Lesson video

Hello, my name's Dr.

George, and this lesson is called The Motor Effect.

It's part of the unit Electromagnetism.

The outcome for the lesson is I can describe the force acting on a current-carrying wire or loop in a uniform magnetic field.

Here the key words for the lesson.

I'm not going to go into these now because I'll introduce them as we go along, but this page is here in case you want to come back anytime and check the meanings.

The lesson has three parts called putting force on a conducting wire, size of force on a conducting wire, and rotating loops of wire.

Let's get started.

When a current flows in a wire, there's a magnetic field around the wire, and we can explore that field using a plotting compass, the type of small compass.

If we move the compass around to different places near the wire, we'll see the effect that the field has on the compass.

This was actually first discovered back in 1820, so there's always a magnetic field around any current-carrying wire.

And if we plot the shape and direction of the field around a straight wire, it looks like this.

So we have circular field lines.

So current here is going from left to right and the magnetic field lines are circles like this, and they have the arrows which show the direction in which a north-seeking pole of a magnet would experience a force.

So let's check if you've been listening, which of the following diagrams shows the shape of the magnetic field around a current-carrying wire? When I ask a short question, I'll wait five seconds.

But if you need longer, press pause, and press play when you're ready.

And the correct answer is B.

It's the same as you saw before, except the wire's been turned in a different direction.

C shows the magnetic field around a bar magnet, and that's not what the field around a straight wire looks like.

If we have a larger current, we get a stronger magnetic field, and that's represented here by field lines that are closer together.

And we actually have a quantity we can measure for the strength of a magnetic field.

It's called magnetic flux density.

And for some reason, it has symbol B, and I'll be using that later in this lesson.

If we change the direction of the current, we've just switched it around.

Can you see what's changed about the field? The direction is opposite.

The arrows are pointing the other way.

Now here are two wires right next to each other with currents in opposite directions as shown by the grey arrows.

They'll each have a magnetic field around them, but the top wire has a magnetic that will force the north-seeking pole of a magnet in the opposite direction to the bottom wire.

And if the size of the current niche wire is the same, the magnetic field around each wire will have the same strength, and they'll actually cancel each other out.

So a plotting compass near these wires won't experience a force.

Now, in which of these diagrams is a magnetic field strongest? So we have some current-carrying wires.

The current in each wire is the same size and its direction is shown by the grey arrow.

Press pause if you need longer than five seconds.

The correct answer is B.

In C, there are three current-carrying wires, but the magnetic fields of two of them will cancel out because of the opposite current directions.

So in fact, the magnetic field around C will be the same as the magnetic field around A.

Whereas in B, we have two wires carrying current in the same direction, so their magnetic fields will reinforce each other.

Many schools have motor kits, which contain the parts you need to make a small motor.

We're not going to do that today.

But in these kits, there are a particular type of magnet that schools usually have, which have north-seeking and south-seeking poles on their large flat faces.

So these are not bar magnets.

And these magnets have been placed here so that their unlike poles are facing each other, so they'll be attracting, but they can't come together because they've been stuck to a shaped piece of steel here that they're attracted to.

And it turns out that if you place magnets like this in this way, the north-seeking pole of another magnet placed between them would be forced to move in a straight line from north-seeking, which it's repelled by, to south-seeking, which it would be attracted by.

And in fact, the magnetic field between the two magnets can be represented by field lines like this.

They're all straight.

They're all pointing in the same direction, and they're evenly spaced.

So that shows that the strength of the field is the same everywhere.

And we call this a uniform magnetic field, and it's a useful kind of field that we can set up to experiment with a current-carrying wire.

So let's place a current-carrying wire in a uniform magnetic field.

If we do, we find it's actually forced in a particular direction.

If you could do this, and if the wire is hanging loosely enough that it's able to move, you'll see the wire jerk in one direction, and it turns out it will move upwards.

We can predict the direction of that force using a rule called Fleming's left-hand rule.

Here's how that works.

You take your left hand, It has to be your left hand, and you hold it so that your thumb and the first two fingers of your left hand are at right angles to each other.

That's not my hand.

This is my hand.

Try to make the two fingers and thumb really at right angles, not like this at smaller angles because then you won't be able to see what the rule is showing you.

Here's another view.

So you point your first finger in the direction of the field from north-facing to south-facing.

Then point your second finger in the direction of the current.

That's from positive to negative.

So here we'd be doing roughly this.

Try and get your hand to do that.

You may have to twist your arm in a strange position rather like this.

Then if you do that, your thumb points in the direction of the movement of the wire because of a force acting on it, like so.

And so we find that there's a force on this wire upwards.

Actually, just from knowing that the three directions are all at right angles to each other, we can already predict that the force must be either up or down.

Those are the only directions that are at right angles to the field lines and the current.

But Fleming's left-hand rule tells us which of those directions is right.

The force isn't downwards.

It's upwards.

To use the rule, you'll have to remember it of course.

And if you use the wrong finger to represent the wrong thing, you'll get the wrong answer.

A way of trying to remember which is which is that first finger begins with F, and so does field.

Second finger has a C in it, and current begins with C.

And thumb has an M in it, and movement begins with M.

And now again, let's see if you've been listening.

What happens to the wire when the current is turned on? So in each picture the wire is shown in white, and its movement is shown by arrows, and its new position is shown in red.

Pause if you need longer than five seconds.

The correct answer is C.

It moves upwards.

You know from Fleming's left-hand rule that the movement should be at right angles to the field direction and to the current direction.

So it's not going to move as in A because that would be a movement in the same direction as a field direction, and it's not going to twist either because that would require two different forces acting in different directions on each end of the wire, and that's not what Fleming's rule shows us.

Now look at the apparatus in this diagram.

There are two metal rails, and they're attached to a power supply, and there's a copper rod just resting on the two rails.

And the copper rod is in a strong uniform magnetic field between a north-facing and south-facing pole.

And this is a clever way of being able to get a current passing through the rod while the rod is still very free to move.

It can roll up and down on the rails.

So what we do is we turn on the current and we notice that the rod moves away from the wooden block.

It rolls along the rails in the direction shown by the arrow.

Then we turn the current off, and we're going to turn the magnet over so that its south-seeking pole will be on the top.

I'd like you to predict to state what will happen to the rod when the current is turned on now, and describe how Fleming's left-hand rule can be used to check your answer.

So take as long as you need to write your answers.

And while you're doing that, pause the video and press play when you're finished.

The answer to the first question is that the rod will move towards the wooden block.

That's opposite from before.

And you can predict that using Fleming's left-hand rule.

So here's a description of how to do that.

The first two fingers and thumb of the left hand are held at right angles to each other.

The second finger is pointed in the direction of current through the rod.

The first finger is pointed upwards towards the new position of the south-seeking pole.

The thumb points towards the wooden block in the direction of the force.

If instead of writing that description, you manage to describe it using a picture, if your picture is clear and the fingers and thumb are labelled, well done.

That will do.

Now let's move on to the second part of this lesson, size of force on a conducting wire.

So we've looked at the direction of the force on a current-carrying wire.

Let's look at the size of it.

And to do that, we need to look again at this quantity called magnetic flux density.

So this is a quantity that we can actually measure, and it describes the strength of a magnetic field.

It has a symbol B, and the unit of magnetic flux density is the tesla, named after an engineer, an inventor called Nicola Tesla.

And we use capital T for the symbol, small t for the word, same as we do with newtons.

So we're thinking about the strength of magnetic field.

Here's the magnetic field around a bar magnet, and we can use the closeness of the field lines to see that the magnetic flux density is smaller further from the magnet than it is closer to the magnet.

For a bar magnet, the maximum magnetic flux density you're likely to get is about.

1 tesla.

Whereas if you have an electromagnet like the electromagnet you could find inside a loudspeaker, it will have a magnetic flux density of around one tesla.

A fridge magnet by the way, will have a magnetic flux density of about 0.

05 tesla.

And the Earth's magnetic field is much weaker, only about 0.

00005 tesla.

And which of the following is the most accurate description of magnetic flux density? Is it how close magnetic field lines are together, the number of magnetic field lines, the strength of a magnetic field? So I'm looking for the best description here.

Press pause if you need longer than five seconds.

The best description is magnetic flux density tells you the strength of a magnetic field.

It is also related to the closeness of magnetic field lines.

Here again, we have a current-carrying wire in a uniform magnetic field.

And if you check with Fleming's left-hand rule, you'll find that the force on the wire is upwards.

But if we double the magnetic flux density, so we've strengthened the magnetic field, we must have swapped these for stronger magnets, it doubles the size of the force.

It turns out the force on the current-carrying wire is directly proportional to the magnetic flux density.

That's that kind of relationship where if you double one quantity, the other one doubles.

If you plot a graph of one variable against the other, it'll be a straight line through the origin.

How does increasing the magnetic flux density by a factor of three, tripling it, affect the force on a current-carrying wire? Press pause if you need longer than five seconds.

And the answer is that it increases it by three times.

It triples it as well.

Because when two quantities are directly proportional, if one quantity is multiplied by a number, the other is multiplied by the same number.

But that's not the only way to increase the force.

If we double the current in the wire, it also doubles the size of the force, and we find that the force is also directly proportional to the current in the wire.

The reason why increasing the current increases the force is increasing the current increases the strength of the magnetic field around the wire, its magnetic flux density.

In fact, it doubles it.

And also, if we double the length of the wire that's in the magnetic field, so it's not the whole length of the wire that matters, it's the part of it that's in the field, that also doubles the force.

So here we've done that by adding more magnets to double the length of the magnets altogether.

And it turns out that the force is directly proportional to the length of the wire that's in the magnetic field.

And it turns out that the force on a current-carrying wire in a uniform field is decided by these three quantities that the force is proportional to, the magnetic flux density of the field that the wire is in, the current in the wire, and the length of the wire that's in the field.

And there's a simple equation that relates these quantities.

It's this.

The force on a current-carrying wire equals BIl.

So we're using F as usual to represent force measured in newton.

B is a magnetic flux density measured in tesla.

I is current in the wire, measured in amps.

And l is the length of the wire that's in the magnetic field, and that's measured in metres because metres, not centimetres, are the standard units of length.

Now let's see how we could use that equation to make a prediction.

I'm going to share you an example calculation.

Although if you're feeling confident, you could pause the video and try it yourself.

So we have a current of.

5 amps flowing through a 15-centimeter long wire in a magnetic field that has a flux density of.

2 tesla.

Flux density is short for magnetic flux density.

If the wire is at right angles to the field lines, what is the force acting on it? Well, we know the equation works when the wire is at right angle to the field line.

So we can use F equals BIl, and we start by writing it down.

Then we take the values from the question, calculate the force, and we get.

015 newtons.

Now here's one for you to try.

Pause the video, and when you finished, press play.

So let's start by writing down the equation.

The I and l can end up looking rather similar to each other, make sure yours are clearly different.

And again, we put the correct quantities into the equation.

Flux density is 1.

2 tesla.

The current is.

2 amps, and the length is.

25 metres.

Notice we're taking care here to convert the length in centimetres to a length in metres.

That's what we need to use in the equation.

And the answer is a force of.

06 newtons.

So well done if you got that.

Here's a diagram of a similar situation to what we saw earlier, a copper rod between the poles of a powerful magnet, and there's an electric current through the rod and the rod is free to roll up and down the rails.

And this time, we turn on the current and the rod moves away from the wooden block as shown by the arrow.

What will happen to the rod if the magnetic Flux density is doubled? And then what will happen to the rod if the magnetic flux density is doubled and the current through the rod is halved? And for that question, I'd like you to explain your answer.

So take as long as you need to think about it and write down your answers.

And press pause, and when you're ready, press play, and I'll show you the answers.

So if the magnetic flux density is doubled, the force on the rod will double, and the rod will move away from the wood with twice the acceleration.

So if you double the force, you double the acceleration.

If you just said the rod will move faster in the same direction, then you've got the right idea.

Now if the magnetic flux density is doubled and the current through the rod is halved, the force on the rod will not change, and it will move away from the wood as it did before.

That's because doubling the flux density doubles the force, but halving the current halves this force until you end up with the same force as before.

Well done if you realised that.

And now for the third part of this lesson, rotating loops of wire.

So we've already seen we can use Fleming's left-hand rule in a situation like this.

The red wire there is going to be pushed upwards by the magnetic field.

If you want to check that, you could pause the video and use Fleming's left-hand rule.

Now the yellow wire has current in the opposite direction, and Fleming's left-hand rule will show that it's going to be pushed down.

So the direction of force on a wire depends on the way the current is flowing.

Here we have a loop of wire, and we've put it in a uniform magnetic field.

And as current flows through this loop, of course it's going to change direction as it goes round the different sides like this.

And that means that in this field, different parts of the loop are going to experience forces in different directions.

We can use Fleming's left-hand rule for each side of this loop to work out which way a force acts on it, and it's down on the left up on the right.

If you want to check that, you could pause the video, and use Fleming's left-hand rule yourself for each side of that wire.

We can't use Fleming's left-hand rule to work out the force on the far side of the loop, and that's because the current is flowing in the same direction as the magnetic field is pointing.

And Fleming's left-hand rule doesn't allow us to show that.

With Fleming's left-hand rule, we have to have the field in the current are right angles to each other.

It turns out that in a situation like this, where the field and the current are parallel to each other, no force acts.

So that part of the loop is going to experience no force.

There's only a force on a current-carrying wire in a magnetic field if the current flows across the magnetic field lines, not if it flows along the magnetic field lines.

Why does the loop of wire shown in this picture turn when an electric current flows through it? So look at the options carefully.

Press pause, and press play when you're ready with your answer.

The correct answer is A.

If two sides of something are pushed in opposite directions, then if the object is able to rotate, it will.

So this loop of wire is going to rotate.

When an electric current flows through a loop of wire in a uniform magnetic field, the loop turns to an upright position.

I'd like you to use Fleming's left-hand rule to add force arrows to size A and B in each of these diagrams. So which way will the force act on each of those sides of the wire that these three different positions that it's in? And then I'd like you to explain why the loop turns first and then stops.

So think carefully about that.

Write down your answers.

Pause the video until you're ready, and then press play.

Here are the answers.

So side A experiences a downward force all the time because its current is flowing more or less into the page, the magnetic field is to the right, and Fleming's left-hand rule shows you that's the direction of the force.

If you got that wrong, you might want to go back to when I explained how to use Fleming's left-hand rule, and check that you're using it correctly.

Side B is always going to be experiencing a force upwards.

It has a current coming outta the page.

Current flows positive to negative, and that's the direction of the force in that magnetic field.

Now that helps us to explain why the loop moves and then stops.

Side A is pushed down, side B is pushed up, making the loop turn.

When it's upright, the forces on sides A and B hold the loop in place.

Can you see that in that third picture those forces are not going to make the loop turn.

They're just going to make it stay like that.

They might make the wires bulge outwards a little bit as well.

Well done if you got that.

By now, you might be wondering, why am I learning about this strange little thing that a loop of current-carrying wire turns a bit when it's in a uniform magnetic field? What's it got to do with me or my everyday life? Well, quite a lot actually, but I'm not going to go into that today.

That's for another lesson.

We're at the end of this lesson.

So here's a summary.

A uniform magnetic field acts with a force on a current-carrying wire that is at right angle to the field.

The size of the force is given by F equals BIl.

F is force in newton, B is magnetic flux density in Tesla, I is current in amps, and l is length of conductor in metres.

The direction of the force can be found using Fleming's left hand rule as shown in the picture.

I hope you've enjoyed this lesson.

You'll certainly find it useful if you find yourself learning about motors at some point.

I hope to see you again in a future lesson.

Bye for now.