Inductance: Solid Cylindrical Conductor

To calculate a solid cylindrical conductor's inductance, consider a 1-meter section of a non-magnetic current-carrying conductor with radius r, disregarding end effects and assuming uniform current density.

Ampere's law calculates a constant concentric magnetic field inside the conductor.

Given a uniform current distribution, the magnetic field and flux density are determined.

Then, the differential flux per unit length is computed, which determines the total flux linkages inside the conductor.

This allows the calculation of the conductor's internal inductance per unit length.

To find the magnetic field outside the conductor, Ampere's law is applied to a contour enclosing all the current. This aids in calculating magnetic flux density, differential flux, and flux linkage outside the conductor.

Integrating between two external points gives the external flux linkage and consequent external inductance per unit length.

The total flux linkage at an external point is the sum of internal and external flux linkages, which determines the total inductance.

Finally, considering an array of cylindrical conductors, each carrying a current, with their total current equaling zero, the flux linkage is calculated.