Energy Stored In A Coaxial Cable

A coaxial cable consists of a central copper conductor for transmitting signals, surrounded by an insulating layer, a metallic braided mesh that prevents signal interference, and an outer plastic layer. This design creates two concentric cylindrical shells where current flows in opposite directions, enabling efficient signal transmission while minimizing electromagnetic interference.

The magnetic field exists only in the region between the two concentric conductors. Inside the inner conductor and outside the outer conductor, the magnetic field is zero because no net current is enclosed in those regions. The oppositely flowing currents in the two cylinders cancel each other outside the cable, while the field between them stores all the cable's magnetic energy.

Magnetic energy is calculated by integrating the magnetic energy density over the cylindrical shell volume between the two conductors. The total magnetic energy per unit length is directly proportional to the square of the current flowing through the cable. This energy can be expressed in terms of the cable's self-inductance, relating electromagnetic storage to circuit behavior.

The self-inductance per unit length depends only on the inner radius R1 and outer radius R2 of the cable. Inductance increases when the outer radius increases or when the inner radius decreases. When the two radii become equal, inductance approaches zero and the cable no longer functions as a coaxial cable.

Ampère's law determines the magnitude of the magnetic field between the two concentric conductors by relating it to the enclosed current. Since opposite currents flow in the inner and outer conductors, the net enclosed current is zero outside the cable, resulting in zero magnetic field in those regions. This principle establishes why magnetic energy concentrates exclusively between the conductors.

When the inner radius R1 equals the outer radius R2, there is no space between the conductors for a magnetic field to exist. Since all magnetic energy is stored in the shell region between the two cylinders, eliminating this gap eliminates the magnetic field and inductance. At this point, the cable loses its coaxial geometry and cannot function as intended.

The magnetic energy per unit length is directly proportional to the square of the current flowing through the cable. Higher currents produce stronger magnetic fields between the conductors, storing more energy. This quadratic relationship means that doubling the current quadruples the stored magnetic energy, making current magnitude a critical factor in cable performance.