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9.3 Motors and generators: 2. The generator

Syllabus reference (October 2002 version)
2. The relative motion between a conductor and magnetic field is used to generate an electrical voltage	Students learn to: outline Michael Faraday's discovery of the generation of an electric current by a moving magnet define magnetic field strength B as magnetic flux density describe the concept of magnetic flux in terms of magnetic flux density and surface area describe generated potential difference as the rate of change of magnetic flux through a circuit account for Lenz's Law in terms of conservation of energy and relate it to the production of back emf in motors explain that, in electric motors, back emf opposes the supply emf explain the production of eddy currents in terms of Lenz's Law	Students: perform an investigation to model the generation of an electric current by moving a magnet in a coil or a coil near a magnet plan, chose equipment or resources for, and perform a first-hand investigation to predict and verify the effect on a generated electric current when: the distance between the coil and magnet is varied the strength of the magnet is varied the relative motion between the coil and the magnet is varied gather, analyse and present information to explain how induction is used in cooktops in electric ranges gather secondary information to identify how eddy currents have been utilised in electromagnetic braking

Extract from Physics Stage 6 Syllabus (Amended October 2002). © Board of Studies, NSW.
[Edit: 30 June 09]

Prior learning: Preliminary module 8.3.

outline Michael Faraday's discovery of the generation of an electric current by a moving magnet

In 1820, Hans Christian Oersted and Andre Marie Ampere discovered that an electric current produces a magnetic field. Faraday's ideas about conservation of energy led him to believe that since an electric current could cause a magnetic field, a moving magnetic field should be able to produce an electric current. Faraday demonstrated this in 1831.
Faraday attached two wires through a sliding contact to touch a rotating copper disc located between the poles of a horseshoe magnet. This was the same as moving a magnetic field near an electric circuit. This induced a continuous direct current. Faraday had invented the first electric generator. Prior to this, continuous electricity could only be produced by batteries or galvanic cells.
Faraday's explanation was that the electric current was induced in the moving disc as it cut a number of lines of magnetic force emanating from the magnet (the magnetic field). The wires allowed the current to flow in an external circuit where it could be detected.

perform an investigation to model the generation of an electric current by moving a magnet in a coil or a coil near a magnet

You should perform a first-hand investigation to model the generation of an electric current by carrying out a planned procedure, recognising where and when modifications to the materials and structures are needed and analysing the effect of these adjustments. Your teacher may plan an investigation for you or you may choose one similar to one of the following procedures.

Sample procedures

An electric current can be produced either by moving a magnet inside a coil or by moving a coil near a magnet, for example, by rotating it.

Connect an air-cored solenoid coil to a centre-reading galvanometer graduated in microamperes (μA). The coil should have a large number of turns or loops of fine wire, around 300–500, and have space to fit a bar magnet through it.

Microammeter connected to coil of many turns around a magnet

Select the strongest bar magnet or disc magnet that will fit into the coil. Move the magnet inside the coil and observe any movement of the galvanometer needle. A reading on the galvanometer demonstrates that an electric current has been generated.

Alternatively, a hand-operated demonstration AC/DC generator, of the kind found in most school science laboratories, can be used. The coil is rotated between the poles of either a horseshoe magnet or a pair of bar magnets with oppositely orientated poles.

Output from the generator can be tested in various ways:

Connect a lamp across the output terminals, with a centre-reading galvanometer graduated in milliamps (mA) in series with the lamp, and a voltmeter in parallel with the lamp.
Connect the output terminals to a CRO or a digital voltmeter.

Turn the generator by hand at different speeds and in each direction. Use the switch on the generator to change between AC and DC. Systematically observe and record the effects of any changes you make to the variables in the procedure.

An excellent Java applet of a simple generator can be seen at the following web site. The speed of coil rotation and the direction rotation can be changed and the commutator can be swapped for slip rings. The effect of these changes on the direction and magnitude of current produced can be seen.

How Do Electric Generators Work by Mark Orwell, eHow editor, eHow, How to do just about everything, USA

How An Electric Generator Works Wisconsin Valley Improvement Company, Wausau, Wisconsin, USA

define magnetic field strength B as magnetic flux density

Visualising a magnetic field involves imagining a large number of invisible magnetic flux lines “flowing” out of the north pole and into the south pole of a magnet. The magnetic flux lines are shown close together near the poles where the magnetic field is strongest but further apart at greater distances from the magnet. The magnetic field of a strong magnet is represented by showing a larger number of magnetic flux lines than for the field of a weaker magnet.
Magnetic flux density is a measure of the number of magnetic flux lines passing through a unit area (one metre squared) and is represented diagrammatically by the number of magnetic flux lines drawn in a particular area. Magnetic field strength B at a point is defined to be the same as magnetic flux density.

describe the concept of magnetic flux in terms of magnetic flux density and surface area

Magnetic flux is the amount of magnetic field threading or “flowing through” a certain area A, such as the area inside a flat coil of wire. This is represented diagrammatically by the total number of magnetic flux lines that pass through area A.
The stronger the magnetic field at a point, the higher the magnetic flux density B is at that point and the more magnetic flux lines there are cutting or threading a given area. B is a measure of magnetic flux per unit area perpendicular to the direction of the field at a point in the field.
To find the total amount of flux passing through area A, we need to multiply the magnetic flux density B by the number of square metres in area A. This can be expressed mathematically as flux = flux density × area, or
In SI units, magnetic flux is measured in Webers (Wb) and magnetic flux density is measured in Webers per square metre (Wb m^-2)

plan, chose equipment or resources for, and perform a first-hand investigation to predict and verify the effect on a generated electric current when:

the distance between the coil and magnet is varied

the strength of the magnet is varied

the relative motion between the coil and the magnet is varied

Plan the investigation by identifying the dependent variable and all of the independent variables involved. Plan to change only one variable at a time, and develop strategies to ensure that all other independent variables are kept constant. Plan how you will identify, measure and record changes in the dependent variable. When planning to investigate the effect of changing the relative motion between the coil and the magnet, consider changes in relative speed, changes in relative direction of motion and changes in rotation.
Choose equipment or resources by identifying and setting up the most appropriate combination of equipment needed to undertake the investigation. Consider what type of coil would be best to use. Consider also how you could choose magnets of different strength without changing any of the other variables.
Perform the first-hand investigation by following your planned procedure. Before making a change to any variable, try to predict the effect of the change on the generated electric current by using what you have already learnt. Verify the effect by making the change and observing the size and direction of any generated current. Systematically record the effect of each change you make to the materials and procedure. When making observations, only write down what you can actually see happening. Remember that you cannot see magnetic flux lines.

Sample procedure

Distance between magnet and coil, strength of magnet and relative motion between coil and magnet are all independent variables. Each of these will be varied in turn while the others are held constant. The dependent variable, the current generated, will be measured with a centre-reading galvanometer graduated in microamperes (μA) which will indicate both the direction and the magnitude of any current generated. Choose a coil with a large number of turns, around 300–500, of fine insulated wire and with a cross sectional diameter large enough to fit a bar magnet through it. Select a pair of bar magnets that are of similar dimensions but different strength.

Varying the distance between the magnet and the coil

Lay a plastic ruler flat on the bench along the length of the coil as a distance guide for the magnet. Place the magnet at right angles to the coil against the edge of the ruler and slide it smoothly. Now turn the ruler on its edge so that only the thickness of the ruler separates the magnet from the coil, and slide the magnet along the ruler again.

For each trial, try to predict the effect of the change you make. Observe and record the direction and maximum deflection of the galvanometer needle to verify your prediction. Control other variables by using the same end of the same magnet and moving it at the same speed and in the same direction for each trial.

Microammeter connected to coil of many turns, magnet moved up and down the length of coil

Varying the relative motion between the magnet and the coil

Using the experimental set-up just described, with the ruler on its edge, vary the relative motion between the magnet and the coil by:

moving the magnet smoothly at different speeds;
moving the magnet smoothly at the same speed in each direction;
using each pole of the magnet in turn.

Other variables are controlled by using the ruler to maintain the same distance between the magnet and the coil and by using the same magnet in each trial.

Now insert one end of the magnet into the coil and vary the relative motion between the magnet and the coil by:

moving the magnet smoothly into the coil at different speeds;
moving the magnet smoothly at the same speed into the coil and out of the coil;
using each pole of the magnet in turn;
moving the magnet right through the coil and out the other end.

Control other variables by using the same magnet for each trial and by keeping the end of the magnet within and central to the coil to minimise the effect of changing distance.

For each trial, try to predict the effect of the change you make. Observe and record the direction and maximum deflection of the galvanometer needle to verify your prediction.

Varying the relative motion by rotating the coil in the field

Use a hand-operated demonstration AC/DC generator, of the kind found in most school science laboratories, to investigate the effect of changing the relative motion between the coil and the field by rotation of the coil. The coil is rotated between the poles of either a horseshoe magnet or a pair of bar magnets with oppositely orientated poles. Observe the orientation of the coils to the magnetic field. When the plane of the coil is parallel to the direction of the field, the long sides of the coil are moving at right angles to the field. When the plane of the coil is perpendicular to the field, the long sides of the coil are moving parallel to the field.

Connect a microammeter to the generator output terminals and turn the generator slowly. Observe the size of the induced current when the long sides of the coil are moving perpendicular to the field, parallel to the field and at intermediate angles.

Using magnets of different strength

Repeat any of the above procedures using another magnet of different strength. Try to predict the effect of changing to a stronger or weaker magnet. Observe and record the direction and maximum deflection of the galvanometer needle to verify your prediction. Control other variables by using two magnets of similar dimensions.

Sample observations

For a magnet of constant strength and the same relative motion between the coil and the magnet, the generated electric current increases as the distance between the coil and magnet decreases.

For a constant distance between the coil and the magnet, and the same relative motion between the coil and the magnet, the generated electric current increases as the strength of the magnet increases.

For a constant distance between the coil and the magnet and for a magnet of constant strength:

the direction of the generated electric current changes when the direction of the relative motion between the coil and the magnet is reversed;
the direction of the generated electric current changes when the polarity of the magnet is reversed; and
the magnitude of the generated electric current increases as the speed of the relative motion between the coil and the magnet is increased.

For a coil rotating in a magnetic field, the induced current varies smoothly from a maximum when the long sides of the coil are moving at right angles to the field, to zero when the long sides are moving parallel to the field

describe generated potential difference as the rate of change of magnetic flux through a circuit

Whenever there is relative motion between a conductor in a circuit and a magnetic field, the circuit cuts the magnetic flux. The rate at which the flux is cut can be increased by:
- decreasing the distance between the conductor and the magnetic field, as the flux lines are closer together nearer the magnet;
- increasing the strength of the magnet, as there are more flux lines in the same space in a stronger field than in a weaker field;
- increasing the speed of the relative motion between the conductor and the magnetic field, as the conductor cuts more flux lines per unit time; and
- increasing the angle between the direction of motion of the conductor and the direction of the magnetic field from near zero towards 90 degrees, as the conductor cuts the maximum number of flux lines per second when its motion is at right angles to the field.
Each of these changes also causes an increase in the current flowing in the circuit, and therefore the potential difference. Thus the generated potential difference increases as the rate of change of flux in the circuit increases.
The generated potential difference or electromotive force (emf) is defined to be equal to the rate of change of flux in the circuit.
Quantitatively, the potential difference or emf induced in a conductor is the amount of flux cut divided by the time taken .

In other words, .

This is Faraday's Law of electromagnetic induction. Where the circuit involves a coil, with multiple loops of the circuit cutting the same flux, the emf generated is in proportion to the number of coil turns (N) that cut the flux.

In this case, the emf generated is .

account for Lenz's Law in terms of conservation of energy and relate it to the production of back emf in motors

Lenz's law was first proposed by Heinrich Lenz (1804–1864). This law says: if an induced current flows, its direction is always such as to oppose the change in flux that produced it.
Consider the example where a current is produced by inserting a magnet into a coil connected into a circuit with a galvanometer to show current flow direction. If the south pole of a bar magnet is inserted into the coil the current induced in the coil will flow in a direction such that it produces a south pole opposing the insertion of the bar magnet. Pushing the bar magnet against that field means that work must be done.
If the same magnet is pulled out of the coil from the same end the current induced in the coil will be in the opposite direction so that it produces a north pole that attracts the south pole of the magnet being withdrawn. This attraction means work must be done to pull the magnet out of the coil.
Lenz's law follows from the Law of Conservation of Energy. That law says energy cannot be created nor destroyed but can simply change form. In the case of the magnet and coil, energy must be transferred to the coil to produce the induced current flow (electrical energy). That energy is the work done in inserting the coil or withdrawing it.
It is therefore necessary that work must be done against the magnet moving relative to the coil if it is to generate the emf in the coil. If it were not so, the induced magnetic field would accelerate the magnet, thus increasing the induced emf which, in turn would increase the strength of the induced field, further accelerating the magnet, and so on, contravening the Law of Conservation of Energy.
Electric motors use an external emf applied to the coils to produce an electtric current in the coils positioned in an external magnetic field. This current produces a magnetic field that interacts with the external magnetic field. As the coils rotate in the external magnetic field, an emf is induced in the coils due to the constantly changing magnetic flux threading the coils. By Lenz's Law, this induced emf is in the opposite direction to the external supply emf causing the rotation, and it has the effect of reducing the net emf applied to the coils. Because the induced emf is in the opposite direction to the supply emf, it is known as the back emf.

explain that, in electric motors, back emf opposes the supply emf

Back emf is the emf induced in the coils of a motor as they spin in the external magnetic field of the stator.
By Lenz's law the direction of that induced emf opposes the emf causing the motion of the armature. The current generated in the motor is an eddy current. The direction of the motor eddy current is such that it opposes the supply emf that produces the motion in the motor. The net emf applied to the coils equals the supply emf minus the back emf.
The back emf increases as the speed of the motor increases, until the net emf is just sufficient to provide the energy for the work the motor is doing, against its own internal friction and any load that is applied to it. If there were no back emf, the motor would continue to spin faster and faster indefinitely.
When a greater load is applied to the motor, the armature rotates more slowly and the back emf is reduced. This allows a greater current to flow through the coils, resulting in an increased torque to match the extra load.
At low speeds, when the back emf is small, the motor coils are protected by a series resistor from the large currents that could flow and burn out the motor. This resistor is switched out at higher speeds when the back emf replaces the role played by the resistor at low speed.

gather, analyse and present information to explain how induction is used in cooktops in electric ranges

Gather the information about how induction cooktops work from as many sources as possible such as the Internet, magazines and advertising material. You might also consider doing field research by seeking information from the sales staff at your local electrical appliance store.
Analyse the information by eliminating both extravagant advertising claims and minor details of difference between competing brands to find the general principles of operation of induction cooktops.
Present the information using diagrams or pictures supported by text.

Sample information

Each cooking area on the ceramic induction cooktop has one or more coils wound on ferromagnetic material under it. A high frequency alternating current is passed through these coils producing a fluctuating magnetic field. When a ferromagnetic-based pan is placed over the coils, eddy currents are induced in the base because of the fluctuating magnetic field. The eddy currents are trapped within the pan because the ceramic cooktop is an electrical insulator.

The pan must be made from a metal that has a high internal resistance to this induced AC current. The resistance to the rapidly oscillating currents within the pan results in heat being produced directly in the base of the pan. That heat is dissipated to the food in the pan and does the cooking. The ceramic cooktop itself is not heated other than by heat lost from the pan. The induction cook top works best when used with pans made of ferromagnetic metals such as stainless steel and cast iron.

An Internet site that gives the basics of an induction cooktop is Induction Cooking: How it Works The Owlcroft Company, USA. Scroll past Here's the basic idea, until you reach the box with 'Induction is a third method...'

gather secondary information to identify how eddy currents have been utilised in electromagnetic braking

To gather information efficiently from secondary sources, make sure that the information clearly identifies a use of electromagnetic braking, and that the braking effect occurs through the induction of eddy currents. Discard any information that is not relevant.
Use the information gathered to identify at least two examples where eddy currents are used to provide an electromagnetic braking effect. Outline how the eddy currents are produced and how this causes the braking effect.

Sample information

Eddy currents are used for electromagnetic braking in many free-fall amusement park rides. A copper plate attached to the ride capsule passes between fixed strong magnets near the bottom of the ride, inducing eddy currents and associated magnetic poles in the copper plate. Each fixed magnet in turn induces a like pole as the plate approaches and an opposite pole as the plate leaves. The combined effect of interaction between the permanent and the induced fields slows the ride down smoothly because the strength of the eddy currents in the plate is directly proportional to the speed of the plate moving between the poles. As the ride slows the braking force is reduced.

Some trains use electromagnets close to the metal rails to induce eddy currents in the rails. These eddy currents produce magnetic fields in the rails, a like pole ahead of each electromagnet and an opposite pole behind it. The interaction between the magnetic fields opposes the forward motion of the electromagnets and the train to which they are attached. Because the strength of the induced eddy currents is proportional to the speed of the train, the braking force is reduced as the train slows, resulting in a smooth stop.

Triple beam balances commonly used in school laboratories have an aluminium plate fixed to the end of the beam. As the beam swings, the plate passes through the field of a permanent horseshoe magnet. Eddy currents are induced in the plate, setting up magnetic fields and damping the motion of the balance.

explain the production of eddy currents in terms of Lenz's Law

An eddy current is a closed loop current that flows in a conductor, such as the iron core of a coil of an electromagnetic brake plate, when there is relative motion between the object and a magnetic field. The eddy current, flowing in a closed loop, acts like the current in a coil or solenoid and produces its own magnetic field. The polarity of this magnetic field depends on the direction in which the eddy current circulates.
Lenz's Law says if an induced current flows, its direction is always such that it will oppose the change of flux that produces it. That is, the polarity of the magnetic field produced by the eddy current is such that it opposes the relative motion of the magnetic field that induced the eddy current.
Consider the north pole of a magnet moving over and close to the face of an aluminium plate. By Lenz's Law, the circulation of an eddy current ahead of the moving magnet should produce a north pole that will repel the moving magnet. The direction of current flow to produce a north pole agrees with the direction of the induced emf in a conductor moving relative to a magnetic field, that is, down the plate within the region of the moving field. Similarly, Lenz's Law predicts that an eddy current induced behind the moving magnet will produce a south pole that will attract the moving magnet. Together these two induced poles oppose the motion of the magnet over the aluminium plate.