A long coaxial cable consists of two concentric cylindrical conductors with radii a and b, where . Its central conductor carries a steady current , and the outer conductor provides the return path. We have to find the inductance of a length l of this cable by calculating the flux through a rectangular surface, of length l and width .

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A long coaxial cable consists of two concentric cylindrical conductors with radii a and b, where . Its central conductor carries a steady current , and the outer conductor provides the return path. We have to find the inductance of a length l of this cable.

The magnetic field inside the coaxial cable will depend on the distance from the central axis. By using Ampere’s law, we note that the magnetic field at a distance r from the axis of central cable when a current is flowing through it will be

.

We consider a Gaussian surface, a rectangle of length l and width in the . The direction of the magnetic field on this surface will be normal to it. Therefore, the flux enclosed by the rectangular Gaussian surface of width and length l will be given by the integral

As the inductance is flux per unit current, the inductance of a length l of the coaxial cable will therefore be