On the equivalence of the laws of Biot–Savart and Ampere

Many elementary physics texts do not explicitly state how the laws of Ampere and Biot–Savart are related. This relationship is explored with the help of an interesting example that seems to imply the paradoxical result that displacement currents are not equivalent to conduction currents in the production of magnetic fields. The equivalence of the two laws is then demonstrated by the use of Maxwell’s equations and the paradox is thereby resolved. Although the proof of equivalence is not suitable for introductory courses, the result that these two laws contain the same physics should be emphasized.