The Magnetic Field of a Steady Current

The magnetic field of a steady line current is given by given by the Biot - Savart law.
        B(P) = μ₀/4π ∫ Ixr/r² dl = μ₀ /4π I ∫dI x r/r²                         … (1)

The integration is along the current path, in the direction of flow. dl is an element of length along the wire. r is the vector from the source to the point P. B is called the magnetic induction.

For surface and volume currents the Biot-Savart law becomes
            B = u₀/4π ∫ K x r/r² da
And            B = μ₀/4π ∫ J x r /r² dτ                            … (2)



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