329sum11hw4 - ECE 329 Homework 4 Due 5PM 1 Consider two...

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Unformatted text preview: ECE 329 Homework 4 Due: June 28, 2011, 5PM 1. Consider two infinite, plane parallel, perfectly conducting plates at z = 0 and z = z o > , which are kept at potentials V = 0 and V = V p > , respectively. The region between the plates is filled with two slabs of perfect dielectric materials having permittivities 1 for < z < d (region 1) and 2 for d < z < z o (region 2). a) Find the solutions for the electric potentials, V = V ( z ) , in the two regions by solving Laplace’s equation and enforcing the continuity of V ( z ) at z = d . b) Given that z o = 2 d = 1 m, V p = 5 V, 1 = o , and 2 = 2 o , what is the surface charge density ρ s of the conductor plate at z = z o ? 2. Consider a simplified model of a vacuum diode consisting of a cathode in the x = 0 plane and an anode in the x = d plane, where the anode is held to a constant potential V a = 1 V relative to the cathode. If the potential distribution in the region < x < d is given by V ( x ) = V a ( x/d ) 4 / 3 , find the following: a) Electric field E at x = d/ 2 , b) Volumetric charge density ρ at x = d/ 4 , c) The surface charge density ρ s on the anode. 3. Consider two conducting plates positioned on z = 0 and z = 2 m surfaces. The plates are grounded and both have zero potential. In between the plates, on z = 1 m surface, there is a uniform and static surface charge of 3 C/m...
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329sum11hw4 - ECE 329 Homework 4 Due 5PM 1 Consider two...

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