Magnetism & electromagnetic induction
The idea
Electricity and magnetism are two faces of one interaction. Moving charges create magnetic fields — that is why a current-carrying wire deflects a compass and why coiling wire around an iron core makes an electromagnet. Magnetic fields in turn push on moving charges and currents, always at right angles to the motion. You already know magnets attract and repel; the deeper story is that magnetism is electricity in motion.
The reverse effect is induction, and it powers civilization: a CHANGING magnetic environment through a loop of wire creates a voltage, called an emf. Faraday's law makes it quantitative — the induced emf equals the number of turns times the rate of change of magnetic flux, emf = N × ΔΦ/Δt, where flux Φ = BA is field strength times the loop area it threads. Lenz's law fixes the direction: the induced current flows so its own magnetic field opposes the change that created it, which is energy conservation wearing a magnetic disguise.
The essential misconception: a strong field does not induce anything. You can park a coil in an enormous steady field forever and get zero current. Only CHANGE matters — a growing or dying field, a moving magnet, a rotating or shrinking loop. Generators spin coils precisely to keep the flux through them perpetually changing.
Worked example
A coil of 50 turns, each with area 0.020 m², sits with its plane perpendicular to a uniform 0.60 T magnetic field. The field is switched off, dying to zero in 0.25 s. Find the average emf induced in the coil and the current driven through its total resistance of 8.0 Ω.
- Compute the initial flux through one turn: Φ = BA = 0.60 × 0.020 = 0.012 Wb, and the final flux is zero once the field is gone.
- The flux change per turn is therefore ΔΦ = 0.012 Wb over Δt = 0.25 s — it is this change, not the field's strength, that drives the induction.
- Apply Faraday's law with all 50 turns contributing: emf = N × ΔΦ/Δt = 50 × 0.012/0.25 = 2.4 V.
- Drive that emf through the coil's resistance with Ohm's law: I = emf/R = 2.4/8.0 = 0.30 A flowing while the field collapses.
- Determine the direction with Lenz's law: the coil's flux is dying, so the induced current circulates to regenerate it, creating its own field in the same direction the vanishing field pointed.
- Sanity-check the time dependence: had the field died in 0.025 s instead, the emf would be ten times larger — faster change, bigger push — while a field merely sitting at 0.60 T would induce nothing at all.
Answer. The collapsing field induces an average emf of 2.4 V, driving a current of 0.30 A through the coil while the change lasts.
Check your understanding
- Why does a magnet resting motionless inside a coil induce no current, no matter how strong the magnet is?
- How is Lenz's law really a statement of energy conservation, and what would go wrong if induced currents aided the change instead?
- What are three physically different ways to change the magnetic flux through a loop, and which does a generator use?
- How does induction explain why pedaling a bicycle dynamo gets harder the brighter the lamp burns?
Build the foundations first
Magnetism & electromagnetic induction builds on these concepts. If any feel shaky, start there.