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Formula: **Induced Voltage due to Magnetic Field Change**

$$U_{\text{ind}} ~=~ - A \, \frac{\class{violet}{\Delta B}}{\Delta t}$$
$$U_{\text{ind}} ~=~ - A \, \frac{\class{violet}{\Delta B}}{\Delta t}$$
$$\class{violet}{\Delta B} ~=~ -\frac{ U_{\text{ind}} }{ A } \, \Delta t$$
$$\Delta t ~=~ - \frac{ A }{ U_{\text{ind}} } \, \class{violet}{\Delta B}$$
$$A ~=~ - U_{\text{ind}} \, \frac{ \Delta t }{ \class{violet}{\Delta B} }$$

## Induced voltage

`$$ U_{\text{ind}} $$`Unit

`$$ \mathrm{V} = \frac{ \mathrm J }{ \mathrm C } = \frac{ \mathrm{kg} \, \mathrm{m}^2 }{ \mathrm{A} \, \mathrm{s}^3 } $$`

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

`$$ \class{violet}{\Delta B} $$`Unit

`$$ \mathrm{T} = \frac{\mathrm{kg}}{\mathrm{A} \, \mathrm{s}^2} $$`

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

`$$ \Delta t $$`Unit

`$$ \mathrm{s} $$`

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

`$$ A $$`Unit

`$$ \mathrm{m}^2 $$`

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.