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Formula: **Coil**

$$L ~=~ \mu_0 \, \mu_{\text r} \, \frac{ A \, N^2 }{ l }$$
$$L ~=~ \mu_0 \, \mu_{\text r} \, \frac{ A \, N^2 }{ l }$$
$$l ~=~ \mu_0 \, \mu_{\text r} \, \frac{ A \, N^2 }{ L }$$
$$N ~=~ \sqrt{ \frac{ L \, l }{ \mu_0 \, \mu_{\text r} \, A } }$$
$$A ~=~ \frac{ L \, l }{ \mu_0 \, \mu_{\text r} \, N^2 }$$

## Inductance

`$$ L $$`Unit

`$$ \mathrm{H} = \frac{ \mathrm{Vs} }{ \mathrm{A} } $$`

Inductance is the property of the coil and tells how good the coil can store magnetic energy. With the formula you calculate only approximately the inductance of the long coil. By long is meant: length \(l\) is much larger than the radius of the cross-sectional area \( A \).

## Coil length

`$$ l $$`Unit

`$$ \mathrm{m} $$`

It is the length from one end to the other end of the coil. The formula is only accurate if the coil length is significantly larger than the radius \( r\) of the coil.

## Number of turns

`$$ N $$`Unit

`$$ - $$`

Number of turns of the coil. ("Number of spirals"). The more turns a coil has, the larger the magnetic field generated by the coil.

## Cross-sectional area

`$$ A $$`Unit

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

Area enclosed by a coil (usually circular).

## Relative permeability

`$$ \mu_{\text r} $$`Unit

`$$ - $$`

This dimensionless quantity describes the medium enclosed by the coil windings.

It is possible to significantly amplify the magnetic field \(B\) generated inside the coil by pushing a certain material into the coil interior. This material is characterized by the relative permeability. If there is vacuum (or air) inside the coil, then \( \mu_{\text r} ~=~ 1 \). If you put an iron core into the coil, the relative permeability can be 300 up to 10000. Thus the magnetic field would be amplified by the factor 300 to 10000.

## Vacuum permeability

`$$ \mu_0 $$`Unit

`$$ \frac{\mathrm{Vs}}{\mathrm{Am}} = \frac{ \mathrm{kg} \, \mathrm{m} }{ \mathrm{A}^2 \, \mathrm{s}^2 } $$`

The vacuum permeability is a physical constant and has the following experimentally determined value:

`$$ \mu_0 ~=~ 1.256 \, 637 \, 062 \, 12 ~\cdot~ 10^{-6} \, \frac{\mathrm{Vs}}{\mathrm{Am}} $$`