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Formula Biot-Savart law for thin conductors Magnetic field    Position vector to field point    Position vector    Electric current    Conductor line    Magnetic field constant

Formula
Formula: Biot-Savart law for thin conductors

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.

Magnetic field constant

Unit
A natural constant with the value \( \mu_0 = 4\pi \cdot 10^{-7} \, \frac{ \text{N} }{ \text{A}^2 } \).