22.4 Ampere's Circuital Law
Figure 5
The mathematical proof of this is beyond the scope of this guide; however it can be said that
the equivalence between BiotSavart and Ampere's Laws will be brought out by determining due to
an infinitely long conductor carrying a steady current through it.
Figure 6
In fig.7, the circle in the plane is perpendicular to the plane of diagram, and is used as an
Amperean loop.
\ Applying Ampere's Circuital Law.
Figure 7
Equations (4) and (5) are identical. That is obvious as each gives due to an infinitely long conductor.
Thus equivalence is established between the BiotSavart and Ampere's Laws.
