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. Moving Conductor in a Magnetic Field. Consider a straight conductor moving with a uniform velocity, v , in a stationary magnetic field.

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Electromagnetic induction

Electromagnetic Induction

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


Moving conductor in a magnetic field

Moving Conductor in a Magnetic Field

  • Consider a straight conductor moving with a uniform velocity, v, in a stationary magnetic field.

  • The free charges in the conductor experience a force which will push them to one end of the conductor.

  • An electric field is built up due to the electron accumulation.

  • An e.m.f. is generated across the conductor such that

    E = Blv.


Induced current in wire loop

Induced Current in Wire Loop

  • An induced current passes around the circuit when the rod is moved along the rail.

  • The induced current in the rod causes a force F = IlB, which opposes the motion.

  • Work done by the applied force to keep the rod moving is

  • Electrical energy is produced from the work done such that

E = E It = W

E= Blv


Lenz s law

Lenz’s Law

  • The direction of the induced current is always so as to oppose the change which causes the current.


Magnetic flux

Magnetic Flux

  • The magnetic flux is a measure of the number of magnetic field lines linking a surface of cross-sectional area A.

  • The magnetic flux through a small surface is the product of the magnetic flux density normal to the surface and the area of the surface.

Unit : weber (Wb)


Faraday s law of electromagnetic induction

Faraday’s Law of Electromagnetic Induction

  • The induced e.m.f. in a circuit is equal to the rate of change of magnetic flux linkage through the circuit.

The ‘-’ sign indicates that the induced e.m.f. acts to

oppose the change.

http://physicsstudio.indstate.edu/java/physlets/java/indcur/index.html


Induced currents caused by changes in magnetic flux

Induced Currents Caused by Changes in Magnetic Flux

  • The magnetic flux (number of field lines passing through the coil) changes as the magnet moves towards or away from the coil.

http://micro.magnet.fsu.edu/electromag/java/lenzlaw/index.html


Faraday disk dynamo

Faraday Disk Dynamo


Simple a c generator

Simple a.c. Generator

  • According to the Faraday’s law of electromagnetic induction,

http://www.walter-fendt.de/ph11e/generator_e.htm


Simple d c generator

Simple d.c. Generator


Eddy current

Eddy Current

  • An eddy current is a swirling current set up in a conductor in response to a changing magnetic field.

  • Production of eddy currents in a rotating wheel


Applications of eddy current 1

Applications of Eddy Current (1)

  • Metal Detector


Applications of eddy current 2

Applications of Eddy Current (2)

  • Eddy current levitator

  • Smooth braking device

  • Damping of a vibrating system


Back emf in motors

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.


Back emf and power

Armature coils, R

Back emf, Eb

Driving source, V

Back emf and Power

  • So the mechanical power developed in motor

MultiplyingbyI, then


Variation of current as a motor is started

I

t

0

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.

Larger load

Zero load


The need for a starting resistance in a motor

The need for a starting resistance in a motor

  • When the motor is first switched on,  =0.

  • The initial current, Io=V/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.


Variation of current with the steady angular speed of the coil in a motor

I

0

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.


Variation of output power with the steady angular speed of the coil in a motor

Po

0

Variation of output power with the steady angular speed of the coil in a motor

  • The output power is maximum when the back emf is ½ V.


Transformer

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)


Transformer energy losses

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.


Designing a transformer to reduce power losses

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.


Transmission of electrical energy

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.


Direct current transmission

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.


Self induction

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.


Definitions of self inductance 1

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)


Definitions of self inductance 2

Definitions of Self-inductance (2)

  • Definition that describes the behaviour of an inductor in a circuit

Lis numerically equal to the emf induced in the circuit

when the current changes at the rate of 1 A in each second.


Inductors

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


Inductance of a solenoid

Inductance of a Solenoid

  • Since the magnetic flux density due to a solenoid is

  • By the Faraday’s law of electromagnetic induction,


Energy stored in an inductor

Energy Stored in an Inductor

  • The work done against the back emf in bringing the current from zero to a steady value Io is


Current growth in an rl circuit

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


Decay of current through an inductor

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.


Emf across contacts at break

-

+

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.


Switch design

-

+

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.


Non inductive coil

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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