HW4-sol - So /L¢+l‘ O “ ECE604 Homework #4 Out:...

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Unformatted text preview: So /L¢+l‘ O “ ECE604 Homework #4 Out: Wednesday, February 4, 2009 Due: Wednesday, February 11, 2009 These problems are from the text by Ramo, Whinnery, and Van Duzer (3rd edition, 1994) or are attached. 1) 7.12h Also give an expression for the added capacitance per unit length AND evaluate numerically. Hints: a) Use a superposition solution (I) = (131+ (1)2, where (131 = Voy/ a is the solution for the parallel plate capacitor without the extra conducting strip. b) In solving for C132, solve separately for x 2 0 and x _<_ 0. Once you have the solution for x 2 0, the solution for x S 0 follows almost by inspection. 0) Use your solution for (132 in computing the added capacitance. 2) Attached 3) Attached 4) Attached 5) 2.3b 6) 2.30 7) 2.4b 8) 2.4e 9) 2.5 10) 2.6c 3) 2) A sphere of radius a has electric charge intentionally distributed on its surface so that the electric field inside is uniform and given by E 2 E02 (for r < a) The sphere is hollow, i.e. a = 80 everywhere inside the sphere. The sphere is embedded in an insulator, with dielectric constant e. a) Determine the surface charge density ps(9) on the surface of the sphere. Hint: First solve for the potential using Laplace’s equation and appropriate boundary conditions. b) Make a sketch showing representative E—field lines and the distribution of surface charge. Comment on the behavior of the field lines at the boundary. permanent polarization , medium P7113037 T hollow cylindrical hole Consider an infinite medium with uniform permanent polarization P = P031 and zero conductivity. There is a hollow cylindrical hole (infinite in z—direction) embedded inside the medium. Solve for the potential and the E and D fields. 4) A conductor on a circuit board has width W and carries a current I. The conductivity of the conductor is 6. There is a small hole of radius a at the center of the conductor. The thickness t of the conductor is small compared to a. (Therefore this problem may be treated as a two—dimensional problem in cylindrical coordinates.) Assume the current is DC. You may also assume that the width of the circuit board W is large compared to the hole radius (W>>a). Let the coordinate origin be at the center of the hole. (i) Sketch qualitatively the sheet current density J 5 (units are A/m) in the vicinity of the hole. 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This note was uploaded on 12/12/2010 for the course ECE 604 taught by Professor Staff during the Spring '08 term at Purdue University-West Lafayette.

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HW4-sol - So /L¢+l‘ O “ ECE604 Homework #4 Out:...

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