My name is Alexander FufaeV and here I will explain the following topic:

# Electromagnetic Induction

## Formula

What do the formula symbols mean?

## Induced voltage

Unit
This electric voltage is formed, for example, between the end points of a wire loop when the magnetic field $$B$$ penetrating the wire loop is changed. Notice: Only as long as the temporal change of the magnetic field happens, the induction voltage is measurable. As soon as the magnetic field is NOT changed ($$B$$ constant), the voltage at the endpoints of the conductor loop disappears.

If the conductor loop is short-circuited, 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

Unit
Magnetic flux density $$B$$ enclosed by the conductor loop, which is changed by the value $$\Delta B$$. If this flux density $$B$$ changes in time, i.e. $$\Delta B \neq 0$$, then an induced voltage or induced current is generated in the conductor loop.

## Time span

Unit
This is a time span within which the magnetic flux density has changed by the value $$\Delta B$$. The smaller the time span within which the magnetic field has changed, the greater the induced voltage.

## Area

Unit
Area enclosed by the conductor loop. According to this formula, $$A$$ is not changed, i.e. in this case it is assumed that the area remains constant. This means: the conductor loop is not bent or manipulated in any other way to change the area penetrated by the magnetic field.
Explanation

## 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:

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• 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 cross-sectional 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:

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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:

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You can then use this induction voltage to light up a small lamp, for example.