ECE309-2008-hw9

ECE309-2008-hw9 - ECE 309 Electromagnetic Fields University...

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ECE 309 — Electromagnetic Fields University of Virginia Fall 2008 Homework # 9 — Maxwell’s Equations and Poynting’s Theorem Due: Friday, November 21 1. For a coaxial cylindrical capacitor or radii a and b and length , find the total displacement current flowing across any cylindrical surface of radius r ( a < r < b ), taking the voltage variation as sinusoidal in time, and the variation of the electric field with radius the same as in statics. Show that the result is independent of radius and equal to the charging current for the capacitor. 2. The instantaneous electric field inside a source-free, homogeneous, isotropic, and linear medium is given by, ~ E = h ˆ xA ( x + y ) + ˆ yB ( x - y ) i cos( ωt ) Determine the relation between A and B . 3. The instantaneous electric field inside a conducting rectangular pipe (a waveguide) is given by, ~ E = ˆ yE 0 sin πx a cos( ωt - β z z ) where β z is called the waveguide’s “phase constant.” Assuming that no sources exist inside
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