Induction & Faraday's Law
A magnet parked inside a coil does nothing at all. Only a changing flux drives a current.
Introduction
Push a bar magnet into a coil of wire and a meter shows a current, with no battery anywhere. What, in the push, makes it?
You push the magnet deep into the coil, then hold it perfectly still. What does the meter read while you hold it?
Faraday's law
Flux is how much magnetic field threads the coil. Faraday's law says the EMF, which drives the current, is set by how fast the flux changes:
is the number of turns: each turn sees the same flux, and their EMFs add.
A case you can check on paper
So far the field changed. Now change the area.
Slide a square loop of side at speed into a region of uniform field . While only its front edge is inside, the area in the field grows steadily.
A 40 mV plateau
A single-turn square loop, 10 cm on a side, enters a 0.40 T field at 1.0 m/s. What does the meter read while the loop is entering?
A square loop with turns, 10 cm on a side, enters a T field at m/s. What is the EMF, with its sign, while it enters?
The loop is now entirely inside the field region, still moving at the same steady speed. What is the EMF?
The minus sign is Lenz's law
You push the magnet into the coil, pause, and pull it back out. Which way does the coil's force on the magnet point?
That is Lenz's law, the minus sign in Faraday's law: the induced current opposes the change in flux.
Fast or slow, the same charge
The fast run's EMF pulse is four times taller and four times narrower than the slow run's. Why did the same charge go round?
Charge from a flux change
A 100-turn coil has radius 5.0 cm and resistance 1.0 Ω. A magnet of moment 1.0 A·m² is pushed from 25 cm away to its middle. How much charge flows?
What comes next
You held a coil full of flux at zero EMF, read an EMF off a flux graph, and watched a coil push back on the magnet that moved it. Next, the other half: a changing magnetic field makes an electric field whether or not a loop is there, and Maxwell added a displacement-current term to Ampère's law, so that a changing electric field makes a magnetic field too. Each sustains the other, and the pair travels through empty space as a wave. Maxwell calculated its speed from electrical measurements and found the speed of light. The wave is light.
Ideas this lesson took on
Each of these is a common intuition the lesson put to the test. If one still feels right, the section that tests it is worth another look.
- “Lots of field through the coil means lots of EMF”
- “The induced current keeps going for a moment after you stop”
- “The coil always attracts the magnet”
- “The EMF is largest where the flux is largest”
Finished with this lesson?
Progress is stored on this device only. There is no account and nothing is sent anywhere.
Research behind this lesson
- Beichner 1994: Students routinely read a graph's height when its slope is what matters, and treat a position–time graph as a picture of the path the object took.
- Jelicic et al. 2017: Nine high-school students were interviewed while observing, describing and explaining six electromagnetism demonstrations, three of them on induction; the analysis found many conceptual and reasoning difficulties, especially with recognising and explaining induction, and identified three student mental models that recurred across the interviews.
- Maloney et al. 2001: The Conceptual Survey of Electricity and Magnetism (CSEM): a 32-question multiple-choice instrument refined over four years and administered to more than 5000 introductory students at 30 institutions. Pretest averages were 31% (calculus-based) and 25% (algebra/trigonometry-based); after instruction they reached only 47% and 44%.
- Thong & Gunstone 2008: Fifteen in-depth interviews with second-year physics students surfaced three previously unreported conceptions, among them that the induced current 'varies proportionately with current in solenoid' and that there must be 'contact' between magnetic flux and the external coil for any EMF to be induced.
- Zuza et al. 2014: In traditional teaching the fundamental concepts of electromagnetic induction are analysed quickly and most of the time goes on solving problems in a rote manner, and physics education research shows students barely understand those fundamental concepts; an interactive teaching sequence linking experimental findings to their theoretical interpretation improved understanding, though multilevel explanations remained hard.