hw08 - Princeton UniversityPhysics 501 Problem Set 8 Due:...

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Unformatted text preview: Princeton UniversityPhysics 501 Problem Set 8 Due: Dec. 13, 2011 1) (J8.2) A transmission line consists of two concentric circular cylinders of metal with conductivity and skin depth and is filled with a uniform lossless dielectric ( , ). A TEM mode is propagated along the this line. a) Show that the time averaged power flow along the line is P = r a 2 | H | 2 ln b a where H is the peak value of the azimuthal magnetic field at the surface of the inner conductor. b) Show that the transmitted power is attenuated along the line as P ( z ) = P e- 2 z where = 1 2 r ( 1 a + 1 b ) ln ( b a ) c) The characteristic impedance Z of the line is defined as the ratio of the voltage between the cylinders to the axial current flowing in one of them at any position, z . Show that for this line Z = 1 2 r ln b a d) Show that the series resistance and inductance per unit length of the line are R = 1 2 1 a + 1 b and L = 2 ln b a + c 4 1 a + 1 b where...
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hw08 - Princeton UniversityPhysics 501 Problem Set 8 Due:...

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