Question

a long cable carries a current in one direction uniformly distributed over its cross section. the current returns along the surface, (there is a very thin insulating sheath separating the currents). find the self-inductance per unit length.

Answer 1

The self-inductance per unit length of a coaxial cable with a current in the central conductor returning along an outer shell is expressed by the formula L = µ_0 * ln(R2 / R1) / (2π), depending only on the geometric configuration of the cable.

Step-by-step explanation:

The student is asking about the self-inductance per unit length of a coaxial cable, where the current flows in one direction in the central conductor and returns along the surface of an outer cylindrical shell separated by an insulating sheath. This configuration can be thought of as two long, concentric cylindrical shells of radii R1 and R2, carrying equal but opposite currents. According to the formula for the self-inductance per unit length of the coaxial cable, expressed as:

L = µ_0 * ln(R2 / R1) / (2π)

where µ_0 is the permeability of free space, and R1 and R2 are the radii of the inner and outer conductors, respectively. This result indicates that the self-inductance depends only on the geometric factors - the radii of the conductors.