Biot-Savart Law

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

B = \frac{\mu_0}{4 \, \pi} \int \frac{I \textrm{d}\vec{I} \times \vec{r}}{|r|^3}

Here, \mu_0 is the magnetic constant, \textrm{d}\vec{I} 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. I \textrm{d}\vec{I} may also be replaced with \vec{J} \, \textrm{d}V 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, these wires can also be drawn on the SIMION View screen. Examples of this include

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.