Electromagnetic induction
Electricity from a moving magnet
- Move a magnet near a coil and a current appears — with no battery.
- This is electromagnetic induction.
- Every power station generates electricity this way.
Magnetic flux
- Flux through an area $A$ at right angles to $B$ is $\Phi = BA$ (unit: weber).
- For a coil of $N$ turns, the flux linkage is $N\Phi$.
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
- 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
- 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)