Chapter 3 of 8

All 8 chapters
  1. 1Magnetic fields, readunderstood
  2. 2Fields around wires and coils, readunderstood
  3. 3The motor effect, readunderstood
  4. 4Electric motors, readunderstood
  5. 5Electromagnetic induction, readunderstood
  6. 6Generators and dynamos, readunderstood
  7. 7Transformers, readunderstood
  8. 8Speakers and microphones, readunderstood

S4.13.3 Chapter 3

The motor effect

Hang a wire between the poles of a magnet and switch on a current. The wire jumps. Which way does it go, and how hard?

Your guess

Pick one before you read on. It is fine to be wrong.

Your guess

  • You picked A. Read on. At the end, the chapter comes back to your guess.

  • You picked B. Read on. At the end, the chapter comes back to your guess.

  • You picked C. Read on. At the end, the chapter comes back to your guess.

By the end you can

  • Use Fleming's left hand rule to find the force on a wire
  • Calculate force using F equals B times I times L

A wire with a current has a magnetic field round it. Put it in the field of a magnet, and the two fields act on each other. The result is a force on the wire. This is the motor effect. It is how every electric motor turns.

Here is why the force has the direction it has. We look at a wire end on, with a current out of the page. The magnet’s field points to the right. The wire’s own field goes anticlockwise round it.

Draw it first

Why the wire is pushed

  1. Two pictures of a wire seen end on, with a dot in a small circle meaning a current out of the page, between a N pole on the left and a S pole on the right. Step 1: four straight arrows run from left to right across the gap, and an arrow labelled force points up from the wire. Step 2: the field lines of the magnet and the wire added together. They bend round the wire. They are crowded below the wire and spread out above it. The arrow labelled force points up.NSforce

    1 The magnet makes a field from left to right. The wire carries a current out of the page. The wire is pushed up.

  2. Two pictures of a wire seen end on, with a dot in a small circle meaning a current out of the page, between a N pole on the left and a S pole on the right. Step 1: four straight arrows run from left to right across the gap, and an arrow labelled force points up from the wire. Step 2: the field lines of the magnet and the wire added together. They bend round the wire. They are crowded below the wire and spread out above it. The arrow labelled force points up.NSforce

    2 Add the two fields. Above the wire, the wire’s field points left and takes away from the magnet’s field, so the field is weaker. Below, they point the same way and the field is stronger.

The wire is pushed from the side where the field is strong to the side where it is weak. Here, that means up. Reverse the current, and the stronger side swaps to the top, so the wire is pushed down. Reverse the magnet, and the force reverses too.

You do not have to add up the fields every time. Fleming’s left hand rule gives the direction at once. Hold the thumb, the first finger and the second finger of your left hand at right angles to each other. Then each finger stands for one quantity.

A left hand drawn with the thumb pointing up, the first finger pointing away from you and the second finger pointing to the right, all at right angles. The first finger ends in a small circle with a cross, meaning into the page. Labels: Thumb, Motion. First finger, Field, into the page. Second finger, Current. Left hand.ThumbMotionFirst fingerFieldinto the pageSecond fingerCurrentLeft hand
First finger Field, seCond finger Current, thuMb Motion. The thumb shows the direction of the force, and so the way the wire moves.

Point the first finger the way the field points, from N to S. Point the second finger the way the conventional current flows. The thumb then points the way the wire is pushed. Turn your hand until the fingers match. The rule works when the wire is at right angles to the field.

Check it on the picture. The field points right, so the first finger points right. The current comes out of the page towards you, so the second finger points at you. Turn the hand until it fits: the thumb points up. That agrees with the force we found.

If the wire lies along the field, there is no force at all. Its current then runs the same way as the field, or the opposite way. The force is biggest when the wire is at right angles to the field. At other angles it is smaller.

How big is the force? For a wire at right angles to the field, F = B × I × L. F is the force in newtons, N. B is the magnetic flux density, the strength of the field, in tesla, T. I is the current in amperes, A. L is the length of wire in the field, in metres, m.

One tesla is the field that gives a force of 1 N on 1 m of wire carrying 1 A across it. So 1 T = 1 N per A per m. The tesla is a big unit. The table gives some typical fields.

A table with the columns Field and Tesla. Rows: Earth, 0.00005 T. fridge magnet, 0.005 T. horseshoe magnet, 0.1 T. strong lab magnet, 1 T.FieldTeslaEarth0.00005 Tfridge magnet0.005 Thorseshoe magnet0.1 Tstrong lab magnet1 T
Rough sizes. A magnet’s field is strongest at its poles, and the Earth’s field varies from place to place.

The force grows in proportion to each of B, I and L. Double the current and the force doubles. Use a magnet twice as strong and the force doubles. A wire twice as long in the field feels twice the force. Look at the graph for a fixed field and length.

A graph with the axes force (N) and current (A). Current runs from 0 to 6 A and force from 0 to 0.6 N. A straight line rises from the origin. A dot at 2 A, 0.2 N and a dot at 5 A, 0.5 N each have dashed lines to the axes.1234560.10.20.30.40.50.60current (A)force (N)
A field of 0.2 T and 0.5 m of wire in it. Force against current is a straight line through the origin: each amp adds 0.1 N.

Rearrange the formula to find the other quantities. The current is I = F ÷ (B × L). The field is B = F ÷ (I × L). Always put the length in metres: change centimetres by dividing by 100.

Worked example

A wire carries 3 A across a field of 0.4 T. 0.15 m of the wire is in the field. Find the force on it.

  1. Use F = B × I × L, with B = 0.4 T, I = 3 A and L = 0.15 m.
  2. F = 0.4 × 3 × 0.15 = 0.18, so F = 0.18 N.

Answer: 0.18 N

A wire seen end on, with a cross in a small circle meaning a current into the page, between a S pole on the left and a N pole on the right. Four arrows run right to left across the gap. An arrow labelled force points up from the wire.SNforce
The wire of the first worked example, with the field pointing left and the current into the page. The force is up.

Worked example

A force of 0.6 N acts on 0.2 m of wire in a field of 0.5 T. What current does the wire carry?

  1. Rearrange F = B × I × L to give I = F ÷ (B × L).
  2. B × L = 0.5 T × 0.2 m = 0.1.
  3. I = 0.6 N ÷ 0.1 = 6 A.

Answer: 6 A

Worked example

A wire with 8 A crosses a field of 0.25 T. 12 cm of the wire is in the field. Find the force.

  1. Change the length to metres: 12 cm ÷ 100 = 0.12 m.
  2. Use F = B × I × L = 0.25 × 8 × 0.12.
  3. 0.25 × 8 = 2.
  4. 2 × 0.12 = 0.24, so F = 0.24 N.

Answer: 0.24 N

Try it

Practise Fleming’s left hand rule

You need: your left hand, a pencil and paper.

  1. Draw a rectangle on the left of the paper and write N in it. Draw one on the right and write S in it. Draw an arrow between them from N to S: that is the field.
  2. Draw a small circle with a dot in the middle of the gap. It is a wire with a current out of the page, towards you.
  3. Hold your left hand flat on the page, then open the thumb, first finger and second finger at right angles. Point the first finger along the field arrow.
  4. Turn your hand so that the second finger points up out of the page, towards you. Look at the thumb. Draw an arrow the way it points from the wire.
  5. Now draw a cross instead of the dot, so the current goes into the page. Repeat the steps and see how the thumb changes.

What you will see: With the dot, the thumb points up the page. With the cross, it points down. Reversing the current reverses the force. Try again with the field pointing the other way, and see that it reverses the force too.

If you cannot try it, this is what happens.
A table with the columns Current and Thumb. Rows: out of the page, up. into the page, down.CurrentThumbout of the pageupinto the pagedown

A wrong idea many people have

The force on the wire points along the field, towards a pole.

Why it feels right: We think of a magnet as pulling things towards its poles, so a force towards a pole seems natural.

The test that breaks it: Use the left hand rule. The thumb is at right angles to the first finger, so the force is at right angles to the field. If you move a wire the way the thumb points, it never goes towards a pole.

What is true: The force is at right angles to both the field and the current. The wire is pushed sideways across the field.

A wrong idea many people have

L in F = B × I × L is the whole length of the wire.

Why it feels right: L is called the length of the wire, so it seems to mean all of it.

The test that breaks it: Take a long wire and put only 5 cm of it between the poles. The rest of the wire is outside the field and feels no force. The force is the same as for a wire that is only 5 cm long.

What is true: L is the length of wire that is in the field. Only that part feels the force.

A wrong idea many people have

A wire along the field feels the biggest force.

Why it feels right: The wire is lying in the strongest part of the field, so it seems it should feel the most.

The test that breaks it: Hold a wire so that the current runs the same way as the field. Your thumb and fingers cannot be at right angles to each other, because two of them would point the same way. There is no force.

What is true: The force is largest when the wire is at right angles to the field. Along the field it is zero.

Key words

motor effect
the force on a wire with a current in a magnetic field.
Fleming's left hand rule
first finger Field, seCond finger Current, thuMb Motion, at right angles.
tesla
the unit of magnetic flux density, T. One tesla is one newton per amp per metre.
magnetic flux density
the strength of a magnetic field, B, measured in tesla.

Back to your guess

The answer is B: It is pushed at right angles to both the field and the current.

The force on the wire is at right angles to the field and at right angles to the current. It does not point towards a pole or along the field. Fleming’s left hand rule gives its direction, and F = B × I × L gives its size.

Check yourself

Try each one before you look. A wrong answer tells you where to go next.

  1. The N pole of a magnet is on the left and the S pole on the right. A wire carries a current into the page. Which way is the wire pushed?

    Tap your answer.

    1. Not this one. That is the direction when the current comes out of the page. Into the page it is the other way. Try another.

    2. Not this one. The force is never along the field. It is at right angles to the field and to the current. Try another.

    3. Not this one. The force is never along the field. It is at right angles to the field and to the current. Try another.

    4. Yes, that is right. The field points right (first finger) and the current points into the page (second finger). The thumb points down the page.

    See the answer

    Down the page.

    The field points right (first finger) and the current points into the page (second finger). The thumb points down the page.

    • If you chose A: That is the direction when the current comes out of the page. Into the page it is the other way.
    • If you chose B: The force is never along the field. It is at right angles to the field and to the current.
    • If you chose C: The force is never along the field. It is at right angles to the field and to the current.

  2. The field points up the page and the current comes out of the page. Which way does the thumb of the left hand point?

    Tap your answer.

    1. Not this one. Check the hand again. Reverse either the field or the current from this case and the thumb points right. With both as given, it points left. Try another.

    2. Not this one. The thumb is at right angles to the first finger, which points up the page. It cannot also point up the page. Try another.

    3. Not this one. The force is at right angles to the current as well. The current is out of the page, so the thumb cannot be. Try another.

    4. Yes, that is right. First finger up the page for the field, second finger out of the page for the current. The thumb is at right angles to both and points to the left.

    See the answer

    To the left.

    First finger up the page for the field, second finger out of the page for the current. The thumb is at right angles to both and points to the left.

    • If you chose A: Check the hand again. Reverse either the field or the current from this case and the thumb points right. With both as given, it points left.
    • If you chose B: The thumb is at right angles to the first finger, which points up the page. It cannot also point up the page.
    • If you chose C: The force is at right angles to the current as well. The current is out of the page, so the thumb cannot be.

  3. In Fleming’s left hand rule, which finger stands for the current?

    Tap your answer.

    1. Not this one. The first finger stands for the Field. The word Field begins with F, like first. Try another.

    2. Not this one. The thumb stands for Motion, the way the wire is pushed. Try another.

    3. Yes, that is right. First finger Field, seCond finger Current, thuMb Motion. The C of Current is the C of seCond.

    See the answer

    The second finger.

    First finger Field, seCond finger Current, thuMb Motion. The C of Current is the C of seCond.

    • If you chose A: The first finger stands for the Field. The word Field begins with F, like first.
    • If you chose B: The thumb stands for Motion, the way the wire is pushed.

  4. A wire lies along the field with the current in the same direction as the field. What is the force on it?

    Tap your answer.

    1. Not this one. The force is largest at right angles to the field. Along the field it is the smallest, which is zero. Try another.

    2. Not this one. Half the largest is the force when the wire is at 30 degrees to the field. Along the field it falls to zero. Try another.

    3. Yes, that is right. The left hand rule needs the field and the current at right angles. When they point along the same line, there is no force on the wire.

    See the answer

    Zero.

    The left hand rule needs the field and the current at right angles. When they point along the same line, there is no force on the wire.

    • If you chose A: The force is largest at right angles to the field. Along the field it is the smallest, which is zero.
    • If you chose B: Half the largest is the force when the wire is at 30 degrees to the field. Along the field it falls to zero.

  5. A wire at right angles to a field of 0.5 T carries 4 A. 0.15 m of the wire is in the field. What is the force on it?

    Tap your answer.

    1. Not this one. That comes from 0.5 × 0.15 without the 4 A. Multiply all three: B, I and L. Try another.

    2. Yes, that is right. F = B × I × L = 0.5 T × 4 A × 0.15 m = 0.3 N.

    3. Not this one. Check the decimal point. 0.5 × 4 × 0.15 is 0.3. Try another.

    4. Not this one. Check the decimal point. 0.5 × 4 = 2, and 2 × 0.15 = 0.3, not 3. Try another.

    See the answer

    0.3 N

    F = B × I × L = 0.5 T × 4 A × 0.15 m = 0.3 N.

    • If you chose A: That comes from 0.5 × 0.15 without the 4 A. Multiply all three: B, I and L.
    • If you chose C: Check the decimal point. 0.5 × 4 × 0.15 is 0.3.
    • If you chose D: Check the decimal point. 0.5 × 4 = 2, and 2 × 0.15 = 0.3, not 3.

  6. What is the unit of magnetic flux density?

    Tap your answer.

    1. Not this one. The newton is the unit of force, not of field strength. One tesla is one newton per amp per metre. Try another.

    2. Not this one. The ampere is the unit of current. The field strength is in tesla. Try another.

    3. Yes, that is right. Magnetic flux density B is measured in tesla. In F = B × I × L, the force is in newtons, the current in amps and the length in metres.

    4. Not this one. The volt is the unit of potential difference. The field strength is in tesla. Try another.

    See the answer

    The tesla, T.

    Magnetic flux density B is measured in tesla. In F = B × I × L, the force is in newtons, the current in amps and the length in metres.

    • If you chose A: The newton is the unit of force, not of field strength. One tesla is one newton per amp per metre.
    • If you chose B: The ampere is the unit of current. The field strength is in tesla.
    • If you chose D: The volt is the unit of potential difference. The field strength is in tesla.

  7. From an earlier chapter

    Which end of a coil is the N pole, when the current goes anticlockwise as you look at that end?

    Tap your answer.

    1. Not this one. Clockwise would make the end you look at a S pole. Anticlockwise makes it N. Check with the right hand grip rule. Go to S4.13.2. Try another.

    2. Yes, that is right. Curl the fingers of the right hand anticlockwise. The thumb points towards you, and the field leaves at that end, which is N.

    3. Not this one. A coil has its poles at its ends, one N and one S. Go to S4.13.2. Try another.

    See the answer

    The end you are looking at.

    Curl the fingers of the right hand anticlockwise. The thumb points towards you, and the field leaves at that end, which is N.

    • If you chose A: Clockwise would make the end you look at a S pole. Anticlockwise makes it N. Check with the right hand grip rule. Go to S4.13.2.
    • If you chose C: A coil has its poles at its ends, one N and one S. Go to S4.13.2.

  8. A wire at right angles to a field of 0.6 T carries 5 A. 4 cm of the wire is in the field. What is the force on it?

    See the answer

    0.12 N

    4 cm = 0.04 m. F = B × I × L = 0.6 × 5 × 0.04 = 0.12 N.

  9. A force of 0.45 N acts on 0.5 m of wire in a field of 0.3 T. What current does the wire carry?

    See the answer

    3 A

    I = F ÷ (B × L) = 0.45 ÷ (0.3 × 0.5) = 0.45 ÷ 0.15 = 3 A.

  10. A wire carries 3 A. 0.2 m of it is at right angles to a magnet’s field, and the force on it is 0.42 N. What is the strength of the field?

    See the answer

    0.7 T

    B = F ÷ (I × L) = 0.42 ÷ (3 × 0.2) = 0.42 ÷ 0.6 = 0.7 T.

Keep it

Copy this into your exercise book.

Left hand: First finger Field, seCond finger Current, thuMb Motion. F = B × I × L, with B in tesla, I in amps, L in metres of wire in the field. No force along the field.

Draw: A left hand with three labelled fingers, and the formula beside it.

Reading with a child? A short page for the adult: what this chapter teaches and three questions to ask.

No internet tomorrow? Save the whole book as one file (913 KB). It opens on any phone.