First Exam300306 - ‫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 30/03/2006 Time: 1 hour Instructor: Dr. Omar Saraereh → ∧ ∧ ∧ → ∧ ∧ Q1: If A = 10 x − 4 y + 6 z and B = 2 x + y , find: → ∧ i) The component of A along y → → ii) The magnitude of 3 A− B → → iii) A unit vector along A+ 2 B → → iv) The angle between A and B (25 marks) → ∧ ∧ Q2: 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)? (35 marks) → ∧ ∧ Q3: Verify Stokes’s theorem for the vector field B = r cos φ + φ sin φ using the path and the surface of the quarter section of a circle shown below? (40 marks) ================================================================ Some useful relations: 1- 234- ∧ 1 ∂V ∧ ∂V ∂V ∇V= r +φ +z ∂r r ∂φ ∂z → ∂Ay ∂Az ∂A ∇. A = x + + ∂z ∂x ∂y ∧ ∂A ∧ ∂A ∧ ∂A ∇T= x +y +z ∂z ∂x ∂y → ∧ 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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