a solenoid
is
• By the Faradays law of electromagnetic induction,

46
Energy Stored in an Inductor
• The work done against the back emf in bringing
the current from zero to a steady value Io is

47
Current growth in an RL circuit
• At t 0, the current is zero.
• So
• As the current grows, the p.d. across the
resistor increases. So the self-induced emf (? -
IR) falls hence the rate of growth of current
falls.
• As t??

48
Decay of Current through an Inductor
• Time constant for RL circuit
• The time constant is the time for current to
decrease to 1/e of its original value.
• The time constant is a measure of how quickly the
current grows or decays.

49
emf across contacts at break
• To prevent sparking at the contacts of a switch
in an inductive circuit, a capacitor is often
connected across the switch.

The energy originally stored in the magnetic
field of the coil is now stored in the electric
field of the capacitor.
50
Switch Design
• An example of using a protection diode with a
relay coil.
• A blocking diode parallel to the inductive coil
is used to reduce the high back emf present
across the contacts when the switch opens.

51
Non-Inductive Coil
• To minimize the self-inductance, the coils of
resistance boxes are wound so as to set up
extremely small magnetic fields.
• The wire is double-back on itself. Each part of
the coil is then travelled by the same current in
opposite directions and so the resultant magnetic
field is negligible.