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### Electromagnetism

## Electromagnetism

Lesson for 16-19

This topic develops a formal description of magnetic fields and moves on to electromagnetic forces and induction.

The scheme described follows a fairly standard approach that is similar to the order in which the topics appear in most exam specifications. The three main electrical machines, motor, generator and transformer, are covered at the end so that all the relevant physics will have been covered before they are discussed. It would be possible to introduce motors after Episode 412 but there would be problems in discussing back emf and eddy currents at this stage. Transformers can be used as a way of introducing the ideas of episode 415.

An alternative approach might be to introduce the idea of flux via the transformer and generator, offering a different way of thinking.

## Episode 410: Preparation for electromagnetism topic

Teaching Guidance for 16-19

- Level Advanced

Magnetic fields will have to be shown; iron filings are a standard way to do this, but you may also find a magnaprobe useful – this is a small magnet mounted in a universal joint so that it pivots freely in three dimensions. Fields will also have to be measured both for permanent magnets and with simple geometries of wires and coils. A Hall probe, especially one that is calibrated, is helpful but search coils can also be used; the latter will need a mains supply that can produce a current of a few amperes and/or a signal generator.

Some form of electron beam tube (Teltron tube

) is helpful in Episode 413 but an old black and white TV or oscilloscope plus a magnet can show the deflection of charged particles.

One or more sets of 120/240 turn coils and C-cores are useful when discussing flux while physically larger coils can help to develop ideas. If C-cores are not available, then retort stands (uprights) can be used for some work but the magnetic circuits will not be as good. A demountable transformer is great for some spectacular demonstrations.

Westminster motor kits

can show both motor and dynamo principles but there are many cheap motors available which will also operate as dynamos when turned by hand or attached to a falling weight.

## Main aims of this topic

Students will:

- describe the magnetic fields of permanent magnets and current-carrying conductors using lines of flux
- use the terms
*flux*and*flux density*in connection with magnetic fields - determine the force (magnitude and direction) on a current-carrying conductor in a magnetic field
- explain the operation of a simple electric motor
- determine the induced current or emf (magnitude and direction) when there is relative motion between a conductor and a magnetic field
- explain the operation of a simple generator and a transformer

## Prior knowledge

Students should have met ideas relating to permanent magnets, the magnetic field due to a current, and motors. They will probably have done some electromagnetic induction, probably including transformers but their ideas in this area are likely to be much hazier.

There are links to be made with other fields. It is helpful, but not essential, if both electric and gravitational fields have been studied. When considering the force on charged particles, particle accelerators etc., students will need to be familiar with the equations governing circular motion.

## Where this leads

An understanding of the motion of charged particles in electric and magnetic fields is vital when studying particle physics.

You may wish to touch on the relationship between electromagnetic fields and electromagnetic radiation (and the work of James Clerk Maxwell), but this idea is rather tenuous for students at this level.

Electromagnetic theory is one of the cornerstones of physics, and a grasp of these ideas is fundamental for students who are going on to future studies of physics, chemistry or engineering.

### Up next

### Describing magnetic fields

## Episode 411: Describing magnetic fields

Lesson for 16-19

- Activity time 110 minutes
- Level Advanced

The field around a permanent magnet should be familiar to your students. In practice, where we want a controllable field, we use electromagnets. In this episode, students learn about these fields and the factors that determine their strength and direction.

Lesson Summary

- Demonstration and discussion: The field around a permanent magnet (20 minutes)
- Student experiment: Field plotting (20 minutes)
- Student questions: Revision questions on magnetic fields (20 minutes)
- Student experiments: Measuring flux densities (30 minutes)
- Discussion: Mathematical formulae (10 minutes)
- Student questions: Calculating flux density (10 minutes)

## Discussion and demonstrations: The field around a permanent magnet

Your specification may require the study of the magnetic field due to a permanent magnet but even if this is not the case, such work forms a good introduction to magnetic fields.

The use of two permanent magnets will remind students that there is a magnetic field around each magnet. (This can be done quickly with an OHP or by allowing the students to experiment with a pair of magnets.)

Like other fields, the magnetic field is a way of describing a region of space where other magnets will experience a force. It can be represented by field lines that show both the size and direction of the force.

Teacher: How is the field strength represented?

Student: By the spacing of lines.

Teacher: How is its direction shown?

Student: By arrows showing the direction a compass points or free north pole

moves.

Teacher: Can we find a unit

or free

pole?

Student: No

A discussion of why not will introduce/remind students of magnetic domains.

If there is no unit pole

, then in any definition of the magnetic field, it is not possible to simply extend the idea of unit charge/mass found in electric and gravitational fields.

How can we show up magnetic fields? This gives the opportunity to do some field plotting with iron filings or plotting compasses. There may be a computer program available to extend this further.

If your specification requires it, then this is a good time to define neutral points as places where two or more fields cancel out.

**Iron filings and a horseshoe magnet (Advancing Physics)**

## Student experiment: Field plotting

Having covered magnetic fields for permanent magnets, you can move on quickly to revise the basic magnetic field patterns due to the electric current in a long straight wire, small flat coil and solenoid. Again, this revision is a reminder of pre-16 ideas and demonstrations.

Students can look at some field patterns. If you use the worksheet, you will have to explain that flux is a new term that, for the moment, is simply being used as another word for the field pattern. Its significance will become much clearer quite quickly and it would probably confuse students if a more formal approach were used at this stage. The work is useful because it introduces alternating fields from an alternating current and shows how a search coil can be used to investigate these.

Episode 411-1: Magnetic field shapes seen as flux patterns (Word, 174 KB)

For some specifications, this will serve as a good revision of the basic pre-16 ideas used to describe magnetic fields and it will be possible to move quickly on to the idea of flux density and the force on a conductor.

## Student questions: Revision questions on magnetic fields

The ideas covered above can be reinforced with an activity based on using magnets in automatic train protection. One section suggests that students check that

but this could be made into a written exercise before a couple of questions are attempted.

Episode 411-2: Brush up on magnetism (Word, 43 KB)

Some more questions, revising basic ideas about magnetic fields.

Episode 411-3: Magnetism reminders (Word, 39 KB)

## Student experiments: Measuring flux densities

Some specifications require a more detailed investigation of the magnetic fields due to currents.

Your students should be able to measure the fields due to a long straight wire (sometimes a difficult experiment in which to get good results), a small flat coil and a solenoid. There are many possible approaches and the choice of apparatus will depend on what you have available. A calibrated Hall probe is useful, but the nature of the relationships can be deduced with ac and a search coil. (If you use a calibrated probe then you will need to explain that the unit for field /flux density is the tesla (T) and that this will be defined very soon.)

Whichever flux measurement technique is available, you need only set your students the task of establishing how the flux density depends on the current flowing and the distance (radial distance from a long wire, and along the axis of a flat coil or solenoid).

Episode 411-4: Fields near electric currents (Word, 198 KB)

## Discussion: Mathematical formulae

For a long, straight, current-carrying wire, students will probably find that the field is proportional to the current but the 1r relationship for distance is not always easy to confirm.

Offer them the equation

*B* = μ_{0}*I*2 π *r*

where
μ_{0} = 4 π × 10^{-7} N A^{-2}
is a constant known as the permeability of free space, and ask if their results are compatible with this.

For a solenoid, students should be able to check the relationship of field to both current and the number of turns per unit length.

Hence

*B* = N *I*μ_{0}*L*

The mathematical formula for the field for a small flat coil is not required.

For a coil wound around iron field is given
*B* = N*I*μ*L* where μ depends on the type of iron or other magnetic core material.

## Student questions: Calculating flux density

Episode 411-5: Flux and flux density (Word, 96 KB)

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### Up next

### The force on a conductor in a magnetic field

## Episode 412: The force on a conductor in a magnetic field

Lesson for 16-19

- Activity time 70 minutes
- Level Advanced

Having reminded your students that magnetic fields can be found near permanent magnets and in the presence of an electric current, the next step is to show how the field

can be quantified. Again, students should know that a conductor carrying a current in a magnetic field will experience a force and will probably remember that Fleming's Left Hand Rule can be used to find the direction of that force.

Lesson Summary

- Demonstrations: Leading to
*F*=*B**I**L*(15 minutes) - Discussion: Factors affecting the force (15 minutes)
- Discussion: Formal definitions (20 minutes)
- Student questions:
*B**I**L*force calculations (20 minutes)

## Demonstration: Leading to *F* = *B**I**L*

Several quick experimental reminders are possible.

Episode 412-1: Forces on currents (Word, 79 KB)

Episode 412-2: An electromagnetic force (Word, 53 KB)

These lead on to a further experiment in which the relationship *F* = *B**I**L* can be established.

Episode 412-3: Force on a current-carrying wire (Word, 43 KB)

## Discussion: Factors affecting the force

The experiments above lead to the conclusion that the force *F* on the conductor is proportional to the length of wire in the field, *L* , the current *I* and the strength

of the field, represented by the flux density *B* . (There is also an angle factor

to consider, but we will leave this aside for now.)

Combining these we get *F* = *B**I**L*

(It can help students to refer to this force as the

.)*B**I**L* force

Students will probably know that electric and gravitational fields are defined as the force on unit charge or mass. So by comparison, *B* = *F**I**L*
, and this gives a way of defining the magnetic field strength

. Physicists refer to this as the *B*-field or magnetic flux density which has units of N A^{-1} m^{-1} or tesla (T).

A field of 1 T is a very strong field. The field between the poles of the Magnadur magnets that are used in the above experiment is about 3 × 10^{-2} T while the Earth's magnetic field is about 1 × 10^{-5} T.

If your specification requires, you will need to develop the angle factor seen in the experiment into the mathematical formula:

*F* = *B**I**L*sin( θ ).

For the mathematically inclined, it can be shown that the effective length of the wire in the field (i.e. that which is at right angles) is *L*sin( θ ). If students find this difficult, then it can be argued that the maximum force occurs when field and current are at right angles,

θ = 90 °

(sin( θ ) = 1),

and that this falls to zero when field and current are parallel,

θ = 0 °

( sin( θ ) = 0 )

## Discussion: Formal definitions

Some specifications require a formal definition of magnetic flux density and/or the tesla.

The strength of a magnetic field or magnetic flux density *B* can be measured by the force per unit current per unit length acting on a current-carrying conductor placed perpendicular to the lines of a uniform magnetic field.

The SI unit of magnetic flux density *B*
is the tesla (T), equal to 1 N A^{-1} m^{-1}. This is the magnetic flux density if a wire of length 1 m carrying a current of 1 A as a force of 1 N exerted on it in a direction perpendicular to both the flux and the current.

Study of the force between parallel conductors leading to the definition of the ampere may be required. Students may already have seen the effect in your initial experiments but this may need to be repeated here. The effect can be explained by considering the effect of the field produced by one conductor on the other and then reversing the argument.

(The most common alternative approach relies upon field lines only and describes a catapult effect

from regions where the field lines are tightly packed into regions where the lines are more widely spaced.)

The force between parallel conductors forms the basis of the definition of the unit of current, the ampere. A formal definition is not usually required but students should realize that in a current balance (such as was used above) measurement of force and length can be traced back to fundamental SI units (kg, m, s) leaving the current as the only unknown

.

Some students are likely to be interested in the formal definition which is:

that constant current which, if maintained in two straight parallel conductors of infinite length, of negligible cross-section, and placed 1m apart in a vacuum, would produce a force of 2 × 10

.^{-7} newton per metre of length

## Student questions: *B**I**L* force calculations

Episode 412-4: Forces on currents in magnetic fields (Word, 35 KB)

Although the electric motor could be discussed here, it is probably better to leave this until after electromagnetic induction has been covered so that the back emf can be included.

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### Up next

### The force on a moving charge

## Episode 413: The force on a moving charge

Lesson for 16-19

- Activity time 150-170 minutes
- Level Advanced

Here you can extend the idea of a magnetic force on a current to consider moving charges.

Lesson Summary

- Demonstration: Bending an electron beam (20 minutes)
- Discussion: Deducing
*F*=*B**q**v*(30 minutes) - Discussion: Applications of
*F*=*B**q**v*(20 minutes) - Demonstration: Measurement of e/m for electrons (20 minutes)
- Discussion: Particle accelerators (10 minutes)
- Discussion: Velocity selectors and mass spectrometers (10 minutes)
- Discussion: The Hall effect (10 minutes)
- Discussion: Astronomical applications (10 minutes)
- Student questions: Applications of
*F*=*B**q**v*(20-40 minutes per set)

## Demonstration: Bending an electron beam

If a fine beam electron tube is available, the sight of the paths left by electrons travelling in a circular path when a magnetic field is applied makes a good introduction to this episode. If the apparatus is not available, then using a magnet to distort a black and white TV picture offers an alternative but avoid a colour TV where lasting damage can occur.

Episode 413-1: Deflecting electron beams in a magnetic field (Word, 139 KB)

## Discussion: Deducing *F* = *B**q**v*

Episode 412 talked about the force on a conductor carrying a current in a magnetic field. Any moving charge is an electric current, whether or not the charge is flowing through a material or not. Therefore, it is not unreasonable to expect to find a force on a charged particle moving through space.

Suppose we have such a particle with a charge *q*, moving at a speed *v*, at right angles to a magnetic field of flux density *B* . In a time *t* , the charge will move a distance *L* = *v* × *t* and is equivalent to a current
*I* = *Q**t*.

force on the current = *B**I**L*

force = *B**I*(*v* × *t*)

Rearrange to get:

force = *B*(*I* × *t*)*v*.

And simplify to get:

*F*_{magnetic} = *B**q**v*

If the field and current are at an angle θ , then the formula will be modified to
*F*_{magnetic} = *B**q**v*sin( θ )

If the particle is moving at right angles to the field, then the left hand rule shows that the force will always be at right angles to the direction of motion. This means that the particle will move in a circle of radius *r*.

centripetal force = *B**q**v*

*B**q**v* = *m**v*^{ 2}*r*

You can rearrange this to get an expression for the momentum:p

*m**v* = *B**q**r*

## Discussion: Applications of *F* = *B**q**v*

If we write *e* for the electronic charge, the equation becomes
*F* = *B**e**v*
, and you might refer to this as the Bev force

.

There are many applications of this force, several of which can provide interesting experiments or demonstrations. You will need to select those that match the requirements of your specification

## Demonstration: Measurement of e/m for electrons

Historically this experiment, performed by J J Thomson in 1897,is of great significance. It may be possible for you to repeat his experiment using electric and magnetic field to deflect the electron.

Episode 413-2: Measuring the charge to mass ratio for an electron (Word, 214 KB)

## Discussion: Particle accelerators

Linear accelerators make use of an electric field to accelerate particles but other accelerators from the early cyclotron to the modern facilities such as at CERN are circular

and make use of magnetic fields. If your specification requires then the operation of the cyclotron will have to be covered.

## Discussion: Velocity selectors and mass spectrometers

There is a wide range of these both of historical and modern interest. Again there is a chance to compare the effects of electric and magnetic fields. If students are studying chemistry, you can draw on their knowledge of mass spectrometers to emphasise the value of these techniques.

## Discussion: The Hall effect

This is worth discussing if your students have used a Hall probe to measure magnetic flux densities in

As electrons move through a piece of n-type semiconductor through which a magnetic field passes, then the electrons experience a force (Fleming's left hand rule) which moves them to one side of the semiconductor slab. An electric field builds up giving a force in the opposite direction. Eventually, the two forces balance such that;

*B**e**v* = *E**e*

and since

*E* = *V*_{Hall}*d*

*B**e**v* = *V*_{Hall}*d**e*

So the Hall voltage,
*V*_{Hall} = *B**v**d* , gives a way of measuring the *B*-field.

## Discussion: Astronomical applications

There is a wide range of interesting possibilities here.

Close to home, the motion of electrons in the ionosphere allows radio communication over large distances and leads to the aurora borealis at times of great solar activity.

This solar activity itself is the result of the interaction of charged particles in the Sun with the magnetic fields on and above the Sun's surface.

At greater distances, the acceleration of electrons in the intense magnetic fields of active galaxies and neutron stars is a source of radio and X-ray emissions (amongst others).

## Student questions: Applications of *F* = *B**q**v*

Many of these applications can be studied further with the questions that follow.

Episode 413-3: Deflection with electric and magnetic fields (Word, 89 KB)

Episode 413-4: The cyclotron (Word, 49 KB)

Episode 413-5: The Hall effect (Word, 65 KB)

Episode 413-6: Charged particles moving in a magnetic field (Word, 65 KB)

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### Electromagnetic induction

## Episode 414: Electromagnetic induction

Lesson for 16-19

- Activity time 200 minutes
- Level Advanced

Students will already have ideas about electromagnetic induction. In this episode, your task is to develop a picture of induction in which it is the cutting of lines of flux by a conductor that leads to an induced EMF or current.

Lesson Summary

- Student experiment: Wire, magnet, meter (10 minutes)
- Discussion and demonstration: Induction effects (20 minutes)
- Discussion: More about flux and flux linkage (40 minutes)
- Student questions: On flux linkage (20 minutes)
- Student experiments: Investigating induction (20 minutes)
- Demonstrations: Related effects (20 minutes)
- Student questions: Induced EMFs (30 minutes)
- Discussion and demonstration: Eddy currents (20 minutes)
- Student questions: Eddy currents and Lenz's law (20 minutes)

## Student experiment: Wire, magnet, meter

Start with a simple experiment involving a coil of wire and a voltmeter. This will give you a chance to assess the knowledge that students bring to this section.

Episode 414-1: Faraday’s law (Word, 26 KB)

## Discussion and demonstrations: Induction effects

A good starting point is to revise the pre-16 level ideas that your students should have about electromagnetic induction.

The first two demonstrations involve moving a wire in a magnetic field and then a permanent magnet into and out of a small coil. In both it is important to emphasise that:

electricity

is only produced while something is moving- the faster the movement, the more
electricity

we get

Introduce the idea of flux cutting

. Use your fingers to represent the flux lines; show how the conductor moves so as to cut the lines of flux. If you move the conductor *along* the lines of flux, no current is induced.

The third demonstration shows that movement is not essential and that changing the field near a coil has similar effects to a moving magnet.

(The demonstration with a dynamo adds little at this stage and could be delayed until generators are discussed further.)

Episode 414-2: Electromagnetic induction (Word, 62 KB)

## Discussion: How is the electricity

made?

The demonstrations have shown that making

electricity involves magnetic fields, but what is really going on? Your students already know that charges moving across a magnetic field experience a force (the *B**I**L* force). Now, the metal of a conductor contains mobile charges, the conduction electrons. What happens to these if the conductor is moved across a magnetic field?

Consider a conducting rod PQ moving at a steady speed v perpendicular to a field with a flux density *B*. An electron (negative charge*e*) in the rod will experience a force (*B**e**v*) (Fleming's left hand rule) that will push it towards the end Q. The same is true for other electrons in the rod, so the end Q will become negatively charged, leaving P with a positive charge. As a result, an electric field *E* builds up until the force on electrons in the rod due to this electric field (*E**e*) balances the force due to the magnetic field.

*E**e* = *B**e**v*

so

*E* = *B**v*

For a rod of length *L*

*E* = *V**L*

Hence the induced EMF

*E* = *B**L**v*

Clearly what we have here is an induced EMF (no complete circuit so no current flows) and already we can see that more rapid movement gives a greater induced EMF.

Now consider what happens when the EMF drives a current in an external circuit. To do this, imagine that the rod moves along a pair of parallel conductors that are connected to an external circuit.

The EMF will now cause a current to flow in the external resistor R. This means that a similar current flows through the rod itself giving a magnetic force, BIL to the left.

(L is now the separation of the two conductors along which the rod PQ moves.) An equal and opposite force (to the right) is needed to keep PQ moving at a steady speed.

The work done in moving the rod will equal the energy dissipated in the resistor.

In a time *t*, the rod moves a distance
*d* = *v* × *t*

Work done on the rod = *B**I**L**v**t*

Energy dissipated in R = power × time

Energy dissipated in R = EMF*v**t*

giving

*B**I**L**v**t* = EMF*v**t*

or, as before,

*E* = *B**L**v*

But in this case it can be seen that the electrical circuit encloses more magnetic field as the rod is moved along and that in one second, the extra area enclosed will be

*v* × *l*.

i.e.
induced EMF, *E* = *B* × area swept out per second

E = *B**A**t*

We have already called *B* the flux density, so it is perhaps not surprising that the quantity *B* × *A* can be called the magnetic flux, *F*.

Thus
induced EMF = *F**t*

induced EMF = rate of change of flux

And more generally

*E* = d *Φ* d *t*.

How can the induced EMF be increased? Discussion should lead to:

- moving the wire faster – d
*A*d*t*increased – rate of change of flux increased - increasing the field (and hence the flux) – rate of change of flux increased

But there is a further possibility and this is to increase the number of turns of wire N in our circuit. By doing this, the flux has not been altered but the flux linkage (N × *F*) will have increased. Hence it is more correct to say that

induced EMF = rate of change of flux linkage

*E* = N × d *F* d *t*

This relationship is known as Faraday's law: – when the flux linked with a circuit changes, the induced EMF is proportional to the rate of change of flux linkage.

Finally, remind your students that the magnetic force on our simple generator (a) (b) was in a direction which would make the bar slow down unless an external force acted. This is an example of Lenz's law: – the direction of the induced EMF is such that it tends to oppose the motion or change causing it.

To include this idea in our formula, a minus sign has to be introduced, giving;

*E* = − N × d *F* d *t*

## Discussion: More about flux and flux linkage

We have two formulae:

Flux,
*F* = *B* × *A*

Flux linkage
N*F* = N*B**A*

When using these formulae, it is important to realize that *B* should be at right angles to the area *A*. If this is not the case, then it is the component of the field perpendicular to *A* that should be used.

## Units:

Recall that the tesla (T) is defined from *F* = *B**I**L* , so
1 T = 1 N A^{-1} m^{-1}.

The units for flux are thus N A^{-1} m. This unit is known as the Weber (Wb).

Flux linkage is measured in Weber-turns (Wb-turns).

## Student questions: On flux linkage

Although it is better to delay questions about Faraday's law until after more experimental work has been done, the relationship between flux, flux density and flux linkage should be reinforced with a question or two.

Episode 414-3: Sketching flux patterns (Word, 269 KB)

## Student experiments: Investigating induction

To support the theory, it is important that students look at electromagnetic induction experimentally in more detail than was met in the initial demonstration. What you choose to do will depend on what apparatus is available.

The experiment suggested here is based on coils (120/240 turns) linked by iron cores. Again the basics of Faraday's law are shown and there is a very strong lead into transformers.

Episode 414-4: Investigating electromagnetic induction (Word, 219 KB)

A simple experiment (or demonstration) can be done by passing a permanent magnet through a coil of wire that is connected to a data logger.

This shows clearly that as the magnet moves into the coil an EMF is generated for a short time.

Episode 414-5: Magnet falling through a coil (Word, 27 KB)

## Demonstration: Related effects

Some ideas for quick demonstrations of effects related to electromagnetic induction.

Episode 414-6: Quick demonstrations of electromagnetic induction (Word, 39 KB)

## Student questions: Induced EMFs

The first link involves some qualitative work, sketching graphs and includes a falling magnet experiment

Episode 414-7: Rates of change (Word, 198 KB)

Some simple calculations.

Episode 414-8: EMF in an airliner (Word, 34 KB)

## Discussion and demonstrations: Eddy Currents

So far, the induced effects have been seen in wires with an associated change in flux. But does the conductor involved have to be a wire

? The answer is that there will be induced currents whenever the flux linked with a conductor of any shape or size changes. If the conductor is not a wire, then these induced currents are referred to as eddy currents

.

Several demonstrations show the effect. From these experiments it should become clear that Lenz's law applies, i.e. the induced effects oppose the motion that is producing them. One of the main uses for eddy currents is in electromagnetic braking.

When eddy currents flow in a resistive metal, eddy current heating results. It is put to good practical use, e.g. in the production of pure alloys where eddy current heating of a metal crucible replaces a dirty

furnace. More frequently the heating is a nuisance as it wastes energy in electromagnetic machines.

Episode 414-9: Introducing eddy currents (Word, 49 KB)

Episode 414-10: Further eddy current demonstrations (Word, 48 KB)

## Student questions: Eddy currents and Lenz's law

Some descriptive work can reinforce these ideas.

Episode 414-11: Eddy currents and Lenz’s law (Word, 69 KB)

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### Electric motors

## Episode 415: Electric motors

Lesson for 16-19

- Activity time 140 minutes
- Level Advanced

The common electromagnetic machines are motors, generators and transformers. All three are described in this episode but you will need to check your specification to find out which you need to cover and in what detail.

Lesson Summary

- Demonstration or student experiment: A model motor (20 minutes)
- Discussion: Motor torque (30 minutes)
- Discussion: Back EMF and power (10 minutes)
- Demonstrations: The practical importance of motors (20 minutes)
- Student questions: DC motor (20 minutes)

## Demonstration or student experiment: A model motor

Although motors could be discussed in

, there is much sense in waiting until after electromagnetic induction has been covered so that a full account of back emf can be included. Again your students are likely to have met motors at pre-16 level. Working with a simple motor will cover the essential physics involved.

Episode 415-1: A simple electric motor (Word, 91 KB)

## Discussion: Motor torque

From this practical work (and previous knowledge), it should be clear to your students that a simple motor is a (rectangular) coil of wire that rotates in a magnetic field when a current is passed through the coil.

The diagram shows a section through a coil that is pivoted at ´ so that it can turn about a horizontal axis. The coil has sides of length *L* and a width *w*, so that its area is *A*. There are N turns of wire in the coil carrying a current *I*. *B* is the flux density between the magnetic poles.

The force *F* on each side of the coil is
*F* = N*B**I**L*

The direction of the forces is found by Fleming's left hand rule and the two forces together produce a couple.

The torque produced = 2 × (F × *w*2)

torque = N*B**I**L**w*

torque = N*B**I**A*

This picture is only valid if *B* is uniform and *B* and *I* are perpendicular. The design of commercial motors tries to make this true for a significant part of the rotation by including a lot of shaped soft iron, both in the armature and in the pole pieces. At the same time this increases the value of *B*.

The current has to be reversed each time the coil is perpendicular to the field so that the forces reverse and the circular motion is maintained. A commutator and brushes are used for this.

## Discussion: Back emf and power

Once the motor starts to turn, the movement of the coil through the magnetic field leads to an induced emf *E* in the coil. This emf will generate a current that opposes the motor current. (Why? – either Lenz's law or conservation of energy).

Now if the supply voltage is *V* and the armature has a resistance *R*, we have:

*V* = *E* + *I**R*

*V**I* = *E**V* + *I*^{ 2}*R*

or

electrical power supplied = mechanical power output + rate of heating of armature

## Demonstration: The practical importance of motors

These two experiments will show some of the ideas discussed.

Episode 415-2: Torque from a motor (Word, 27 KB)

Episode 415-3: Using an electric drill (Word, 28 KB)

## Student questions: DC motor

These questions emphasize the design features of a dc motor.

Episode 415-4: Thinking about the design of a simple DC motor (Word, 43 KB)

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### Generators and transformers

## Episode 416: Generators and transformers

Lesson for 16-19

- Activity time 145 minutes
- Level Advanced

In a generator, motion of a conductor in a magnetic field induces an EMF. In a transformer, it is the changing field that induces an EMF in a fixed conductor.

Lesson Summary

- Discussion: Generators (30 minutes)
- Demonstrations: A motor in reverse (15 minutes)
- Student questions: On ac generators (20 minutes)
- Demonstration: Transformers (20 minutes)
- Student experiment: Testing the relationships (30 minutes)
- Student questions: Transformer equations (20 minutes)
- Further discussion: Practical transformers (10 minutes)

## Discussion: Generators

The structure of a simple generator is essentially the same as a motor. The difference is that now mechanical working is used to generate a potential difference. The electrical current to a load is via a commutator for an ac generator or slip rings if ac is required.

Basic ideas can be understood by thinking about a coil rotating in a uniform magnetic field.

Consider a coil of area *A* with N turns of wire rotating at a constant angular velocity ω in a uniform magnetic flux density *B*. As the coil rotates, it cuts through the lines of flux. Another way to express this is to say that the flux linking the coil is changing.

At what point is the rate of flux-cutting greatest? (When it is horizontal in the diagram above; when it is vertical, the rate of flux cutting is instantaneously zero.)

Rate of flux cutting = induced EMF

*E*_{induced} = *B**A*Nωcos(ω*t*)

with a maximum value,

*E*_{0} = *B**A*Nω
when the coil is parallel to the field.

## Demonstration: A motor in reverse

Show that a motor can operate in reverse, as a generator. One starting point is simply to attach a weight to a small motor and to drop the weight. The motor works in reverse as a generator; the induced EMF can be monitored with a meter.

Further experimental work will reinforce the discussion.

Episode 416-1: The effect of loading a generator (Word, 57 KB)

An alternative approach is to think about a magnet rotating to give changing flux in one or more pairs of coils. A useful demonstration follows but you may decide to show only the first stages of this.

Episode 416-2: Building up an alternator (Word, 304 KB)

## Student questions: On ac generators

Episode 416-3: Alternating current generators (Word, 80 KB)

## Demonstration: Transformers

Experiments with transformers can be used as a way of investigating and confirming the laws of electromagnetic induction and could be done earlier. This work can also be a means of rounding off the whole of this section of post-16 work.

The aim is to show that a transformer is an electrical machine that converts one ac voltage into another ac voltage. Working through parts or all of the following presentation will illustrate both the structure and the operation of a transformer.

Episode 416-4: Building up a transformer (Word, 172 KB)

## Discussion:Transformer equations

Having defined the quantities involved, you can deduce the transformer equations. Emphasise that the deduction of these equations depends on an assumption of 100% efficiency; in most transformers the efficiencies are so high that the inequalities can be treated as being approximate equalities.

## Student experiment: Testing the relationships

The theory presented above can be tested by experiment.

Energy losses become very apparent with the apparatus described in this experiment. It is worth repeating the measurements with 120/240 turn coils (if available) or with a small commercial transformer.

Episode 416-5: Transformers (Word, 31 KB)

## Student questions: Transformer equations

Episode 416-6: Transformers (Word, 108 KB)

## Further discussion: Practical transformers

Discuss reasons for energy losses in real transformers. These are readily identified as:

- ohmic heating of the coils
- eddy current heating of the core
- hysteresis effects which heat the core
- magnetic flux escaping

But even with these it is not unusual to find efficiencies of 95% and higher. Large transformers used in power transmission may be as much as 99.5% efficient.

Where electronics are being used, low voltage ac supplies are usually required so step-down transformers will be an essential part of the power supply. The output from a transformer is ac, so there will have to be some form of rectification (with diodes) and smoothing (with capacitors).

A second widespread use is within the Grid

that supplies electricity to the consumer. The connection from a power station to the consumer involves a long length of wire and often, high currents. For a given section of the grid, the resistance, *R* is fixed and the rate of heating generated in the wire will be *I*^{ 2}*R*; this energy is wasted. To minimise this energy loss, the current should be as small as possible. To deliver a particular power (*V**I*), a smaller current can be achieved by using as high a voltage as possible. The grid is designed so that transformers are used to step up the voltage at the power station before transmission. Step down transformers reduce the voltage in stages to the level required by industrial and domestic consumers.