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
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)
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^
' is means that the integration
should be carried out around the circuit C.