This law gives the magnetic field **B** at some point P due to a circuit C carrying a steady current I in a thin wire.

From Maxwell's equations when the electric field is constant in time (d**D**/dt=0) we have the relation

curl **B**= μ_{O}**J**

where μ

_{O} is the

permeability of free space and

**J** is the

current density.

This can be expressed in integral form as the *Biot-Savart law*.

**B** = (μ_{O}I /4π) ∫_{c} (**dl'** X **r^**/r²)

where

**dl'** is a

differential element of the circuit, r is the distance from the circuit element to the point P (where the field is to be measured) and

**r^** is a

unit vector such that

**r**= r

**r^**. '∫

_{c}' is means that the

integration should be carried out around the circuit C.