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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. - 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

- 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

Lenzs Law

- The direction of the induced current is always so

as to oppose the change which causes the current.

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)

Faradays 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/ja

va/indcur/index.html

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/lenzla

w/index.html

Faraday Disk Dynamo

Simple a.c. Generator

- According to the Faradays law of electromagnetic

induction,

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

Simple d.c. Generator

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)

- Metal Detector

Applications of Eddy Current (2)

- Eddy current levitator

- Smooth braking device
- Damping of a vibrating system

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

Multiplying by I, then

- So the mechanical power developed in motor

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.

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.

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

- The output power is maximum when the back emf is

½ V.

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

- 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

- 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

- 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

- 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

- 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)

- 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)

- 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.

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

- Since the magnetic flux density due to a solenoid

is

- By the Faradays law of electromagnetic induction,

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

- 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

- 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

- 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

- 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

- 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.