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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 μO 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.

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