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Section v 23 Electromagnetic Induction

### Transcript of Section v 23 Electromagnetic Induction

Electromagnetic Induction23. Electromagnetic Induction Content

23.1 Laws of electromagnetic inductionLearning Outcomes (a) define magnetic flux and the weber. (b) recall and solve problems using = BA. (c) define magnetic flux linkage. * (d) infer from appropriate experiments on electromagnetic induction: (i) that a changing magnetic flux can induce an e.m.f. in a circuit, (ii) that the direction of the induced e.m.f. opposes the change producing it, (iii) the factors affecting the magnitude of the induced e.m.f. (e) recall and solve problems using Faraday's law of electromagnetic induction and Lenz's law. (f) explain simple applications of electromagnetic induction.

Magnetic flux The pattern of all magnetic lines should be continuous Early experimenters thought that there was a flow of something along these lines. This gave rise to the idea of magnetic flux which means flow Magnetic flux density can be considered as the number of lines of magnetic force per unit area of an area at right angles to the lines Magnetic flux (phi) can be thought of as the total number of lines

So, magnetic flux is the product of the magnetic flux density and the area normal to the lines of flux For a uniform magnetic field of flux density B which makes an angle with an area A, the magnetic flux is given by the expression = BA sin

The unit of magnetic flux is weber (Wb). 1 Weber is equal to 1 tesla m2 The concept of magnetic flux is used frequently when studying electromagnetic induction

Electromagnetic induction The link between electric current and magnetic field was discovered by Oersted in 1820. In 1831 Henry in US and Faraday in England demonstrated that an e.m.f. could be induced by a magnetic field. This effect is called electromagnetic induction Apparatus to demonstrate electromagnetic induction pg 336 fig 12.35 Physics by Chris Mee Following observations were made: An e.m.f is induced when The wire is moved through the magnetic field across the face of the pole-pieces The magnet is moved so that the wire passes across the face of the pole-pieces

An e.m.f. is not induced when The wire is held stationary between the pole pieces

The magnet is moved so that the pole pieces move along the length of the wire The wire moves lengthways so that it does not change its position between the poles of the magnet

Conclusions to be drawn That an e.m.f. is induced whenever lines of magnetic flux are cut. The cutting may be caused by a movement of either the wire or the magnet

The magnitude of the e.m.f. has been found to increase As the speed at which the wire is moved increases As the speed at which the magnet is moved increases If the wire is made into a loop with several turns

As the number of turns on the loop increases

Therefore the magnitude of the induced e.m.f. depends on the rate at which the magnetic flux lines are cut The term magnetic flux linkage is introduced to take into account 2 factors whereby change in magnetic flux linkage (N) = N All the above observations are summarised in Faradays Law of Electromagnetic Induction as, the e.m.f. induced is proportional to the rate of change of magnetic flux linkage

Now what about the direction of the e.m.f ? It has been noticed that the direction of the induced e.m.f. changes and that the direction is dependent on the direction in which the magnetic flux lines are being cut

This can be determined using Flemings RH rule First finger is the direction of the magnetic field Thumb is in the direction of motion Second finger gives the direction of the induced e.m.f. or current

Try pg 338 fig 12.38 Physics by Chris MeeConclusion from the above fig considering the law of conservation of energy, is that an electric current is a form of energy and this energy must have been converted from some other form.

movement of the wire against the electromagnetic force means that work has been done in overcoming this force and it is this force that is seen as electrical energy

Lenzs Law Lenzs law states that the direction of the induced e.m.f. is such as to cause effects to oppose the change producing it

Faradays Law of Electromagnetic Induction and Lenzs Law may be summarised using the equation,E = - d(N)/dt where E is the e.m.f. induced by a rate of change of flux linkage of d(N)/dt. The minus sign indicates that the induced e.m.f. causes effects to oppose the change producing it. g

Demonstation of convertion from mechanical energy to electrical energy Pg 339 fig 12.39 Physics by Chris Mee of spinning disc in a permanent magnetic field

As the disc spins it cuts through the flux lines of the magnet causing e.m.f. to be induced in the disc But, because the rate of cutting varies from one part of the disc to another as the radius varies, the e.m.f. will have different magnitudes in different regions

This e.m.f. induces currents of varying magnitude and direction in the disc called eddy currents which cause heating in the disc and dissipation of energy of rotation of the disc referred to as eddy current damping If the permanent magnet were to be replaced by an electromagnet, the spinning disc will slow down whenever there is a current in the electromagnet. This is the principle behind electromagnetic braking used in high speed trains

Example The uniform flux density between the poles of a magnet is 0.080 T. A small coil of area of cross-section 6.5 cm2 has 250 turns and is placed with its plane normal to the magnetic field. The coil is withdrawn from the field in a time of 0.26 s. Determine: a) the magnetic flux through the coil when it is between the poles of the magnet b) the change in magnetic flux linkage when the coil is removed from the field c) the average e.m.f. induced in the coil whilst it is being withdrawn Solution a) magnetic flux = BA sin = 5.2 x 10-5 Wb b) change in flux linkage = (N)final (N)initial = 0 (250 x 5.2 x 10-5) = -1.3 x 10-2 Wb c) induced e.m.f. = change in flux linkage/time taken = 0.050 V

The principle of the transformer In a transformer, an alternating current in one coil induces an alternating e.m.f. in the second coil. The ratio of the output (secondary) e.m.f. to the applied (primary) e.m.f. equals the ratio of the number of turns on the secondary coil to the number of turns on the primary coil Vs/Vp = Ns/Np gtb

Transformer considerations For a transformer which is 100% efficient (i.e. ideal transformer), input power = output power VpIp = VsIs hence Ns/Np = Vs/Vp = Ip/Is

In practice a transformer will have losses, some sources of losses being Loss of magnetic flux between the primary and secondary coils Resistive heating in the primary and secondary coils Heating of the core due to eddy currents

Heating of the core due to repeated magnetisation and demagnetisation

Although the use of soft iron reduces heating due to magnetisation and demagnetisation, due to its use to obtain high magnetic flux linkage, eddy currents cannot be prevented

This is reduced by laminating the core i.e. building the core from thin strips of soft iron which are electrically insulated from one another

Transmission of electrical energy Generating plants are often situated a long way from the cities they serve This means that whatever the means of generation, it is likely to be transmitted over long distances Thus there is power loss due to the I2R effects These effects can be reduced if the power is transmitted at a high voltage using transformers as step-up and step-down transformers Transformers used in transmission networks have very high efficiencies often over 98%

Example A town several kilometres from an electricty generating station, requires 120 kW of power on average. The total resistance of the transmission lines is 0.40 ohms. Calculate the power loss if the transmission is made at a voltage of (a) 240 V (b) 24 kV Solution Current using 240 V is calculated to be 500 A, and using 24 kV is 5.0 A

Using power loss P = I2R,for (a) we obtain power loss is 100 kW, i.e. more than 80% lost (b) we obtain power loss is 10 W, i.e. less than one-hundredth of 1% of the power requirement

Summary of laws of electromagnetic induction

Faraday's Law states that the magnitude of the emf induced is directly proportional to the rate at which the conductor cuts the magnetic field lines i.e. rate of change of magnetic fluxLenz's Law states that the induced current always flows in a direction so that it opposes the change which is causing it

when the N pole of a magnet moves towards one end of a solenoid, that end will become a magnetic N pole to oppose the motion of the magnet when the N pole is pulled away from the end of a solenoid, that end will become a magnetic S pole so as to oppose the motion of the magnet

The production of the electrical energy in the form of an induced current is actually the work done or a transformation from the mechanical energy required to go against the motion (conservation of energy).

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Application of electromagnetic inductionElectromagnetic induction is used to generate electricity in DC & AC generators

A small generator used to produce light in a bicycle lamp is called a dynamoThe huge generator that supplies electricity to our homes is called an alternator

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DC Generator

A generator is a device used for the generation of current through the rotation of rectangular conducting coils (armature) in a magnetic field. Together with a commutator and carbon brushes to convert AC to DC in one direction only i.e. rectification Reverse of a DC motor without the battery

When the coil is horizontal, the e.m.f. is a maximum. When the coil is vertical, the e.m.f. is zero.

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AC generator - AlternatorsAlte