Electromagnetic Induction

Faraday: “ convert magnetism into electricity”

What we know…• Current in a wire generates magnetic field

• Field of a solenoid is similar to that of a bar magnet

• Strength of magnetic field depends on permeability ( magnetic properties of magnet)

• Interaction between magnetic field and electric field results in a magnetic force ( as in electric motor)

Can a magnetic field induce a current in a wire?

Electromagnetic inductionElectromagnetic induction is the process of generating current by:

- moving a wire through a magnetic field, or -moving a magnetic field across a wire ( conductor)

[ relative motion between the magnetic field and a wire]

Michael Faraday’s Experiment

Closed loop of wire ( attached to galvanometer) is placed in a magnetic fieldNo current generated in wire if:

-Wire is stationary ( not moving)

-Wire moves parallel to magnetic field

Current is generated in wire if:

-Wire moves relative to the magnetic field

-Wire moves perpendicular to magnetic field

( maximum current generated)

Direction of the current

When the direction of magnetic field changes, the direction of the current changes

How can you tell the direction of the current?

4th Right Hand Rule

Thumb –

direction the wire moves ( velocity)

To determine the force on a charge or direction of conventional current

Fingers- magnetic field (B)

Palm-

direction of current

(Force on the charge)

Use the 4th Right Hand Rule to find the direction of the induced current in this wire

If the wire moves to the right, in which direction does the induced current move?

In what direction should the wire be moved, relative to the magnetic field to generate the minimum voltage?

0 voltage - Parallel to magnetic field

Electromotive Force (EMF)

EMF is the Potential Difference across a wire moving in a magnetic field ( or voltage given to a charge by a battery)

Measured in Volts (V)

Makes current flow from lower to higher potential

Wire moves through a magnetic field

Force is exerted on a charge in the wire

Charge moves in the direction of the force = work is done

Electrical Potential energy increases

Difference in potential is called induced EMF

-velocity of the wire, [v]

- the length of the wire [L]

- the magnetic field, [B]

EMF = BLv( sin θ) [ sin θ – if wire in not perpendicular to magnetic

field- find the perpendicular component of the velocity]

The Current induced in the wire depends on:

- v, L B and resistance in the wire

EMF depends on:

V= Voltage

v= velocity

Units of EMF• EMF = BLv

=

=

s

m x mx

Am

N

units

As

Nm=

C

J= Volts Q= It

C= As

W=Fxd

J=Nm

Potential energy is work done per unit charge = J/C = Volts

Solve 1• A 20m long wire moves at 4m/s at an angle of

450 through a magnetic field. An EMF of 40V is induced in the wire. What is the strength of the magnetic field?

EMF = BLv sinθ40V = B x 20 x 4 x sin 45B = 0.707 T

calculationsA straight wire, 0.30 m long, moves at a constant

speed of 10.0 m/s perpendicular to a 0.20-T

magnetic field.a.What is the induced EMF in the wire?

b. What is the current in the wire if it is part of a circuit with a resistance of 25Ω ?

L

v B900

R

Solve 2

EMF = Blvsinθ = 0.2 x 0.3 x 10 sin 90 = 0.6V

V = I x R0.6 = I x 25

• What is the induced emf in a wire 0.5m long moving at right angles to a 0.04T magnetic field with a velocity of 5m/s?

0.1

ChallengeA square wire loop moves perpendicularly through a magnetic

field of strength 1.75 T at a velocity of 2.5 m/s, The direction of the magnetic field is out of the page.

1. If the wire loop is 10 cm on a side, calculate the magnitude of the induced electromotive force in the wire segment:

a. AB.b. BC.

c. CD.d. With a total resistance of 130 Ω, calculate the induced current

in the wire loop.

EMF = Blvsin 90Use 4th right hand rule – EMF = 0V

No magnetic field – EMF = 0V

Complete exercise pg 675 no. 1-4

In which of these will maximum EMF be induced?

C A

D B

A C

B D

C

A

A

C

D

B

B

D

A: 0 degreesB: 90 degrees

C: 180 degrees D: 270 degrees

A and C

Application of induced EMF

e.g. Microphone

Application of induced EMF a diaphragm in a microphone is

attached to a coil of wire that is free to move in a magnetic field.

1. Sound waves vibrate the diaphragm

2. This moves the coil in the magnetic field.

3. The motion of the coil induces an EMF across the ends of the coil.

• Voltage can be increased by electronic devices

How is an EMF produced in a microphone

Sound wave converted to electrical signal

The induced EMF varies as the frequency of the sound varies. This converts sound energy to electrical signal

Magnetic flux

• Magnetic flux is the number of magnetic field lines passing through a surface placed in a magnetic field.

Magnetic flux and Faraday’s law of Induction

Magnetic field

Perpendicular component of magnetic field = Bcosθ

θ

Magnetic flux Φ is the product of the perpendicular component of the magnetic field and cross sectional area A

An external magnetic field passes through a region at an angle θ to the region

area

Φ = BA cos θ

Magnetic flux and Faraday’s law of Induction

Φ = magnetic flux Weber (Wb)

B = magnetic field strength Tesla (T)

A = cross sectional area (m2)

1 Wb = 1 T.m2

Magnetic flux Φ is the product of the perpendicular component of the magnetic field and cross sectional area A

Magnetic field linesperpendicular toSurfaceFlux is maximum

Magnetic field linesparallel to surfaceFlux is 0

Φ = BA cos 0

= BA

Φ = BA cos 90

= 0

Perpendicular to surface

Perpendicular to surface

The circular loop in the figure has a radius of 4 cm and makes an angle of 230 with a 2-T magnetic field. What is the flux through the loop?

Φ = BA cos θ

A = πr2

= π (4/100)2

= 5 x 10-3 m2= 2 x (5 x 10-3) cos 23= 9 x 10-3Wb

A square with sides of length 2 m is perpendicular to a magnetic field of strength 10 T. If the square is rotated by 60º, what is the change in magnetic flux through the square?

=BA cos θ - = BA cosθ

= 10 x 2 x 2 x cos 0 - 10 x 2 x 2 x cos 600

= 40 - 20

= 20 Wb

Magnetic field strength

Magnetic flux density = magnetic flux per cross sectional area

= Wb/m2

Φ = BA

Φ/A = B ( magnetic field strength)

= magnetic flux density

Adensity flux

magnetic

Faraday’s law of Induction :

Δt

ΔΦemf

Induced motional EMF is due to the rate of change of the magnetic flux

If a coil has a number of turns use the equation:

Δt

ΔΦemf N

problemA coil is made of 10 turns of wire and has a diameter of 5cm. The coil is passing through the field in such a way that the axis of the coil is parallel to the field. The strength of the field is 0.5T. a. What is the change in the magnetic flux? B. If an average EMF of 2V is observed, for how long was the flux changing?

-9.8 x 10-4

4.9 x 10-3s

recap:

1. What is the induced EMF in a wire that is 20 cm long, moving at an angle of 300 to a 0.08 T magnetic field with a velocity of 5 m/s

2. A flat 300 turn coil has a resistance of 3Ώ. The coil covers an area of 15cm2. At what rate must the magnetic field change in order to induce a current of 0.75 A in the coil? ( find the rate of change of magnetic field)

Δt

ΔΦemf N

Φ = BA cos θ

EMF = BLv( sin θ)

EMF = I x R

Electrical generators

Pg 675 PPP

Electrical generators• Invented by MICHAEL FARADAY• Electrical generators change mechanical energy to electrical

energyMade up of: Wire loop placed in

Magnetic field

How an electric generator works

The armature rotates in the magnetic field

When the wire is perpendicular to magnetic field, it cuts the magnetic field- EMF induced

To determine the direction of the induced current – use 4th right hand rule

How does the strength and direction of the current change?

To increase the strength of the magnetic field:

1. Wire is wound around an iron core – called an armature

To increase the induced EMF:

- Increase the length of the coil by increasing the number of turns

Wire is perpendicular to magnetic field

Wire is parallel to magnetic field

When is maximum current produced?

When coil is horizontal ( 900 to magnetic field)Maximum EMF induced

When coil is vertical (00 to magnetic field)Minimum (0) EMF induced

EMF is not induced in this side of the coil (AB or CD)

Using the 4th right hand ruleWe see that the current will move to the side of the wire- no EMF induced.

if the coil moves clockwise ( as shown), current moves anticlockwise ( use right hand rule)

Magnetic field reverses direction every ½ turn- produce alternating current

Is current induced in all sides of the loop?

A B

CD

EMF induced = BLv(sinθ) L= AD or BC

Voltage-time graph for ac current

Equation for this graph:

V= Vmax cos 2πft f = frequency of alternation

How can we increase the frequency of a generator?

Increase the number of magnetic pole pairs

Motors and Generators

Converts mechanical energy to electrical energy

Mechanical energy turns armature in a magnetic field.

Induced voltage cause current to flow

Converts electrical energy to mechanical energy

Voltage is placed across an armature in a magnetic field

Voltage cause current to flow in the coil- armature turns

EMF depends on the length of wire.Increasing the number of loops in the armature increases the wire length,magnetic field induces an EMF.

Electric generatorMade up of a number of wire loops placed in a strong magnetic field

to increase the strength of the magnetic field, wire is wound around an iron core (armature) which rotates freely

As the armature turns, the wire loops cut through the magnetic field lines and induce an EMF.

the induced EMF produces an electric current

Electric generators

http://www.animations.physics.unsw.edu.au/jw/electricmotors.html#DCmotors

• PrincipleWhen a straight conductor is moved in a magnetic field, then a current is induced in the conductor.

• It is based on electromagnetic induction.

Explain the construction and working of an AC generator

Explain the construction and working of an AC generator

Made up of Permanent magnets

armature

•An energy source turns the armature at a fixed frequency. E.g. 60Hz in US, 50Hz - UAE

made up of a number of turns of wire on a soft iron core

brush & slip-rings: allows the armature to turn freely and allows the current to pass into the external circuit

The Current changes direction in the external circuit

• As the armature turns, the alternating current varies between a maximum value and zero

• How is the AC generator different from a motor?

Alternating current AC generators

• As the armature turns the velocity vector perpendicular to the magnetic field changes.The flux changes continuously with timeThis change in magnetic flux induces an emf

The direction of the induced emf is reversed after every half rotation of the coil.Thus in one rotation of the coil, the current changes its direction twice in the coil

Average power

• power varies because both current and voltage vary.

• Power is always positive because

I and V are either both positive or both negative.

The power produced by a generator is the product of the current and the voltage.

P = I x V

DC generators

Split ring commutators :

Act as full-wave rectifiers

change the alternating current in the coil to DC in the external circuit

AC generator DC generator

Similarities: Both change mechanical energy to electric energy both have commutators with brushes, magnetic field with armature

Differences:1.2 Slip rings which causes AC current in the external circuit

1.Has split rings which changes AC current in the internal circuit to DC in external circuit- act as full wave rectifier. ( Diodes also act as rectifiers)

Average power

PAC, is half the maximum power

Effective currentP = I2R

If we express AC POWER in terms of effective current, then

PAC = I2eff R

But PAC = ½ PACmax

I2eff R = ½ I2

max R

Ieff = 0.707 Imaxmaxeff I

2

2I

Effective Voltage

• Effective voltage, known as RMS (root mean square) voltage. ( In US – 120V, in UAE- 220V).

• Why is effective current ( voltage) less than the maximum value?

In AC generators, power varies from a maximum to zero value.

The effective current ( voltage) is a constant value of current that would cause the average power to be dissipated

formulae

Ieff = 0.707 Imax

Veff = 0.707 Vmax

http://www.thatquiz.org/tq/classpage?0010123468a4d03