# Formula: Biot-Savart Law for a Thin Wire Magnetic field    Position vector to field point    Position vector    Electric current    Conductor line    Vacuum permeability

## Magnetic field

Unit
Magnetic flux density tells how strong the magnetic field is at the location $$\boldsymbol{r}$$ generated by a steady-state current $$I$$ through the conductor.

## Position vector to field point

Unit
Position vector from the coordinate origin to any point in space at which the magnetic field is to be calculated.

## Position vector

Unit
Location vector points from the coordinate origin to the infinitesimal conductor element $$\text{d}\boldsymbol{s}$$.

Here $$\boldsymbol{r} - \boldsymbol{R}$$ is the connection vector pointing from the infinitesimal conductor element $$\text{d}\boldsymbol{s}$$ to the field point. $$|\boldsymbol{r} - \boldsymbol{R}|$$ is the distance of the infinitesimal conductor element $$\text{d}\boldsymbol{s}$$ to the field point.

## Electric current

Unit
Constant electric current inside the conductor.

## Conductor line

The conductor through which the current flows.

Here $$\text{d}\boldsymbol{s}$$ is an infinitesimal length element. This length element runs along the conductor.

## Vacuum permeability

Unit
The vacuum permeability is a physical constant and has the following experimentally determined value: $$\mu_0 ~=~ 1.256 \, 637 \, 062 \, 12 ~\cdot~ 10^{-6} \, \frac{\mathrm{Vs}}{\mathrm{Am}}$$

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