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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
Faradays work
  • Faraday suggested that an e.m.f. is induced in a
    conductor when
  • 1. there is a change in the number of lines
    linking it,
  • 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
Faradays law
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
Larger load
Zero load
  • 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
    follow is increased.

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
  • Advantages
  • 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.
  • Disadvantage
  • 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.
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