**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)
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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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