# Biot-Savart Law¶

The Biot-Savart Law derives the magnetic field **B** due to a current:

Here, is the magnetic constant,
is the infinitesimal length and direction of a section of infinitesimally
thin wire current
we are integrating over, I is the amount of current in that section,
and **r** is the displacement vector from the section of wire current to the point
where **B** is measured.
may also be replaced with if a current density **J**
occupies a volume element dV.

## SIMION Specific¶

SIMION 8.0.3 can compute magnetic fields from wire currents using the Biot-Savart law using the simionx.MField - Biot-Savart magetic field calculations library. In SIMION 8.1.0.19, these wires can also be drawn on the SIMION View screen. Examples of this include

- SIMION Example: solenoid (see also Solenoid Magentic Field)
- SIMION Example: helmholtz_coil (see also Helmholtz Coil)

See also Magnets and Wikipedia:Biot-Savart_law.

A thick wire can be approximated with many thin wires.
See Example(helmholtz_coil) (`thick_coil`

sub-example) added 2018-03-08.