Electromagnetic inductionElectromagnetic induction

In this section you will learn:The concept of electromagnetic inductionWhat effects the size and direction of the induced current/emfExperiment to demonstrate the electromagnetic induction.Concept of magnetic flux and unitUnderstand and use Faraday's laws of electromagnetic induction.Understand and use Lenz's lawHow electricity is generated using generators.Experiment to demonstrate Lenz's lawUnderstand a.c. current and voltage.Calculate r.m.s I and V values for a.c.Understand mutual and self inductionEffect of inductors ón a.c.Uses of inductors.a.c. And capacitanceTransformers, step up and step down and uses.

We have seen that if you have a current flowing in a magnetic field, a force will act on it to try to move it.

A current is induced in a conductor which moves inside a magnetic field.

What might happen if you move a wire in a magnetic field?

Electromagnetic inductionElectromagnetic induction

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Electromagnetic inductionElectromagnetic induction

If you rotate the magnet in the coil or move it in or out of the coil or move the coil around the magnet an Emf is induced.Rem: show phet simulation

Electromagnetic inductionElectromagnetic induction

As long as there is a changing magnetic field an emf is induced.

Whenever the magnetic field passing through a coil changes and emf is induced. This is called electromagnetic inductionelectromagnetic induction.Show using datastudio with a coil, voltage and current sensor.Show using datastudio with a coil, voltage and current sensor.

The size of the emf depends on:The strength of the magnetic fieldThe number of loops (turns) in the coilThe speed of the coil or magnet.

The direction of the emf depends ón:If the magnet is approaching the coil or moving away from it.If a north or south pole goes in first.

Electromagnetic inductionElectromagnetic induction

Magnetic FluxThis a measure of the strength of the magnetic field. The greater the magnetic flux the greater the induced emf.It depends on:

The area of the magnetic field at right angles to the wire/coil.The magnetic flux density B (strength of the magnetic field/unit

area

Magnetic flux = magnetic flux density x area

= BA (usually measured in Wb)

1 Wb = 1T m2

Faraday’s law of electromagnetic inductionThe emf (E) induced in a conductor, due to a changing

magnetic field, is proportional to the rate of change of flux

E = (d/dt).

Rotating Magnet

Doubling the speed of rotation will double the emf i.e. Faraday’s law is shown to be true.

For leaving certificate physicsE = change in or E = final flux – initial flux Time time

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Electromagnetic inductionElectromagnetic induction

You must be able to discribe and experiment to demonstrate Faraday's law of electromagnetic induction

Electromagnetic inductionElectromagnetic induction

Clearly if you have a coil of N turns, = BAN

In fact for a coil of N turns (loops)

E = NChange in flux

Time taken

Lenz’s law

The induced emf, E, is created such as to oppose the motion that created it.

Induced emf

Opposes the motion that created it

Rate of cutting of flux

Electromagnetic inductionElectromagnetic induction

E = - dϕdt

You must be able to discribe and experiment to demonstrate Lenz's law (show using Al ring, copper wire, strong magnet)

Electromagnetic inductionElectromagnetic induction

Notice the S pole in the coil to oppose the motion of the magnet towards it. (How?)

Notice the N pole of the coil to oppose the motion of the magnetic away from the coil. (How?)

Mains electricity is high voltage and its direction changes 100 times every second (alternating current). This makes its behaviour very different to the electricity that we get from a cell or battery.

Time Time

VoltageVoltageThis is direct

current (dc).This is direct

current (dc).

VoltageVoltage

Time Time

This is

alternating

current (ac) just

like the mains!

This is

alternating

current (ac) just

like the mains!

Alternating Current Alternating Current

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VoltageVoltage

Time Time

T

The arrow marks the time taken for one complete oscillation. This is the time period. In Ireland and Europe it is 0.02s (1/50th of a second).

The frequency is the number of complete cycles per second. That is 50 in Ireland. We say the mains frequency is 50Hz.

Alternating Current Alternating Current

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The European Commission has mandated that all EU countries harmonise their mains voltages.

The regulations state that the voltage should be in the range of 230V plus 8% and minus 10%

I.e. between 207.0V and 243.8V.

Alternating Current Alternating Current

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This value, 230V, is called the RMS value – the root mean square value.

It is the DC equivalent that would cause the same heating effect.

We can obtain the peak voltage by multiplying the RMS voltage by √2.

Alternating Current Alternating Current

Time Time

Peak voltage

Vp

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Alternating Current Alternating Current

R.M.S values of a.c.When we give a value of say 5A to an a.c current we mean it has the same heating effect as 5A d.c.

It has a maximum value of greater 5A in each direction. This 5A value is called the rms value.(Note we take rms (root meán square) values as way averaging the the a.c I and V as an ordinary average would give zero.)The following are the rms equations for I, V and P

Irms

= I0 / 2 or I

o = I

rms x 2

Vrms

= V0 / 2 or V

o = V

rms x 2

P = Irms

X Vrms

or P = Irms

R2

I0 and V

0 are the max values of I and V respectively

Getting the electricity to your home is not an easy business. A great deal of energy could be lost in the cables that go from the power station to the local distribution point.

We know that V = IR and that P=IV

so we can see that P = I2R - this is an important result.

Suppose a long wire has a resistance of 2 and we pass a current of 10A through it. P = I2R = 102 x 2 = 200W

that means that 200W of power are wasted in the wireWhat if we put 10 times the current through it: 100A?

P = I2R = 1002 x 2 = 20000W

that means that 20kW of power are wasted in the wire10 times the current and 100 times the wasted power. For this very reason electricity companies must transmit their high powers at low currents.

Alternating Current Alternating Current

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Fortunately it is possible to do this by first stepping up the voltage (this lowers the current) and then transmitting it. It can finally be stepped down when it is close to the place that it will be used in.

Power Station

Step up transformer

Step down transformer

Consumer

High voltage, low current, low power loss

Low voltage, high current, less

dangerous for consumer

Alternating Current Alternating Current

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Consider two coils which are placed close to each other.

Induction Induction

If an alternating current is passed through one coil, it will produce an alternating magnetic field around that coil.

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Induction Induction

Notice how the changing magnetic field due to one coil, cuts the other coil.

It is just as if somebody is moving a magnet next to the coil on the right.

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Induction Induction

The result is that an alternating emf is induced in the coil on the right.

It is just as if somebody is moving a magnet next to the coil on the right.

Alternating

emf

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Induction Induction

Induction Induction

If a changing magnetic field in one coil induces an emf in a nearby coil this is called mutual induction.

The voltages across the two coils vary in direct proportion to the ratio of the number turns (N) on the coils. I.e.

Alternating

emf

N 1

N 2

=V 1

V 2 © TPS 2010

Induction Induction

The size of the induced emf is increased byHaving the coils closer togetherWinding the coils on the same soft iron core.Increasing the number of turns of both or either of the coils.

Demostrate mutual inductance using two coils.

Induction Induction

Self-inductance.Self-inductance.When an a.c current passes through a coil it induces an emf due to the changing magnetic field of the current. This induced emf oposes the varying emf that causes it. (called back emf)

The size of the back emf can be increased by winding the coil on a soft iron core.

Induction Induction

A.C. and inductorsA.C. and inductorsA coil has a greater resistance to a.c than d.c.

When a d.c flows through a coil its resistance is simply its ohmic resistance using V = I R

When a.c flows through a coil because of the constantly changing magnetic field the resistance is the ohmic resistance plus the resistance due to the back emf which opposes the current causing it.

The greater the self inductance the more resistance a coil offers to a.c.

Induction Induction

Uses of Inductors.Uses of Inductors. Smooth out variations in d.c power supply units. Tuning circuits for radios. Dimmer switches used in stage lighting.

Capacitors and a.cCapacitors and a.cCapacitors do not allow d.c to flow. (once charged)Capacitors do allow a.c to flowThis is because the capacitor charges and discharges as the current changes direction

Induction Induction

Induction Induction

If a changing magnetic field in one coil induces an emf in a nearby coil this is called mutual induction.

The voltages across the two coils vary in direct proportion to the ratio of the number turns (N) on the coils. I.e.

Alternating

emf

N 1

N 2

=V 1

V 2 © TPS 2010

Induction Induction

TransformersTransformers

This is the principle of a transformer – a device for changing voltages and currents.

If the voltages increase, the currents decrease and vice versa.

If the voltages increase, it is called a step-up transformer.

If the voltages decrease, it is called a step-down transformer.

If it was 100% efficient, then P1, the power input in the first coil (the primary) would be equal to P2, the power output in the second coil.

Since P=IV we can see that

IpVi = IsV0 and

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N p

N s

=V i

V 0

Induction Induction

However, two coils just placed next to each other would make a very inefficient transformer as much of the magnetic field from the primary windings would not pass through the secondary windings.

The field can be concentrated by placing both coils onto a continuous, laminated, soft iron core.

Primary

The input

Secondary

The output

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Induction Induction

However, two coils just placed next to each other would make a very inefficient transformer as much of the magnetic field from the primary windings would not pass through the secondary windings.

The field can be concentrated by placing both coils onto a continuous, laminated, soft iron core.

Primary

The input

Secondary

The output

The continuous nature of the core makes sure that as much of the field from the primary, passes through the secondary.

© TPS 2010

Induction Induction

However, two coils just placed next to each other would make a very inefficient transformer as much of the magnetic field from the primary windings would not pass through the secondary windings.

The field can be concentrated by placing both coils onto a continuous, laminated, soft iron core.

Primary

The input

Secondary

The output

Soft iron is used as it has no residual magnetism.

Work is not wasted by overcoming residual magnetism in the soft iron.

© TPS 2010

Induction Induction

However, two coils just placed next to each other would make a very inefficient transformer as much of the magnetic field from the primary windings would not pass through the secondary windings.

The field can be concentrated by placing both coils onto a continuous, laminated, soft iron core.

Primary

The input

Secondary

The output

The laminations of the core mean that it is made of thin sheets of soft iron, insulated from each other.

This stops eddy currents flowing in the core which would be a waste of energy, producing unwanted heat in the core.

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Induction Induction

Uses of TransformersUses of Transformers

Electricity in power stations is generated a high voltages 20 -30 kVand then stepped up to220- 400 kV to reduce loses in transmission of the power in the grid. This has to be reduced down to 220V for the domestic use.

Computers, televisions and all manor of electronic devices need transformers to supply the necessary voltage for the device.

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