First exam term2 0607 - The Hashemite University First Exam...

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Unformatted text preview: The Hashemite University First Exam Electrical Engineering Department Electromagnetic I second Sem. 07/08 Faculty of Engineering Instructors: Dr. Omar Saraereh Time: 1 hour → → Q1: Find a vector G whose magnitude is 4 and whose direction is perpendicular to both vectors E → → ∧ ∧ ∧ → ∧ ∧ and F , where E = x + y 3 − z 2 and F = y 3 − z 6 . Q2: Consider the object shown in Figure 1. Calculate (a) The distance BC (b) The distance CD (d) The surface area ABO (e) The surface area AOFD (4 marks) (c) The surface area ABCD (f) The volume ABDCFO (12 marks) → ∧ ∧ Q3: Find the directional derivative of M = rz 2 cos 2φ along the direction A = 2 r − z and evaluate it at (1, π 2 , 2)? (6 marks) Q4: Using your own words, explain the following terms: Orthogonal coordinate system, Gradient operator? (3 marks) Fig. 1 ----------------------------------------------------------------------------------------------------------∧ ∂V ∧ 1 ∂V ∧ ∂V +φ +z ∇V= r ∂r ∂z r ∂φ → ∂Ay ∂Az ∂A + ∇. A = x + ∂x ∂y ∂z ∧ ∂A ∧ ∂A ∧ ∂A +y +z ∇T= x ∂x ∂y ∂z → ∧ 1 ∂A ∧ ∂A ∧1 ∂ ∂Aφ ∂A ∂A z Δ × D = r( − ) + φ ( r − z ) + z ( rAφ − r ) ∂z ∂z ∂r ∂φ r ∂φ r ∂r www.Husni.net ...
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