A 1.0 m long piece of coaxial cable has a wire with a radius of 1.1 mm and a concentric conductor with inner radius 1.3 mm. The area between the cable and the conductor is filled with a dielectric. If the voltage drop across the capacitor is 6000 V when the line charge density is
8) 8 μC/m, find the value of the dielectric constant. (k = 1/4πε₀ = 8.99 × 10⁹ N ∙ m²/C²)

Question

Quizplus · Accepted Answer

The capacitance per unit length of a coaxial cable is given by C = (2πε/ln(b/a)), where ε = ε₀ε_r, a is the radius of the inner conductor, and b is the inner radius of the outer conductor. The voltage V is related to the charge density λ by V = λ/(C). Solving for ε_r using the given values, we find ε_r ≈ 4.4.

A 10 M Long Piece of Coaxial Cable Has a Wire