F. Electricity and Magnetism · Electricity and MagnetismElectromagnetic Induction: Faraday's Law and Lenz's Law
F2.7 F3.4 F3.2 F3.5About 75 minutes
Learning goals- I can describe how a changing magnetic field induces a current in a conductor (Faraday's law).
- I can list the factors that increase an induced current.
- I can use Lenz's law, conservation of energy and the right-hand rules to find the direction of an induced current.
- I can describe technologies that use electromagnetic induction.
Words to know
electromagnetic induction
Producing a potential difference (and a current, if the circuit is closed) in a conductor by changing the magnetic field around it.
Faraday's law (law of electromagnetic induction)
A potential difference is induced in a conductor whenever the magnetic field in the region of the conductor changes; the faster the change, the larger it is.
Lenz's law
The induced current flows in a direction that makes a magnetic field opposing the change that produced it.
induced current
A current produced by electromagnetic induction rather than by a battery.
galvanometer
A sensitive meter that detects small currents and shows their direction (the needle swings either way from zero).
Turning the trick around
Oersted showed that a current makes a magnetic field. Scientists then asked the obvious question: can a magnetic field make a current? In 1831, the English scientist Michael Faraday found the answer. A magnet sitting still inside a coil does nothing. But moving the magnet, or switching a nearby electromagnet on or off, makes a current flow.
That discovery, electromagnetic induction, is how nearly all the electricity in Ontario is generated, from Niagara Falls to the Pickering, Darlington and Bruce nuclear stations to the wind farms along Lake Huron. It is also how a wireless phone charger, an electric guitar pickup and a transformer work.
Faraday's law
When the magnetic field in the region of a conductor changes, a potential difference is induced in the conductor. If the conductor is part of a closed circuit, an induced current flows.
Ways to change the field through a coil:
- move a magnet into or out of the coil, or move the coil past the magnet;
- rotate a coil in a magnetic field (or rotate a magnet near a coil);
- switch on, switch off or change the current in a nearby coil.
A steady field, however strong, induces nothing. Only change counts.
The induced current is larger when:
- the change is faster (move the magnet more quickly),
- the coil has more turns,
- the magnet is stronger, and
- the coil has a soft-iron core, which concentrates the field.
Looking ahead: in later courses you will write this as a formula: the induced potential difference equals the number of turns times the rate of change of a quantity called magnetic flux.
Lenz's law: which way does the current go?
The induced current flows in the direction that creates a magnetic field opposing the change that produced it.
- Push a magnet's N pole toward a coil: the near end of the coil becomes N and repels it.
- Pull the N pole away: the near end becomes S and attracts it, trying to hold it back.
Why it must be this way (conservation of energy): suppose the coil did the opposite and attracted an approaching magnet. The magnet would speed up, inducing a bigger current, which would pull harder, and so on. You would get endless kinetic energy and electrical energy from nothing. Energy cannot be created, so the induced current must oppose the motion. That is why it takes work to push the magnet in: your work becomes the electrical energy in the coil.
A three-step method
- What is changing? (For example: an N pole is approaching the left end, so the field pointing into the coil from the left is growing.)
- What pole must the coil make to oppose it? (Make the left end N, to repel.)
- Use RHR #2 to find the current that makes that pole. (Thumb points to the left; your fingers show the current in the loops.)
Worked exampleExample 1: N pole moving in
The N pole of a bar magnet is pushed into the left end of a coil. (a) What pole forms at the left end of the coil? (b) Looking from the left end, which way does the conventional current circulate? (c) What happens when the magnet stops inside the coil?
- (a) The approaching N pole must be opposed (repelled), so the left end becomes an N pole.
- (b) RHR #2: point your right thumb toward the N end, to the left. As you look at the left end, your fingers curl counterclockwise.
- (c) When the magnet stops, the field stops changing, so the induced current drops to zero.
(a) N; (b) counterclockwise; (c) no current.
Worked exampleExample 2: N pole moving out
The magnet from Example 1 is now pulled back out of the left end. Find the induced pole and current direction. How does the galvanometer reading compare with Example 1?
- The N pole is leaving; the coil must try to hold it, so it attracts: the left end becomes an S pole.
- RHR #2: the N end is now on the right, so the thumb points right. Looking at the left end, the current goes clockwise.
- The current is in the opposite direction to Example 1, so the galvanometer needle swings the other way. If the magnet moves faster, the swing is bigger.
The left end becomes S; the current is clockwise (viewed from the left), opposite to Example 1.
A metal rod slides to the right along two rails in a field pointing into the page. The induced current in the rod flows up the page. The motor-principle force on that current points left, opposing the motion, exactly as Lenz's law requires.Worked exampleExample 3: A moving straight conductor
A metal rod is pulled to the right along two metal rails connected by a lamp, in a field pointing into the page (see the diagram). Find the direction of the induced current in the rod.
- Lenz's law: the induced current must create a force that opposes the motion, so the force on the rod must point left.
- Use the motor rule (RHR #3) backwards: fingers into the page (field), palm facing left (force). Your thumb points up the page.
- So the induced conventional current in the rod flows up the page, and around the circuit through the lamp.
- Energy check: the person pulling must keep doing work against that leftward force. That work becomes the light and heat from the lamp.
Worked exampleExample 4: Two coils on an iron ring
Two coils are wound on the same iron ring. Coil 1 is connected to a battery and a switch; coil 2 is connected to a galvanometer. Describe the galvanometer reading (a) when the switch is closed, (b) while it stays closed, (c) when it is opened.
- (a) Closing the switch makes the field in the ring grow from zero, a change, so a brief current is induced in coil 2 and the needle flicks.
- (b) With a steady current in coil 1, the field is steady, so there is no induced current and the needle reads zero.
- (c) Opening the switch makes the field collapse, another change, in the opposite sense, so the needle flicks the other way.
- This experiment, first done by Faraday, is the idea behind the transformer (Lesson: Transformers). A transformer needs a field that changes all the time, so it runs on AC.
A brief flick, then zero, then a brief flick the other way.
Induction at work
- Generators at power stations rotate coils and magnets past each other (next lesson).
- Transformers change AC voltages up and down.
- Wireless (inductive) phone chargers and electric toothbrush chargers: a changing current in a coil in the base induces a current in a coil in the device.
- Induction cooktops: a rapidly changing field induces currents in the bottom of an iron or steel pot, which heat the pot directly.
- Electric guitar pickups: a vibrating steel string changes the field of a small magnet wrapped in a coil, inducing a tiny signal current.
- Vehicle detector loops under the pavement at intersections and metal detectors sense the induced effects when metal moves near a coil.
- Regenerative braking in hybrid and electric cars: the motor acts as a generator, and Lenz's law supplies the braking force while charging the battery.
Just for funDrop a strong magnet down a copper pipe and it drifts down in slow motion, even though copper is not magnetic. The falling magnet induces currents in the copper, and by Lenz's law their fields push back against the fall. It looks like a magic trick; it is just physics refusing to let anything change without an argument.
Hands-on activitySee induction for yourself
Option A (computer): open the free PhET simulation "Faraday's Law" (or "Faraday's Electromagnetic Lab"). Drag the magnet in and out of the coil. Watch the bulb or voltmeter. Try fast and slow motion, the N end and the S end, one coil and two coils.
Option B (with materials): a coil of 50 to 100 turns of thin insulated wire (wound around a toilet-paper tube), a strong bar or stack of disc magnets, and a sensitive meter (a multimeter on its lowest mA or mV DC setting). Grown-up note: keep strong magnets away from young children, phones and bank cards.
- Connect the coil to the meter. Hold the magnet still inside the coil. Record the reading.
- Push the N pole in quickly. Record the direction and size of the reading. Pull it out quickly.
- Repeat slowly. Then repeat with the S pole.
- Make a table: motion (in/out), pole (N/S), speed (fast/slow), reading.
What to look for: zero reading when the magnet is still; opposite readings for in and out; the S pole reverses each reading; faster motion gives larger readings; two coils (more turns) in the simulation give larger readings. Each row of your table should agree with Lenz's law.
Your turn
1State Faraday's law in words.
When the magnetic field in the region of a conductor changes, a potential difference (and, in a closed circuit, a current) is induced in the conductor.
2A strong magnet rests inside a coil connected to a galvanometer. What does the galvanometer read? Why?
Zero. The field is not changing, so nothing is induced.
3List three ways to increase the current induced by moving a magnet into a coil.
Any three: move the magnet faster; use more turns; use a stronger magnet; put a soft-iron core in the coil.
The induced current flows in a direction that makes a magnetic field that opposes the change that produced it.
5The S pole of a magnet is pushed into the right end of a coil. What pole forms at the right end of the coil?
An S pole, to repel the approaching S pole.
6For the last question, looking at the right end of the coil, which way does the conventional current circulate?
The right end is S, so the N end is the left end and your right thumb points left (away from you as you look at the right end). Your fingers curl clockwise as you look at the right end. (Check: an end where current looks clockwise is an S pole ✓.)
7Use conservation of energy to explain why Lenz's law must be true.
If the induced current helped the change, the magnet would speed up and produce more and more current with no input: energy from nothing, which is impossible. So the induced field must oppose the change, and someone must do work to keep it going. That work becomes the electrical energy.
More practice: warm-up
1Who discovered electromagnetic induction, and in what year?
Michael Faraday, in 1831.
2Does a magnet held still near a coil induce a current?
No. Only a changing field induces a current.
3What instrument detects a small current and shows its direction?
4Name two everyday devices that use electromagnetic induction.
Any two: generator, transformer, wireless phone charger, induction cooktop, electric guitar pickup, metal detector, vehicle detector loop.
5When a magnet is pulled out of a coil, does the coil attract or repel it?
It attracts it, opposing the motion away.
More practice: on your own
1A magnet's N pole is pushed into a coil, giving a needle deflection to the right. Predict the deflection for: (a) N pole pulled out, (b) S pole pushed in, (c) S pole pushed in twice as fast.
(a) Left (the motion reverses). (b) Left (the pole reverses). (c) Left, and larger (faster change gives a bigger current).
2A metal rod moves to the left along rails in a magnetic field pointing out of the page. Find the direction of the induced current in the rod.
The force on the rod must oppose the motion, so it points right. Motor rule: fingers out of the page, palm facing right: the thumb points up the page. So the current flows up the page. (Check with v × B on positive charges: left × out = up ✓.)
3In Faraday's iron-ring experiment, why does the galvanometer show nothing while the switch stays closed?
With a steady current in the first coil, the magnetic field in the ring is constant. A constant field induces no potential difference in the second coil.
4Explain why it is harder to push a magnet into a coil when the coil is connected to a lamp than when its ends are not connected.
With the circuit closed, an induced current flows and makes a field that repels the magnet (Lenz's law), so you must do extra work, which becomes the lamp's light and heat. With the circuit open, a potential difference is induced but no current flows, so there is no opposing field.
5How does an induction cooktop heat a steel pot without its surface getting very hot itself?
A coil under the glass carries a rapidly alternating current, making a rapidly changing magnetic field. This induces currents in the steel bottom of the pot, and the pot's resistance turns that electrical energy into thermal energy. The glass is heated only indirectly, by the hot pot.
Challenge
1A bar magnet falls N-pole first through a horizontal coil connected to a galvanometer. Describe the readings as the magnet approaches, passes through and leaves the coil. Compare the two pulses.
As the N pole approaches, current flows one way (the top of the coil becomes N, repelling it). As the S pole leaves the bottom, current flows the opposite way (the bottom of the coil becomes N, attracting the S end back). The second pulse is larger and shorter, because the magnet is moving faster after falling farther. In the middle the reading passes through zero.
2Explain the slow fall of a magnet through a copper pipe using Lenz's law and energy conservation.
As the magnet falls, the field changes in each ring of the copper pipe, inducing eddy currents. By Lenz's law the rings ahead of the magnet repel it and the rings behind attract it, both producing an upward force. The magnet quickly reaches a slow terminal speed. Its lost gravitational potential energy becomes thermal energy in the copper instead of kinetic energy.
3A coil is placed on a table with its axis vertical. A magnet is held above it with its S pole down, and then is moved upward, away from the coil. Viewed from above, which way does the induced current circulate?
The S pole is leaving, so the coil must attract it: the top of the coil becomes N. RHR #2: thumb up (toward the N end, toward you as you look down). Your fingers curl counterclockwise as seen from above.
Quiz
1. Which situation induces a current in a coil?
2. Lenz's law is a consequence of which principle?
3. The N pole of a magnet is pulled away from the end of a coil. What pole forms at that end of the coil?
4. Which change would NOT increase the induced current?
5. A switch connecting a battery to coil 1 is closed. Coil 2, on the same iron ring, is connected to a galvanometer. What does the galvanometer show?
6. A rod moves right on rails in a field into the page. What is the direction of the magnetic force on the rod caused by its induced current?
Big idea: Faraday's law and Lenz's law (F3.4) explain how moving magnets make electricity. Students investigate induction and use Lenz's law, conservation of energy and the right-hand rule to find the direction of an induced current (F2.7, F3.2). Every generator and transformer in the next lessons depends on this.
How to help: The free PhET Faraday's Law simulation is excellent for building intuition. Ask your teen to predict each result before trying it, then explain it with the three-step Lenz's law method.
Common difficulties:
- Thinking a strong magnet near a coil always makes current. Only change matters.
- Getting the induced pole backwards. Ask: "Is the coil trying to push it away, or hold it back?" The coil always opposes the change.
- Mixing up the hand rules. For coils use RHR #2 (fingers = current, thumb = N); for moving rods use the motor rule with the force opposing the motion.