Explain how Biot-Savart’s law enables one to express the Ampere’s circuital law in the integral form, viz.

where, I is the total current passing through the surface.

Consider any arbitrary closed path perpendicular to the plane of paper around a long straight conductor XY carrying current from X to Y, lying in the plane of paper. Let the closed path be made of large number of small elements, where

be the angles subtended by the various elements at point O through which conductor is passing. Then

Suppose these small elements AB, BC, CD are

small circular arcs of radii r1, r2, r3,… respectively.

In case of each element, the magnetic field induction B and current element vector d\ are in the same direction. Line integral of B around closed path is