The speed of an electromagnetic wave in a certain filler material is 0.82 c, whe
ID: 1413833 • Letter: T
Question
The speed of an electromagnetic wave in a certain filler material is 0.82 c, where c is the speed of an electromagnetic wave in vacuum. This material is used in a coaxial cable that has an inner wire diameter of 1 mm. The characteristic impedance of this cable is 100 ohm. The permeability mu of the filler material is approximately mu_0. Find the permittivity e for this material. What is the radius of the outer conducting shell in this coaxial cable? What is the inductance per length of this coaxial cable? What is the capacitance per length of this coaxial cable? Assume that the resistance per length of the cable of Problem 2 is 0.05 ohm/m. How far can a voltage/current wave travel in the cable before its voltage amplitude is reduced by a factor of 2? How far can a voltage/current wave travel in the cable before its voltage amplitude is reduced by a factor of 100?Explanation / Answer
2) a) permittivity for this material = 1/(4 * 3.14 * 10-7 * 0.82 * 0.82 * 3 * 108 * 3 * 108)
= 1.3156 * 10-11 F/m
b) radius of outer conducting shell = 0.5/0.82
= 0.6097 mm
c) inductance per unit length = 100 * 4 * 3.14 * 10-7/10-3
= 0.1256 H/m
d) capacitance per unit length = 100 * 1.3156 * 10-11/10-3
= 1.3156 * 10-6 F/m
2) a) far can voltage/current wave travel = 2 * 0.82 * 3 * 108 * 0.05
= 2.46 * 107 m
b) far can voltage/current wave travel = 100 * 0.82 * 3 * 108 * 0.05
= 1.23 * 109 m
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