Electromagnetic induction
| English | Chinese | Pinyin |
|---|---|---|
| electromagnetic induction | 电磁感应 | diàn cí gǎn yìng |
| magnetic flux | 磁通量 | cí tōng liàng |
| weber | 韦伯 | wéi bó |
| flux linkage | 磁链 | cí liàn |
| Faraday's law | 法拉第定律 | fǎ lā dì dìng lǜ |
| Lenz's law | 楞次定律 | léng cì dìng lǜ |
Electricity from a moving magnet
- Move a magnet near a coil and a current appears — with no battery.
- This is electromagnetic induction 电磁感应.
- Every power station generates electricity this way.
Magnetic flux 磁通量
- Flux through an area $A$ at right angles to $B$ is $\Phi = BA$ (unit: weber 韦伯).
- For a coil of $N$ turns, the flux linkage 磁链 is $N\Phi$.
A bar magnet pushed into a coil connected to a galvanometer induces an e.m.f. and deflects the needle
Electromagnetic induction
Move the magnet through the coil — a current is induced only while the field is changing. Faster gives more current; flip the magnet to reverse it.
The magnetic flux through an area $A$ at right angles to a field $B$ is:
$\Phi = BA$ (weber). For a coil of $N$ turns the flux linkage is $N\Phi$.
A $0.50\ \text{m}^2$ coil sits at right angles to a $0.20\ \text{T}$ field. What is the flux?
$\Phi = BA = 0.20 \times 0.50 = 0.10\ \text{Wb}$.
Faraday's law 法拉第定律
- The induced e.m.f. equals the rate of change of flux linkage: $|\varepsilon| = N\dfrac{d\Phi}{dt}$.
- A faster change of flux gives a bigger e.m.f.
The induced e.m.f. equals the rate of change of flux ____.
$|\varepsilon| = N\dfrac{d\Phi}{dt}$ — the rate of change of the flux linkage $N\Phi$.
Lenz's law 楞次定律
- The induced e.m.f. always opposes the change that makes it: $\varepsilon = -\dfrac{d(N\Phi)}{dt}$.
- This is conservation of energy — if it helped the change, energy would come from nothing.
Lenz's law says the induced e.m.f.:
It opposes the change — the minus sign in $\varepsilon = -\dfrac{d(N\Phi)}{dt}$.
Lenz's law follows from conservation of energy.
If the induced effect reinforced the change, energy would be created from nothing — so it must oppose it.
Making it bigger
- The flux changes by changing $B$, the area $A$, or the coil's orientation.
- Bigger e.m.f.: more turns, stronger field, larger area, or a faster change.
Select all the changes that increase the induced e.m.f.
A bigger $N$, $B$, or rate of change all raise the e.m.f. A stationary magnet gives no change of flux — no e.m.f.
You've got it
- magnetic flux $\Phi = BA$; flux linkage $N\Phi$
- Faraday: induced e.m.f. = rate of change of flux linkage
- Lenz: it opposes the change (conservation of energy)