Magnetic field generated by the flow of AC current through finite length nonmagnetic conductors (cylinders, tubes, coaxial cables)

The magnetic field circulation counterpart to Biot-Savart’s law

“…Recently, [9] used the integral form of Ampère-Maxwell's law in conjunction with Coulomb's law in the zero retarded-time limit to obtain a simple formula that allows the circulation, around an arbitrarily shaped loop, of the magnetic field generated by a current in an arbitrarily shaped finite wire, to be expressed in terms of the wire current and of the solid angles subtended by the circulation path and each of the wire's endpoints. More recently, [10,11] used the formula in [9] to determine the magnetic fields generated by finite length conducting tubes, cylinders, and coaxial cables. While Biot-Savart's law gives the same result as the formula in [9] if applied to a finite length of straight conducting wire, there is no evidence that this is true if the wire and/or the circulation path are arbitrarily shaped.…”

Using Biot–Savart’s law to determine the finite tube’s magnetic field

“…[1][2][3][4][5][6][7][8][9][10][11] and references therein. By contrast, even though a finite length tubular conductor's magnetic field can be obtained by superposition of filamentary wire segments carrying infinitesimal current, Biot-Savart's law has not previously been applied to such problem, which as far as known to us has only been addressed in two recent studies [12,13], of which [12] is the most relevant in the present context. In [12] the magnetic field of a finite length tubular conductor of negligible thickness was determined by applying an oblique solid angle formula derived therein to an expression for magnetic field circulation obtained in [14] from the application of Ampère-Maxwell's law for magnetic field circulation to an arbitrarily-shaped finite length wire segment in the zero retarded-time limit.…”