hw3 - ECE604 Homework 3 Out Tuesday Due Tuesday February 1...

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Unformatted text preview: ECE604 Homework 3 Out: Tuesday, January 25, 2005 Due: Tuesday, February 1, 2005 Note: There is now a class website at . Problem sets, solutions, and other handouts will be posted there. These problems are from Chapter 1 of the text by Ramo, Whinnery and Van Duzer (3rd edition, 1994). 1) 2) 3) 4) 5) 6) 7) 7.9a 7.11a parts (i) and (ii) only. Assume both functions have period L. 7.1 lb 7.12a 7.12b 7.12e Note: Make sure you can identify all the important boundary conditions before you jump into the math. 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 S (units are A/m) in the vicinity of the hole. (The sheet current density is the uniform current density J integrated over the thickness of the conductor, that is J S = J ><t) (ii) Derive an expression for J5. Express your answer in terms of I, W, r and (1). (iii) What is the maximum magnitude of J S? Express your answer in terms of I and W. (The answer does not include the hole radius a.) Note that the maximum should be located along the x = 0 line (where the current is maximally constricted). (iv) Give an expression for the sheet surface charge density (units Coulomb/m) along the edge of the hole. ...
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