First Exam291006 - ‫ﺑﺴﻢ اﷲ اﻟﺮﲪﻦ...

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Unformatted text preview: ‫ﺑﺴﻢ اﷲ اﻟﺮﲪﻦ اﻟﺮﺣﻴﻢ‬ Department of Electrical and Computer Engineering Module: Electromagnetic (I) First Exam 29/10/2006 Time allowed: 1 hour Instructor: Dr. Omar Saraereh → Q1: ∧ ∧ ∧ → ∧ ∧ ∧ Point P(-4, 2, 5) and the two vectors, A = 20 x + 18 y − 10 z and B = −10 x + 8 y + 15 z , define a triangle. i) Find a unit vector perpendicular to the triangle. → ii) Find a unit vector in the plane of the triangle and perpendicular to B . iii) Find a unit vector in the plane of the triangle that bisects the interior angle at P. (6 marks) Q2: The following coordinates, r = 2 and 4, θ = 30 o and 50 o , and φ = 20 o and 60 o identify a closed surface. a) Find the enclosed volume. b) Find the total area of the enclosing surface. c) Find the length of the twelve edges of the surface. d) Find the length of the longest straight line that lies entirely within the surface. (8 marks) Q3: A vector field D = r r 3 exists in the region between two concentric cylindrical surfaces defined by r = 1 and r = 2, with both cylinders extending between z = 0 and z = 5. Verify the divergence theorem. (6 marks) → ∧ ================================================================ Some useful relations: ∂V ∧ ∂V ∧ ∂V +φ +z ∂r ∂φ ∂z → 1 ∂ (rAr ) 1 ∂Aφ ∂Az ∇. A = + + ∂z r ∂r r ∂φ ∧ ∂A ∧ ∂A ∧ ∂A ∇T= x +y +z ∂x ∂y ∂z ∧ 123- ∇V= r www.Husni.net ...
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