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) A) 3.0 mm B) 2.0 mm C) 4.0 mm D) 1.0 mm E) 0.50 mm

Question

Quizplus · Accepted Answer

The capacitance per unit length of a coaxial cable is given by:C = (2πε₀/ln(b/a))where:C is the capacitance per unit lengthε₀ is the permittivity of free spacea is the radius of the inner cylinderb is the radius of the outer cylinderWe are given that C = 50 pF/m and a = 1.0 mm. We can solve for b:b = a * e^(C*ln(2)/2πε₀)= 1.0 mm * e^((50 pF/m)*ln(2)/(2*8.99 × 10^9 N ∙ m^2/C^2))= 3.0 mmTherefore, the radius of the outer cylinder is 3.0 mm.

The Capacitance Per Unit Length of a Very Long Coaxial