The capacitance per unit length of a very long coaxial cable,made of two concentric cylinders,is
50 pF/m.What is the radius of the outer cylinder if the radius of the inner one is 1.0 mm?
(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 = 2πεk * (ln(b/a)) / ln(10)where:C is the capacitance per unit lengthε is the permittivity of the dielectrick is the dielectric constanta is the radius of the inner conductorb is the radius of the outer conductorIn this problem, we are given that C = 50 pF/m, a = 1.0 mm, and k = 8.99 × 10^9 N • m^2/C^2. We can use this to solve for b:50 pF/m = 2πε(8.99 × 10^9 N • m^2/C^2) * (ln(b/1.0 mm)) / ln(10)Solving for b, we get:b = 3.0 mmTherefore, the radius of the outer cylinder is 3.0 mm.

The Capacitance Per Unit Length of a Very Long Coaxial