A coaxial cable used in a transmission line has an inner...

A coaxial cable used in a transmission line has an inner
radius of 0.10 $\mathrm{mm}$ and an outer radius of 0.60 $\mathrm{mm}$ . Calculate the
capacitance per meter for the cable. Assume that the space
between the conductors is filled with polystyrene.

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Key Concepts

Coaxial Cable Geometry

Coaxial cables consist of an inner conductor and a concentric outer conductor with a dielectric material in between. The geometry leads to an electric field that is radially symmetric, and this radial symmetry produces a logarithmic relationship between the radii of the two conductors when analyzing capacitance or inductance.

Capacitance per Unit Length

The capacitance per unit length of a coaxial cable is determined by the formula C = (2??)/(ln(b/a)), where 'a' is the inner radius, 'b' is the outer radius, and ? is the permittivity of the dielectric material between the conductors. This formula encapsulates how the physical geometry influences the ability of the cable to store electrical charge.

Dielectric Permittivity

Dielectric permittivity quantifies the ability of the insulating material between the conductors to store electrical energy in an electric field. It is a crucial factor in determining the capacitance, as materials with higher permittivity allow for a greater capacitance in a given geometric configuration.

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