Electromagnetic Induction and Faraday's Law
| English | Chinese | Pinyin |
|---|---|---|
| electromagnetic induction | 电磁感应 | diàn cí gǎn yìng |
| magnetic flux | 磁通量 | cí tōng liàng |
Wave a magnet near a coil — and make electricity
- Push a magnet in and out of a coil of wire and a current flows, with no battery at all.
- Moving the magnet generates a voltage — the reverse of the motor effect.
- This is electromagnetic induction 电磁感应, and it powers every generator on Earth.
- Every power station, from coal to wind, is really just spinning magnets near coils.
A changing field induces a voltage
- What matters is a change in the magnetic field through the coil — its flux 磁通量.
- A changing flux induces a voltage (an EMF) in the coil.
- Move the magnet, spin the coil, or switch a current on or off — any change works.
- Hold everything still and the induced voltage vanishes; it is the change that counts.
Induce a current
Move a magnet through a coil at different speeds and watch the induced current change.
What is needed to induce a voltage in a coil?
Only a changing flux induces an EMF; a steady field does nothing.
Faraday's law
- Faraday's law: the induced EMF equals the rate of change of flux, $\varepsilon = -N\dfrac{\Delta\Phi}{\Delta t}$.
- $N$ is the number of turns, and $\Phi$ the magnetic flux through each.
- A faster change, or more turns, gives a bigger induced voltage.
- The minus sign is Lenz's law — the induced current opposes the change that made it.
A $100$-turn coil has its flux change by $0.02\ \text{Wb}$ in $0.5\ \text{s}$. What is the size of the induced EMF, in $\text{V}$?
$|\varepsilon| = N\Delta\Phi/\Delta t = 100 \times 0.02/0.5 = 4\ \text{V}$.
Increasing the number of turns in the coil makes the induced EMF:
$\varepsilon = -N\Delta\Phi/\Delta t$: more turns $N$ gives a bigger EMF.
The minus sign in Faraday's law is ____ law: the induced current opposes the change.
Lenz's law: the induced current opposes the change in flux that produced it.
Generators and transformers
- A generator spins a coil in a field, constantly changing the flux to make AC electricity.
- A transformer uses a changing current in one coil to induce a voltage in another.
- Both are just Faraday's law at work, converting motion (or changing current) into voltage.
- Induction is the two-way bridge between electricity and magnetism.
A magnet held still inside a coil induces a steady current.
No change in flux means no induced current — the magnet must be moving.
Select all ways to increase the induced EMF in a coil.
A faster change, more turns, or a stronger magnet all raise the EMF. Holding still induces nothing.
Induction needs a changing flux, not just a field. A magnet sitting still inside a coil induces no current — only moving it (changing the flux) does. And Lenz's law (the minus sign) means the induced current always opposes the change causing it.
A coil of $N = 100$ turns has the flux through it change by $\Delta\Phi = 0.02\ \text{Wb}$ in $\Delta t = 0.5\ \text{s}$. Find the size of the induced EMF.
- $|\varepsilon| = N\dfrac{\Delta\Phi}{\Delta t} = 100 \times \dfrac{0.02}{0.5} = 4\ \text{V}$.
Change the flux faster (smaller $\Delta t$) and the induced voltage grows.
Electromagnetic induction: a changing magnetic flux induces an EMF. Faraday's law: $\varepsilon = -N\dfrac{\Delta\Phi}{\Delta t}$ — faster change or more turns means more voltage. The minus sign is Lenz's law (the induced current opposes the change). Generators and transformers all run on this.