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) A) 4.4 B) 4.8 C) 5.3 D) 5.7

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Quizplus · Accepted Answer

The capacitance of a coaxial cable is given by:C = (2πε₀L)/(ln(b/a))where:C is the capacitance in faradsε₀ is the permittivity of free space (8.85 × 10^-12 F/m)L is the length of the cable in metersa is the radius of the inner conductor in metersb is the radius of the outer conductor in metersWe are given that:L = 1.0 ma = 1.1 mm = 1.1 × 10^-3 mb = 1.3 mm = 1.3 × 10^-3 mV = 6000 Vλ = 8.8 μC/m = 8.8 × 10^-6 C/mWe can use the formula for capacitance to find the dielectric constant:C = Q/VQ = λLV = 6000 VC = (8.8 × 10^-6 C/m)(1.0 m) = 8.8 × 10^-6 Ck = C/(2πε₀L/ln(b/a))k = (8.8 × 10^-6 C)/(2(8.85 × 10^-12 F/m)(1.0 m)/ln(1.3 × 10^-3 m/1.1 × 10^-3 m))k = 4.4Therefore, the dielectric constant is 4.4.

A 10 M Long Piece of Coaxial Cable Has a Wire