The inner conductor of a coaxial cable has a radius of 0.800 mm, and the outer conductor's insid

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The inner conductor of a coaxial cable has a radius of 0.800...

The inner conductor of a coaxial cable has a radius of $0.800 \mathrm{mm},$ and the outer conductor's inside radius is $3.00 \mathrm{mm} .$ The space between the conductors is filled with polyethylene, which has a diclectric constant of 2.30 and a dielectric strength of $18.0 \times 10^{6} \mathrm{V} / \mathrm{m} .$ What is the maximum potential difference that this cable can withstand?

Key Concepts

Breakdown Voltage in Dielectric Materials

The breakdown voltage of an insulating system is determined by integrating the electric field across the region that contains the dielectric. By knowing the maximum allowable electric field (i.e., the dielectric strength), one can compute the maximum voltage difference the insulation can handle before electrical breakdown occurs.

Application of Gauss's Law in Cylindrical Systems

Gauss's Law provides a method for determining the electric field in systems with cylindrical symmetry, such as coaxial cables. This principle is used to relate the charge distributions on the conductors to the resulting electric field in the insulating region, which is essential for estimating the maximum potential difference the system can endure.

Dielectric Strength

Dielectric strength is a material property that defines the maximum electric field an insulating material can sustain before breakdown occurs. This concept is crucial because it determines the maximum voltage that can be applied across an insulator without causing a failure, making it a key factor in designing safe electrical systems.

Electric Field Distribution in Cylindrical Coordinates

In a coaxial cable, the electric field is not uniform but varies with the radial distance from the inner conductor. The field is typically strongest at the surface of the inner conductor and decreases with distance, making it essential to understand how the field distribution affects the overall potential difference that the system can safely support.

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