Energy Stored In A Coaxial Cable

A coaxial cable consists of a copper conductor that transmits the signals, followed by an insulator, a metallic braided mesh that prevents signal interference, and the outer insulating layer.

It can be represented by two long hollow concentric cylindrical shells of radii R₁ and R₂, wherein the current flows in opposite directions.

Applying Ampere's law, the magnitude of the magnetic field between the two conductors is obtained.

Since no net current is enclosed in the region outside the cable and inside the inner conductor, the magnetic field is zero.

Recall the expression for magnetic energy density. Its product with volume is equivalent to the energy stored in the given shell.

Upon integration, the total magnetic field energy in a given length l is obtained.

Magnetic energy can also be expressed in terms of self-inductance.

Equating these two expressions gives a coaxial cable's self-inductance per unit length.

It increases if the outer radius R₂ increases or if the inner radius R₁ decreases.

When the two radii become equal, inductance goes to zero, and there is no coaxial cable.