Electromagnetic Induction and Faraday's Law
Введено| English | Значение |
|---|---|
| electromagnetic induction/ɪˌlektrəʊməɡˈnetɪk ɪnˈdʌkʃn/ | Электромагнитная индукция |
| magnetic flux/mæɡˈnetɪk flʌks/ | Магнитный поток |
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?
Сложность 1/5 · 100 монет + небольшой бонус за первое выполнение сегодня
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 $\text{V}$?
Сложность 2/5 · 140 монет + небольшой бонус за первое выполнение сегодня
$|\varepsilon| = N\Delta\Phi/\Delta t = 100 \times 0.02/0.5 = 4\ \text{V}$.
Increasing the number of turns in the coil makes the induced EMF:
Сложность 1/5 · 100 монет + небольшой бонус за первое выполнение сегодня
$\varepsilon = -N\Delta\Phi/\Delta t$: more turns $N$ gives a bigger EMF.
The minus sign in Faraday's law is ____ law: the induced current opposes the change.
Сложность 1/5 · 100 монет + небольшой бонус за первое выполнение сегодня
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.
Сложность 1/5 · 100 монет + небольшой бонус за первое выполнение сегодня
No change in flux means no induced current — the magnet must be moving.
Select все ways to increase the induced EMF in a coil.
Сложность 2/5 · 140 монет + небольшой бонус за первое выполнение сегодня
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.
Write from an induced EMF of 5 V
- A 50-turn coil has its flux change by 0.30 Wb in 3 s.
- Find the size of the induced EMF.
A coil of 50 turns has the flux through it change by 0.30 Wb in 3 s. What is the size of the induced EMF, in volts?
50 times 0.30 divided by 3 is 5.
What is the size of the induced EMF?
Сложность 1/5 · 100 монет + небольшой бонус за первое выполнение сегодня
Turns times flux change, divided by time, is 5 V. Other options — 4 V (the lesson example's EMF); 15 V (the product before dividing by the time).