The Bio Savart Law

Consider a conductor XY carrying a current i. Consider an element  AB of length d I. O is the important of AB. P is a point at a distance r from O. θ is the angle between dt and r. Magnetic induction dB at a point P due to the current element dt is

            dB = (μ / 4π) i (dl X r) / r²

where r is a unit vector along r.
The magnitude of dB is
            dB = (μ / 4π) I dl sin θ / r²

The direction of dB is that of the vector dI X r.
The total magnetic induction B at P due to the current flowing in entire length of the conductor is

        B = ∫ dB = (μ / 4π) ∫ i (dl X r) / r²

In vacuum B is related to H (magnetic field intensity) by the formula.

        B = μ₀H
where, μ₀ is a constant, called the permeability of free space



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