Ampere’s Law study with the finite length wire hypothesis

This article proposes the study of Ampere’s Law, which is taught in the Physics course of undergraduate engineering courses in Brazil, using the hypothesis of the finite-length conductor instead of the infinite-length conductor. For this, it is necessary to use Stokes’ Theorem, which in the case of infinite conductor is dispensed with. The feasibility of this proposal is supported by the fact that the techniques to calculate the line integrals and flux integrals, necessary in our proposal, are taught in the disciplines of Calculus. This approach allows a clear distinction between the “current enclosed” by the closed curve of the amperian line integral and the current actually flowing through the conductor. With the assumption of the infinite length conductor these two currents are indistinguishable. Another benefit of this approach is that the displacement current can be introduced intuitively as the flux integral of the curl of the magnetic field that appears in one of the members of the Stokes equation.

Keywords:
Ampere’s law; Stokes’s theorem; Finite length wire; Displacement current