Physics · 4 Electricity and magnetism
4.5.1 Electromagnetic induction
Before you start
- Magnetic field lines run from N to S outside a magnet, and lines closer together mean a stronger field (4.1).
- Like poles repel and unlike poles attract (4.1).
- An e.m.f. is measured in volts, and a current flows only round a complete circuit (4.2.2, 4.2.3).
- A coil carrying a current behaves like a bar magnet, with an N pole at one end and an S pole at the other, as in an electromagnet (4.1; the field of a solenoid is covered fully in 4.5.3).
Syllabus objectives covered (5)
- Know that a conductor moving across a magnetic field or a changing magnetic field linking with a conductor can induce an e.m.f. in the conductor
- Describe an experiment to demonstrate electromagnetic induction
- State the factors affecting the magnitude of an induced e.m.f.
- Know that the direction of an induced e.m.f. opposes the change causing it
- State and use the relative directions of force, field and induced current
Part 1 of 6
Two ways to get an e.m.f. without a cell
- Up to now every e.m.f. you have met came from a cell or a power supply. Electromagnetic induction is a way to produce an e.m.f. using only a magnetic field and a conductor, such as a wire or a coil of wire.
- Way 1: a conductor moving across a magnetic field. The word that matters is across. The conductor has to cut through the field lines as it moves. Each time it cuts field lines, an e.m.f. is induced in it.
- A wire that moves along the field lines, parallel to them, cuts none of them. No e.m.f. is induced, however strong the field and however fast the wire moves.
- Way 2: a changing magnetic field linking a conductor. 'Linking' means the field lines pass through the conductor, for example through the middle of a coil. If the field through the coil gets stronger, gets weaker or reverses, an e.m.f. is induced in the coil.
- Both ways come down to one word: change. A magnet held still beside a still coil induces nothing, even if the magnet is very strong. A steady field does nothing. A changing field, or a conductor cutting through a field, does.
- Only the relative motion counts. Pushing a magnet towards a coil that stays still and pushing the coil towards a magnet that stays still give the same effect.
- Notice that the objective says an e.m.f. is induced, not a current. The e.m.f. appears whether or not the conductor is part of a circuit. A current flows only if the conductor is part of a complete circuit, for example with a meter connected across the ends of the coil.
Part 2 of 6
The experiment: a magnet and a coil
- Apparatus. A coil of insulated wire, a bar magnet, and a sensitive centre-zero galvanometer (a meter for small currents). Connect the two ends of the coil to the galvanometer, so the coil and the meter form a complete circuit.
- Why these two features of the meter? It must be sensitive because the induced current is small. It must be centre-zero because the induced current can flow either way round the circuit, and a centre-zero needle can swing to either side. That lets you see the direction as well as the size.apparatus diagram — not drawn yet
A horizontal coil of insulated wire whose two ends lead to a centre-zero galvanometer below it. A bar magnet lies to the left of the coil with its N pole facing the coil's left end, and an arrow shows the magnet moving into the coil. The galvanometer needle is drawn deflected to one side of the central zero.
The needle moves only while the magnet moves. Hold the magnet still and the needle returns to zero. - Step 1. Push the N pole of the magnet into the coil. The needle deflects to one side, say to the right. A current is flowing, so an e.m.f. has been induced in the coil.
- Step 2. Hold the magnet still inside the coil. The needle returns to zero. The field through the coil is strong, but it is not changing, so no e.m.f. is induced.
- Step 3. Pull the magnet back out. The needle deflects the other way, to the left. Reversing the motion reverses the direction of the induced e.m.f., and so of the current.
- Step 4. Push the magnet in again, faster. The deflection is larger. You can also push the S pole in instead of the N pole: the needle then deflects to the left, the same way as when the N pole was pulled out.
- What it shows. An e.m.f. is induced in the coil only while the magnetic field linking it is changing. Moving the coil over a still magnet gives the same results, because only relative motion counts.
- The straight-wire version. Connect a single straight wire to the galvanometer and move it down through the gap between the poles of a U-shaped magnet. The needle flicks one way. Move it up and the needle flicks the other way. Hold it still, or move it from one pole towards the other (along the field lines), and the needle stays at zero.
- In a written answer, give each observation as its own sentence: what you do, then what the needle does. 'The needle deflects while the magnet moves into the coil' is a point you can score. 'Electricity is made' is not, because it does not say what you observe.
Part 3 of 6
What decides the size of the e.m.f.
- There are three factors to state. Each one makes the induced e.m.f. larger when you increase it.
- 1. The speed of the motion. Moving the magnet or the wire faster cuts the field lines at a greater rate, so the field through the coil changes faster and the e.m.f. is larger.
- Notice the trade-off. Pushing the magnet all the way in cuts the same field lines whether you go fast or slowly. Going fast does it in less time, so the e.m.f. is larger but lasts for a shorter time.
- 2. The strength of the magnetic field. A stronger magnet means more field lines are cut in each second, so the e.m.f. is larger. Write 'a stronger magnet', not 'a bigger magnet'. A magnet's size does not tell you its strength.
- 3. The number of turns on the coil. Each turn of the coil has its own small e.m.f. induced in it. The turns are connected one after another, in series, so their e.m.f.s add up. Twice as many turns, all linked by the same changing field, give twice the e.m.f.
- So the three things to write are: speed of movement, strength of the field (magnet) and number of turns on the coil. Name the quantity and the direction of the change, for example 'move the magnet faster'.
Part 4 of 6
Induction with nothing moving
- The second way in the objective, a changing field linking a conductor, does not need a magnet to move at all. You can change the field by switching a current on and off.
- Put two coils side by side. Coil A is connected to a cell and a switch. Coil B is connected only to a sensitive centre-zero galvanometer. There is no electrical connection between the two coils.
- Close the switch. The current in coil A grows from zero, so its magnetic field grows. That growing field passes through coil B, so the field linking coil B changes. The galvanometer needle gives a brief flick.
- Keep the switch closed. The current in coil A is now steady, so its field is steady. Coil B is still inside a magnetic field, but the field is not changing. The needle reads zero.
- Open the switch. The field of coil A collapses to zero. The field linking coil B changes again, in the opposite sense, so the needle flicks the other way.
- This is the same rule as before: an e.m.f. is induced only while the field changes. If coil A carried an alternating current, its field would change all the time and an e.m.f. would be induced in coil B all the time. That is the idea behind the transformer, which you meet in 4.5.6.
Part 5 of 6
The induced e.m.f. opposes the change
- The rule for direction is short: the direction of the induced e.m.f. opposes the change that causes it. (This is sometimes called Lenz's law.) The induced current makes the coil into a magnet, and the coil's poles are always the ones that push against what you are doing.
- N pole approaching. You push the N pole of a magnet towards end P of a coil. The change is 'an N pole coming closer'. To oppose that, the coil must push the magnet back. Like poles repel, so end P becomes an N pole.
- N pole moving away. Now you pull the magnet away from P. The change is 'an N pole moving away'. To oppose that, the coil must try to hold the magnet back. Unlike poles attract, so end P becomes an S pole.
- The trap is to remember the rule as 'the coil opposes the magnet' and always give the repelling pole. The coil opposes the change, which is the motion. It repels a magnet that comes closer and attracts a magnet that moves away.
- Why it must be this way. Because the coil always pushes against the motion, you have to do work to move the magnet, both in and out. That work is the energy that the circuit receives as electrical energy.
- Imagine the opposite. If end P became an S pole as the N pole approached, the coil would pull the magnet in faster and faster, and the circuit would also gain electrical energy. Energy would come from nothing, and the principle of conservation of energy says that cannot happen.
- In this lesson you answer with a pole. To turn a pole into a current direction round the coil, you use the right-hand grip rule for a solenoid from 4.5.3.
Part 6 of 6
Fleming's right-hand rule
- For a straight wire moving across a magnetic field, three directions matter: the motion of the wire (the direction of the force moving it), the field, and the induced current. When the wire moves at right angles to the field, the three are at right angles to each other.
- Fleming's right-hand rule gives the third direction when you know two. Hold your right hand with the thumb, first finger and second finger all at right angles to each other.forces diagram — not drawn yet
A right hand with the thumb pointing up, the first finger pointing straight ahead and the second finger bent to point sideways, all three at right angles. Labels: thumb 'thuMb = Motion', first finger 'First finger = Field (N to S)', second finger 'seCond finger = induced Current'.
Right hand for induced current. Each finger matches one direction. - thuMb = Motion. First finger = Field, pointing from N to S. seCond finger = induced Current, the conventional current. The capital letters are the memory aid.
- How to use it. First point your first finger along the field, from the N pole to the S pole. Then turn your hand, keeping that finger in place, until your thumb points the way the wire moves. Your second finger now points along the induced current.
- An example. The N pole is on the left and the S pole is on the right, so the field points to the right. A wire between them runs straight into the page and is moved upwards. First finger to the right, thumb up: your second finger points into the page. The induced current flows into the page.forces diagram — not drawn yet
End-on view: an N pole block on the left and an S pole block on the right, with straight field lines running left to right between them. A small circle between the poles represents a wire running into the page; a cross inside the circle shows current into the page, and an arrow above the circle shows the wire moving upwards.
Field to the right, motion up, current into the page. A cross means into the page, a dot means out of it. - Reversals. Reverse the motion (move the wire down) and the current reverses: out of the page. Reverse the field instead (swap the poles) and the current also reverses. Reverse both, and the two reversals cancel, so the current flows the original way.
- Right hand, not left. Fleming's left-hand rule is for the force on a current-carrying wire, the motor effect in 4.5.4. If you use your left hand here, you get the exact opposite of the correct current. Induced current means right hand.
Worked examples
Example 1. Describe an experiment to demonstrate electromagnetic induction using a coil of wire, a bar magnet and a sensitive centre-zero galvanometer. Include what you would observe.
Show the working
- Start with the circuit, because nothing will be seen without it: connect the two ends of the coil to the galvanometer so that the coil and meter form a complete circuit.
- Give the first action and what you see: push the N pole of the magnet into the coil, and the needle deflects to one side.
- Give the observation that shows change is needed: hold the magnet still inside the coil, and the needle returns to zero.
- Give the reversal: pull the magnet out, and the needle deflects the opposite way.
- Add the size effect: repeat faster, and the deflection is larger.
- Finish with what it shows, in one sentence: an e.m.f. is induced in the coil only while the magnetic field linking it is changing.
Answer: Connect the coil to the galvanometer. Push the N pole into the coil: the needle deflects. Hold the magnet still: the needle reads zero. Pull the magnet out: the needle deflects the opposite way. Move it faster: the deflection is larger. An e.m.f. is induced only while the field linking the coil changes.
Example 2. The N pole of a bar magnet is pushed towards end P of a coil. The coil is connected to a galvanometer. (a) State the magnetic pole produced at end P, and explain why. (b) The magnet is then pulled away from P. State the pole at P now.
Show the working
- Name the change first. In (a) the change is an N pole moving closer to P.
- Apply the rule: the induced e.m.f., and so the induced current, opposes the change. Opposing an approaching magnet means pushing it away.
- Like poles repel, so P must be an N pole. That is the answer to (a), with its reason.
- In (b) the change is now an N pole moving away from P. Opposing that means trying to hold the magnet back, so the coil must attract it.
- Unlike poles attract, so P becomes an S pole. Notice that P has changed pole, because the direction of the change has reversed.
- Check with energy: in both parts you must push or pull against a force, so you do work, and that work becomes electrical energy in the circuit.
Answer: (a) N pole. The induced current opposes the change causing it, so P repels the approaching N pole. (b) S pole, which attracts the magnet and opposes it moving away.
Example 3. A straight wire lies between the poles of a magnet, with the N pole on the left and the S pole on the right. The wire runs straight into the page and is part of a complete circuit. (a) The wire is moved vertically upwards. Determine the direction of the induced current. (b) The wire is then moved vertically downwards. State the direction of the induced current now.
Show the working
- Find the field direction first. Field lines run from N to S, so the field points to the right.
- Use your right hand. Point your first finger to the right, along the field.
- Turn your hand so your thumb points upwards, the direction of motion, while your first finger still points right.
- Your second finger now points into the page. That is the induced current for (a).
- For (b), only the motion has reversed. Reversing one of the three directions reverses the current, so it now flows out of the page. Check it with your hand: thumb down, first finger right, second finger out of the page.
Answer: (a) Into the page. (b) Out of the page.
Example 4. Coil A is connected to a cell and a switch. Coil B is placed next to coil A and is connected only to a sensitive centre-zero galvanometer. Predict what the galvanometer shows when the switch is closed, while it stays closed, and when it is opened. Explain each answer.
Show the working
- There is no wire joining the coils, so any current in coil B must come from induction. Look for when the field linking coil B changes.
- Switch closed: the current in A rises from zero, so A's field grows and the field through B changes. Prediction: a brief deflection.
- Switch kept closed: the current in A is steady, so the field through B is steady. No change means no e.m.f. Prediction: zero.
- Switch opened: A's field falls to zero, a change in the opposite sense to switching on. Prediction: a brief deflection the other way.
Answer: A brief deflection when the switch is closed; zero while it stays closed, because the field is steady; a brief deflection in the opposite direction when it is opened. An e.m.f. is induced in B only while the field linking it changes.
Where people go wrong
Mistake: Saying the needle stays deflected while the magnet sits inside the coil.
Instead: The needle deflects only while the magnet moves. With the magnet at rest, the reading is zero.
An e.m.f. is induced only while the field linking the coil changes. A strong steady field induces nothing.
Mistake: Thinking the coil always repels the magnet.
Instead: The coil opposes the change. It repels a magnet that approaches and attracts a magnet that moves away.
The rule is that the induced e.m.f. opposes the change causing it. When the magnet moves away, the change is the moving away, so the coil attracts.
Mistake: Using the left hand to find the direction of an induced current.
Instead: Use Fleming's right-hand rule: thumb for motion, first finger for field, second finger for induced current.
The left-hand rule is for the motor effect. Used for induction, it gives the opposite current direction.
Mistake: Saying that no e.m.f. is induced if the coil is not connected to anything.
Instead: The e.m.f. is still induced. Only the current needs a complete circuit.
The objective is about an induced e.m.f. A meter, or any complete circuit, is needed to make a current flow and to show it.
Mistake: Thinking any movement of a wire in a magnetic field induces an e.m.f.
Instead: The wire must cut field lines. Moving it parallel to the field lines induces no e.m.f.
The objective says a conductor moving across the field. A wire moving along the field lines cuts none of them.
Check yourself
- State the two ways, given in this subtopic, that an e.m.f. can be induced in a conductor.
Answer
The conductor moves across a magnetic field (cutting the field lines), or the magnetic field linking the conductor changes. - A magnet is pushed into a coil whose ends are not connected to anything. Is an e.m.f. induced? Does a current flow?
Answer
Yes, an e.m.f. is induced. No current flows, because there is no complete circuit. - Why is a sensitive centre-zero galvanometer used in the induction experiment, rather than an ordinary ammeter?
Answer
The induced current is small, so the meter must be sensitive. The current can flow in either direction, so a centre-zero needle, which can swing either way, shows the direction as well as the size. - State three factors that affect the magnitude of the e.m.f. induced when a magnet moves into a coil.
Answer
The speed of the magnet, the strength of the magnet, and the number of turns on the coil. - A wire is moved between the poles of a U-shaped magnet, from the N pole towards the S pole. What does a galvanometer connected to the wire show, and why?
Answer
Zero. The wire moves along the field lines, parallel to them, so it cuts no field lines and no e.m.f. is induced. - The S pole of a magnet is pulled away from end Q of a coil in a complete circuit. State the pole produced at Q, and say why.
Answer
An N pole. It attracts the S pole that is moving away, so it opposes the change (the motion) causing the induced e.m.f. - In Fleming's right-hand rule, state what the thumb, the first finger and the second finger each represent.
Answer
Thumb: the motion of the conductor. First finger: the magnetic field, from N to S. Second finger: the induced (conventional) current. - A magnetic field points into the page. A wire lying up and down the page is moved to the right across the field. State the direction of the induced current in the wire.
Answer
Up the page. First finger into the page, thumb to the right, second finger points up the page.
Exam questions
Try each part first. Open the mark scheme after you have written your answer.
Question 1. A student connects the two ends of a coil of insulated copper wire to a sensitive centre-zero galvanometer. She holds a bar magnet with its N pole facing end P of the coil.
(a) Describe how the student can use this apparatus to demonstrate electromagnetic induction. Include what she observes. 3 marks No calculator
Mark scheme
- B1 the magnet is moved into or out of the coil (or the coil is moved relative to the magnet)
- B1 the needle deflects while the magnet is moving
- B1 any one from: no deflection when the magnet is at rest / deflection in the opposite direction when the magnet is moved out or the S pole is used / larger deflection when the magnet is moved faster
(b) State two changes that would give a larger deflection, using the same galvanometer. 2 marks No calculator
Mark scheme
- B1 any one from: move the magnet faster / use a stronger magnet / use a coil with more turns
- B1 a second, different change from the same list; 'a bigger magnet' is insufficient
(c) The student holds the magnet at rest inside the coil. Explain why the galvanometer reads zero. 2 marks No calculator
Mark scheme
- B1 the magnetic field linking the coil is not changing / no field lines are being cut / no relative motion between the magnet and the coil, owtte
- B1 so no e.m.f. is induced (and so no current flows)
(d) The student pushes the N pole of the magnet towards end P. State the magnetic pole produced at end P. 1 mark No calculator
Mark scheme
- B1 N pole
(e) Explain your answer to (d). 2 marks No calculator
Mark scheme
- B1 the induced e.m.f. (or current) opposes the change (the motion of the magnet) causing it
- B1 like poles repel, so an N pole at P pushes back against the approaching N pole
Question 2. A straight copper wire XY lies between the poles of a U-shaped magnet. The wire is connected to a sensitive centre-zero galvanometer. Looking at the magnet from the front, the N pole is on the left and the S pole is on the right. The wire runs straight into the page, with end X nearer to you and end Y further away.
(a) The wire is moved vertically upwards. Determine the direction of the induced current in the wire. 1 mark No calculator
Mark scheme
- B1 into the page / from X to Y
(b) The magnet is turned round so that the N pole is on the right, and the wire is moved vertically downwards. Predict the direction of the induced current, and give a reason. 2 marks No calculator
Mark scheme
- B1 into the page / from X to Y (the same direction as in (a)); ecf from (a)
- B1 both the field and the motion are reversed, so the two reversals cancel, owtte
(c) With the N pole back on the left, the wire is moved horizontally from the N pole towards the S pole. Explain why the galvanometer shows no deflection. 2 marks No calculator
Mark scheme
- B1 the wire moves parallel to (along) the magnetic field lines
- B1 so it cuts no field lines and no e.m.f. is induced
Question 3. A student moves a straight wire at steady speeds at right angles to a uniform magnetic field. The wire is connected to a data-logger that records the induced e.m.f. Her results: at 0.10 m/s the e.m.f. is 2.0 mV; at 0.20 m/s it is 4.0 mV; at 0.30 m/s it is 6.0 mV; at 0.40 m/s it is 8.0 mV.
(a) Deduce the relationship between the speed of the wire and the induced e.m.f. Use the results to support your answer. 2 marks
Mark scheme
- B1 the induced e.m.f. is (directly) proportional to the speed
- B1 evidence from the data, e.g. doubling the speed from 0.10 m/s to 0.20 m/s doubles the e.m.f. from 2.0 mV to 4.0 mV / e.m.f. divided by speed is 20 mV per m/s for every result
(b) Determine the induced e.m.f. when the wire moves at 0.25 m/s. 2 marks
Mark scheme
- C1 20 × 0.25 seen, or a value halfway between 4.0 mV and 6.0 mV
- A1 5.0 mV (or 0.0050 V); unit required
(c) State one change, other than the speed, that would make the e.m.f. larger at every speed. 1 mark No calculator
Mark scheme
- B1 use a stronger magnet / stronger magnetic field (accept: loop the wire into a coil so that more turns cut the field)
How this is examined
- Describing the magnet-and-coil experiment: what you do, and what the needle does: a three- or four-mark Describe, with the apparatus drawn or named in the stem One mark for each separate point: the coil connected to a sensitive (centre-zero) galvanometer; magnet moved into the coil, needle deflects; magnet held still, needle at zero; magnet pulled out, deflection in the opposite direction; magnet moved faster, larger deflection. 'Electricity is produced' does not say what is observed.
- Which pole forms at the end of the coil, and why: a one-mark State of N or S at a labelled end of the coil, then a two-mark Explain The same pole as the approaching magnet pole (N for an approaching N), and the opposite pole when the magnet moves away. The reason must contain the rule: 'the induced e.m.f. (current) opposes the change (motion) causing it', plus 'like poles repel' or 'unlike poles attract' as the case needs.
- The three things that make the induced e.m.f. bigger: a State two or State three; the list rule applies, so a wrong extra answer counts against you Any of: move the magnet (or wire, or coil) faster; use a stronger magnet; use a coil with more turns. 'A bigger magnet' is not the same as 'a stronger magnet'.
- Why nothing is induced when nothing changes: a one- or two-mark Explain about a magnet at rest in a coil, a steady current in a nearby coil, or a wire moving along the field lines First the cause: 'the magnetic field linking the coil is not changing', or 'the wire does not cut any field lines'. Then the result: 'so no e.m.f. is induced'. The safest cause links the stillness to the field: 'there is no relative motion, so the field linking the coil does not change'.
- Finding the induced current direction with Fleming's right-hand rule: a Determine or State with a wire between two poles; the answer is a direction such as 'into the page' or 'from X to Y' The correct direction, found with the right hand: first finger along the field from N to S, thumb along the motion, second finger gives the current. Reversing either the motion or the field reverses the current; reversing both leaves it unchanged.
Words to know
- Electromagnetic induction
- Producing an e.m.f. in a conductor when it moves across a magnetic field, or when the magnetic field linking it changes.
- Induced e.m.f.
- The e.m.f. produced by electromagnetic induction, measured in volts. It drives a current only if the conductor is part of a complete circuit.
- Field linking a coil
- The magnetic field lines that pass through the coil. A change in this field induces an e.m.f. in the coil.
- Centre-zero galvanometer
- A sensitive meter for small currents whose needle rests in the middle of the scale, so it can deflect either way and show the current's direction.
- Lenz's law
- The direction of an induced e.m.f. opposes the change that causes it.
- Fleming's right-hand rule
- With thumb, first finger and second finger of the right hand at right angles: thumb = motion, first finger = field (N to S), second finger = induced current.