HW84_1 - Electromagnetics School of Electrical and Computer...

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Electromagnetics School of Electrical and Computer Engineering University of Tehran Homework 1 Fall Semester 1384 Due 84/7/16 Problem 1 The scalar field () ) 2 exp( ) 2 sin( , y x y x π π = Φ is defined in the region 1 0 x and 0 y . a) Evaluate Φ = r r F , and show that the resulting F r is a divergence-less vector field. b) What is the maximum and minimum value of ) , ( y x Φ in the region 1 0 x and 0 y ? c) Obtain the mathematical expression of the equipotential curves corresponding to 5 . 0 = Φ and 5 . 0 = Φ , and draw these curves in the region 1 0 x and 0 y . d) Consider a circle of radius 0.0005 whose center is at ) 1 , 8 1 ( ) , ( = y x . Determine the point on this circle for which the function ) , ( y x Φ attains a maximum. Problem 2 The volume v of a three-dimensional region V should be determined. Assume that both the position vector r r and the unit normal vector n ˆ are known at every point on V . Obtain a mathematical expression for
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HW84_1 - Electromagnetics School of Electrical and Computer...

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