Electromagnetic induction

What is it about?

When the magnetic flux $\Phi = B \cdot A \cdot \cos\varphi$ through a coil changes, a voltage is induced:

Only the change of the flux counts. The three experiments change it in different ways: a moving magnet changes $B$; a rod on rails changes the area $A = l \cdot x$, giving $U = B \cdot l \cdot v$; a generator changes the angle, giving $U(t) = \hat U \sin(\omega t)$ with $\hat U = n \cdot B \cdot A \cdot \omega$.

Lenz’s law: the induced current opposes its cause – an approaching north pole meets a north pole of the coil, and the rod is braked by $F = B \cdot I \cdot l$. In the picture the generator runs ten times slower; the graph shows real time.

Try it

1. Watch the voltmeter while the magnet moves in and out. Load example
2. Switch off “automatic” and drag the magnet yourself. Drag it
3. Rod on rails: how does $U$ depend on $v$, $l$ and $B$? Rod on rails
4. Generator: in which position is the voltage largest? Generator

Tasks

Task 1: Moving rod

$l = 0.20\,\text{m}$, $v = 2.0\,\frac{\text{m}}{\text{s}}$, $B = 0.50\,\text{T}$. Find $U$. Load task

Task 2: Generator

$n = 100$, $A = 100\,\text{cm}^2$, $B = 0.10\,\text{T}$, $f = 5\,\text{Hz}$. Find $\hat U$ and $U_\text{eff}$. Load task

Task 3: Lenz’s law

A north pole is pushed into a coil. Which pole appears at the near end of the coil?

Ideas for the classroom

• Start qualitatively with the magnet, derive $U = B \cdot l \cdot v$ with the rod, finish with the generator.
• Common stumbling blocks:
  • “A strong magnet inside the coil gives a voltage.” – Only a change of flux does.
  • “The generator voltage is largest when the coil area is perpendicular to the field.” – Then the flux is largest but does not change.