22.4 Ampere's Circuital Law

The mathematical proof of this is beyond the scope of this guide; however it can be said that the equivalence between Biot-Savart and Ampere's Laws will be brought out by determining due to an infinitely long conductor carrying a steady current through it.

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 Biot-Savart and Ampere's Laws.

Index

22.1 Oersted's Experiments
22.2 Ampere's Rule
22.3 Biot-Savart or Laplace's Law
22.4 Ampere's Law

Chapter 23