School Physics notes: Motor effect of current, simple d.c./a.c. motors, loudspeaker

Electricity and magnetism 11: The motor effect of an electric current

Fleming's left-hand rule - applications e.g. electric motor and loudspeaker

Doc Brown's school physics revision notes: GCSE physics, IGCSE physics, O level physics,  ~US grades 8, 9 and 10 school science courses or equivalent for ~14-16 year old students of physics

This page will help you answer questions such as ...  Why does a current carrying wire experience a force when placed in a magnetic field?   What is Fleming's left-hand rule?   How does a simple electric motor work?  How does a loudspeaker work?

1. The motor effect - current and magnetism

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5. A simple a.c. motor

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1. The motor effect - the interaction of a current carrying wire and a magnet

When a conductor e.g. a wire, carrying an electric current, is placed between the poles of a magnet the magnetic field around the conducting wire interacts with the magnetic field it is placed in.

We are dealing with the interaction of two magnetic fields, each with their own north and south poles.

This will cause the magnet and the conductor to exert a non-contact force on each other.

The force will cause the wire to move and this phenomena is called the motor effect.

Here you are dealing with two magnetic fields (from the wire and magnet) each with its north and south pole, hence the interaction (as you get with any two magnets)

The resulting magnetic field is stronger in one area and weaker in another, so there is a resultant force.

To get the maximum full force effect the wire should be at 90o to the direction of the magnetic field flux.

If the wire is parallel to the magnetic field, it won't experience a force at all.

So from 0o to 90o you get a steady increase in the force exerted on the wire.

The diagram above illustrates the 'kicking wire' experiment and Fleming's left-hand rule which allows you to predict the direction of wire's motion - the direction of the resultant force or thrust.

The force always acts at right angles to the magnetic field of the magnet AND the direction of the current in the wire see more on Fleming's left-hand rule below.

The magnitude of the force increases with ..

(i) increase in current flow, which increases the strength of the magnetic field around the wire,

(this could be by increasing p.d. (V) or a thicker wire creating a smaller resistance (R in Ω) for the same p.d.

(ii) the strength of the magnetic field of the permanent magnet - a 'stronger 'magnetic field around the magnet,

(iii) the length of wire exposed to the magnetic filed, greater length or area where the two magnetic fields interact.

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2. Predicting the direction of maximum force - the direction motion in the motor effect

You can predict the direction of the force-motion effect from Fleming's left-hand rule (illustrated below with doc b's handsome left hand!).

Diagram of Fleming's left-hand rule prediction

Imagine a set of x,y, z axes at 90o to each other, represented by the thumb, first finger and second finger of your left hand.

The thuMb represents the direction the force acts - direction of motion (phonetically emphasise M).

The First Finger represents the direction of the magnetic field N => S (phonetically emphasise the F).

The SeCond finger represents the direction of the convention current (phonetically emphasise the 'hard' C).

Fleming's left-hand rule and the motor effect are 'combined' in the diagram above.

Imagine a current carrying wire at the most favourable angle of 90o to a magnetic field created by permanent magnets.

If you do this in the lab you will see the wire kick to the right with respect the magnetic N=>S pole alignment.

The direction of force creating the motion can be predicted from Fleming's left-hand rule (top right).

However!, you have to twist your hand around, physically (or in your head) to fit in with a given diagram situation.

The result of twisting your hand around is shown in the bottom right of the diagram - check it out!

Note the 'change in direction' rules ....

(i) if you reverse the direction of the current (e.g. to ↓), you reverse the direction of the force and the wire kicks the other way,

and (ii)  if you reverse the direction of the magnetic field (e.g. N=>S to S<=N), you also reverse the direction of the force and the wire kicks the other way.

The motor effect has all sorts of applications e.g. electric motors, loudspeakers, generators, microphones, so see

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3. Calculating the size of the force produced by the motor effect

The mathematics of the 'kicking wire'!

The size of the force on the conductor depends on:

The magnetic flux density (B) - the closer together the lines of force, the greater the field strength, the greater the resulting force.

The current in the conductor (I) - the greater the rate of charge flowing, the stronger the magnetic effect, the greater the resulting force.

the length of conductor (L) (e.g. copper wire) in the magnetic field - if the force operates over a greater length, so overall a greater force is exerted on the wire.

The net force (F) is proportional to all these three factors combine into one simple equation:   F = B I L

The diagram illustrates the variables in the equation to calculate the force acting on a current carrying wire.

Note that I've made the left of the diagram ~match the application of Fleming's left-hand rule.

To calculate the size of the force

For a conductor at right angles to a magnetic field and carrying a current:

force = magnetic flux density × current × length,    F = B I L

force F, in newtons, N;       magnetic flux density, B, in tesla, T

current, I, in amperes, A;    length, L, in metres, m  (watch out to convert from cm to m = cm/100))

Rearrangements: B = F / IL,  I = F / BL  and  L = F / BI,  and in ANY calculation, watch out to match the units!

You also need to be able to use Fleming's left-hand rule to predict the direction of the resultant force.

Examples of calculations

Q1 A 10 cm length of wire carrying a current of 8.0 A is at right angles to a magnetic field of strength 0.25 Tesla.

(a) If the directions of the magnetic field and current are in the plane of the screen, deduce the direction of the force on the wire.

From Fleming's left-hand rule you should deduce the direction of force-motion is directly towards you!

(b) Calculate the size of the force on the wire.

F = BIL = 0.25 x 8.0 x (10/100) = 0.2 N

Q2 A 5.0 cm length of wire carrying a current of 3.0 A experiences a force of 5.0 N.

Calculate the magnetic flux density around the wire.

F = BIL,  B = F/IL,   B = 5.0/(3.0 x 5.0/100) = 3.3 T

Q3 What current must flow through a 1.5 m wire for it to experience at 90o a force of 9.0 N in a magnetic flux density of 3.0 T?

F = BIL,   I = F/BL,   I = 9.0/(3.0 x 1.5) = 9.0/4.5 = 2.0 A

Q4 In cm, what length of wire carrying a current of 20 A, will experience a force of 25 N at 90o to a magnetic flux density of 5.0 T?

F = BIL,  L = F/BI,  L = 25/(5 x 20) = 25/100 = 0.25 m = 25 cm

Q5 Calculate the force on a 50 m stretch of telephone wire carrying a current of 50 milliamps and the Earth's magnetic field flux acting on the wire is 40 000 nanotesla.

B = 40 000 x 10-9 = 4.0 x 10-5 T,  I = 50 x 10-3 = 5.0 x 10-2 A,  L = 50 m

F = B x I x L = 4.0 x 10-5 x 5.0 x 10-2 X 50 = 1.0 x 10-4 N

Q

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4. A simple d.c. electric motor - an application of the motor effect - uses of electric motors

The basics

To understand how a simple dc electric motor works consider the diagram above to get the idea.

Instead of a single linear wire, consider placing a d.c. current carrying loop (or many turns of wire loops) in the magnetic field of a permanent magnet (U shaped) or opposite poles from two permanent magnets.

The wire is at 90o to the direction of the magnetic field - lines of force in blue.

Now we apply Fleming's left-hand rule because the same forces are in operation as for the single wire demonstration.

I've drawn the rule and applied it to both sides of the loop to show the directions the forces produced operate.

The left side of the loop will move downwards and the right side of the loop moves upwards giving anticlockwise rotation.

This produces an anticlockwise rotation movement - and that's quite simply, the basis of an electric motor, but you will not get continuous rotation without some further modifications and added 'bits' described below!

Explaining how a simple dc electric motor works

However, as described previously, the above 'diagram' needed a few more bits to be a working electric motor!

are an axle (spindle) about which the coil can freely rotate between the poles of a permanent magnet,

a split ring commutator that swaps the contacts around every half-turn (swapping the +/-polarity, swapping the direction of resulting force) and keeps the rotation in the same direction, it also enables electrical contact to the external circuit, together with the ...

... brush contacts (of graphite block or copper strip) which enable rotation movement to continue but still maintain a complete electrical circuit - the 'brushes' sweep over the surface of the contacts on the axle,

and of course a frame structure to hold all the components in place!

The way the forces operate was explained in the previous diagram, but I have repeated the application of Fleming's left-hand rule to show the coil will rotate anticlockwise.

theoretically, when the copper wire coil is vertical, the circuit is broken for a split second, but the momentum of the coil carries the rotation a bit further, the circuit is complete again, and continuous rotation is conserved.

You can reverse the direction of rotation either by either ..

(i) swapping the polarity of the d.c. supply to change the direction of current flow,

and (ii) swapping the magnetic poles of the permanent magnet to change the direction of the magnetic field.

A simple, but practical, working model of a simple d.c. electric motor

Notice in the right-hand diagram the rotation is now clockwise, but current flow is opposite in direction compared to the previous diagram - so check it out with Fleming's left-hand rule!

However, there are several sources of energy loss - decreasing the efficiency of the motor

(a) When the electric motor starts running the current decreases a little from its initial value.

As the current flows, the thin wire coils act as a resistance, the coil heats up a little as heat energy is lost: electrical energy ==> thermal energy store of the motor and surroundings.

Since the temperature of the coils increases, its resistance increases a bit more, leading to a greater increase in wasted energy.

(b) Although this machine is acting as an electric motor, simultaneously it acts as a generator!

As the coil rotates in the magnetic field it induces a current to flow in the opposite direction.

How can you make a simple dc (or any) electric motor more powerful?

There are three ways to do this, all involve increasing the strength of the magnetic field ...

(i) Increasing the number of turns of wire in the coil.

The magnetic lines of force 'cut' through more wire per unit time.

(ii) By winding the coil on a soft-iron armature to increase the magnetic flux. through the coil.

The ion concentrates the lines of force, so more lines of force are 'cut' through per unit time.

(iii) By making the field magnet as strong as possible.

The stronger the magnet, the greater the magnetic flux - the lines of force are closer together, so more lines of force are 'cut' per time as the armature rotates.

(iv) Increasing the p.d. across the coil to increase the current.

Increase the charge flow will intensify and strengthen the magnetic field around the coil.

These factors apply to any electric motor design.

These factors can be used to increase the speed of rotation of the motor.

To make an electric motor less powerful or slow its rotation down, (i) reduce the current (by reducing the pd across the coils), (ii) reduce the number of turns of wire coils and (iii) decrease the strength of the magnet to reduce the magnetic flux density.

Factor (i) is used to control the speed of an electric motor e.g. an electric car or train. You can't really change any other factor in a working machine!

Practical electrical motors

The d.c. motor described above is pretty simple and very inefficient.

In more practical motors, the magnetic pole pieces are curved in shape to give a more radial magnetic field.

This means the coil is always at right angles to the magnetic field - maximising the resultant force from the interaction of the two magnetic fields.

The usefulness of electric motors

Where do we start!

There are hundreds of uses in the home, in industry and transport systems.

They speed up many processes once done by manual labour, and increase the efficiency of machines once powered by coal (eg steam locomotives) or wind (eg windmills).

Electric motors power semi- or fully-automated production lines e.g. packaging of food, car assembly lines etc.

You can build electric motors of any required power from little motors in toys to powerful machines in heavy industry.

Powerful electric motors (ac or dc) drive electric trains.

Electric cars are slowly replacing fossil fuelled cars.

microwave cooker, food mixer, hair dryer, toothbrush, CD player,

we would be rather lost without all our electrically powered 'gadgets'!

This British Railways 'INTERCITY' electric locomotive has a maximum speed of 140 mph (225 km/hour) derived from a 4700 kW a.c. electric motor powered from 25 kV overhead power lines. Note that electric motors can be a.c. or d.c. current driven.

5. A simple a.c. electric motor

A simple a.c. electric motor

The a.c. power supply is connected to the rotating coils of the armature by two slip rings and carbon brush contacts.

Note the difference - two slip rings in an a/c. motor, instead of a split-ring commutator in a d.c. motor.

As the coil rotates, the direction of the current passing through the coil reverses direction.

When the coil has moved through half a turn, the direction of the current has reversed.

This ensures the force, produced by the interaction of the two magnetic fields, always operates in the same net direction, so the rotation of the coil is always in the same direction (clockwise or anticlockwise, depending on the poles of the permanent magnet).

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6. The loudspeaker - an application of the motor effect

A loudspeaker works in the opposite way to a .

How a loudspeaker works

The motor effect of a magnetic field and conducting coil is used in the function of loudspeakers, often of the small headphone variety these days!

In loudspeakers, an a.c. current conducting coil is moved by in a magnetic field to convert electrical energy into sound energy by way of a vibrating cone (diaphragm).

The cone vibrates the air and the oscillations produce the sound waves you hear.

An a.c. (must be an alternating) current is passed through a coil of insulated copper wire attached to the base of a paper-cardboard cone (or plastic cover).

The coil is wrapped around one pole of a permanent magnet and is itself surrounded by the other pole - you can see this in the diagram where the magnet is specially shaped to allow the coil/cone base to fit in.

The cylindrical magnet produces a strong radial magnetic field and at right angles to the coil - both contribute to the maximum vibration affect.

(You can't see that the south pole continues to the left into the hollow base tube of the cone - diaphragm).

When the current passes through the coil, it produces a magnetic field and around the coil wire which interacts with the magnetic field of the permanent magnet.

This causes a force to move the cone (to which the coil is attached).

The larger the current 'signal' the larger the movement of the cone.

In this case we are not dealing with rotation as in an electric motor, but with a mechanical 'to and fro' vibration effect, but it still involves what we call the 'motor effect'.

When the ac current reverses, the force acts in the opposite direction, so the cone moves in the opposite direction too.

Therefore the variation in the a.c. current signal makes the cone vibrate (oscillate) in the same varied way, which in turn makes the air particles vibrate and it is these variations in pressure that causes sound waves to emanate from the speaker.

Therefore the frequency of the sound waves produced by the cone vibrations is the same as the frequency of the a.c. signal.

In reality, the a.c. signal is very complex enabling us to hear a full sound picture of e.g. music generated from a complex music wave superimposed on a carrier wave.

The diagram below is a reminder of a simplified sound wave model.

They both work in the same way, converting electrical wave signal into a sound signal.

However, as well as the difference in size, the power input and output are much lower for a headphone, particularly if it consists of small earbuds.

A loudspeaker needs to fill a much larger space e.g. room or dance hall, whereas a headphone only has to fill your ear lobe!

With the onset of mobile phones, they have enough power to allow you to use a pair of earbud headphones for several hours.

If you want to power some loudspeakers from your mobile phone, you will need some extra battery power!

Note that a microphone is a bit like loudspeaker working in reverse - illustrated below,

See detailed explanation of how a microphone works

and also

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