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 (dD/dt=0) we have the relation
curl B= μOJ
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 = (μOI /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.