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

Electromagnetic Induction

Formula

Formula: Induced Voltage due to Magnetic Field Change
Bar Magnet Induces Current in a Metal Ring Hover the image!
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.