## 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)