Electromagnetic Induction
Formula
What do the formula symbols mean?
Induced voltage
$$ U_{\text{ind}} $$ Unit $$ \mathrm{V} = \frac{ \mathrm J }{ \mathrm C } = \frac{ \mathrm{kg} \, \mathrm{m}^2 }{ \mathrm{A} \, \mathrm{s}^3 } $$If the conductor loop is shortcircuited, i.e. the two contacts are connected, then an induction current \( I_{\text{ind}} \) is generated in the conductor loop.
The minus sign in the induction law is justified by the Lenz rule in order not to violate the conservation of energy.
Magnetic field change
$$ \class{violet}{\Delta B} $$ Unit $$ \mathrm{T} = \frac{\mathrm{kg}}{\mathrm{A} \, \mathrm{s}^2} $$Time span
$$ \Delta t $$ Unit $$ \mathrm{s} $$Area
$$ A $$ Unit $$ \mathrm{m}^2 $$Video
Electromagnetic induction states that a change in the magnetic flux \( \class{purple}{B} \) in a closed electrical circuit induces a voltage \( U_{\mathrm{ind}} \) or a current \( I_{\mathrm{ind}} \) in this circuit:

Here, \( U_{\text{ind}} \) is the induced voltage. This voltage is formed, for example, between the end points of a conductor loop when the magnetic field \( B \) penetrating the conductor loop is changed.

Magnetic flux density \( B \) enclosed by the conductor loop, which is changed by the value \( \Delta B \). If this flux density \( B \) changes over time, that is \( \Delta B \neq 0 \), then an induced voltage or induced current arises in the conductor loop.

Time period \( \Delta t \) within which the magnetic flux density has changed by the value \( \Delta B \).

area \( A \) enclosed by the conductor loop, for example. According to this formula, \( A \) is not changed, that is, in this case it is assumed that the area remains unchanged.
How does a dynamo work?
With a dynamo (e.g. a bicycle dynamo) you convert mechanical work (here: pedaling) into electrical energy.
How does it work? A dynamo consists of a coil with a certain number of turns \( N \) and a crosssectional area \( A \). This coil is rotated in the magnetic field \( B \) of a permanent magnet, which generates an alternating voltage \( U_{\text{ind}}(t) \) according to Faraday's law of induction 1
.
If the coil rotates at a fixed angular frequency \( \omega \), the magnetic flux through the coil changes as follows:
All you have to do is to differentiate the magnetic flux 2
with respect to time and you get the voltage induced by the dynamo:
You can then use this induction voltage to light up a small lamp, for example.