What is the capacitance per unit length (F / m) of a coaxial...

What is the capacitance per unit length $(\mathrm{F} / \mathrm{m})$ of a coaxial cable whose inner conductor has a $1.0-\mathrm{mm}$ diameter and the outer cylindrical sheath has a 5.0 -mm diameter? Assume the space between is filled with air.

Key Concepts

Logarithmic Dependence on Conductor Radii

For coaxial configurations, the relationship between the capacitance and the physical size of the conductors involves a logarithmic function of the ratio of the outer to inner conductor radii. This arises from the integration of the radial electric field in cylindrical coordinates and is key to deriving the standard capacitance expression.

Coaxial Cable Geometry

This involves a pair of conductors where one is located inside the other in a concentric cylindrical arrangement. The precise geometry, characterized by the radii of the inner and outer conductors, heavily influences the electrical field distribution between them, which in turn determines the capacitance.

Capacitance per Unit Length

Capacitance per unit length is a parameter that describes how much electric charge can be stored per meter of a transmission line. It is especially important in the analysis and design of cables and waveguides since it relates to the signal propagation and the energy storage characteristics over the length of the device.

Permittivity of the Dielectric Medium

The permittivity of the dielectric material, often taking the value of vacuum permittivity for air-filled systems, quantifies the ability of the medium to support an electric field. It directly influences the capacitance by determining the amount of charge stored for a given electric potential difference between the conductors.

Transcript

Please give Ace some feedback