First Exam071105 - ‫ﺑﺴﻢ اﷲ اﻟﺮﲪﻦ...

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Unformatted text preview: ‫ﺑﺴﻢ اﷲ اﻟﺮﲪﻦ اﻟﺮﺣﻴﻢ‬ Department of Electrical and Computer Engineering Module 0404215 Electromagnetic (I) First Exam 07/11/2005 Time allowed: 1 hour Q1 Using your own words, explain the following terms: Scalar quantity, Dot product, Orthogonal coordinate system, Divergence operator? (6 marks) Q2 Derive the cosine formula A 2 = B 2 + C 2 − 2 BC cos α ? (Hint: use the triangle shown in Figure 1 and the dot product ) (4 marks) C α B γ ω A Figure 1 Q3 Calculate the gradient of M = x 2 y 2 + xyz and the directional derivative dM ∧ ∧ in the ∧ direction 3 x + 4 y + 12 z at (2,-1,0)? Q4 dl (4 marks) ∧ ∧ Determine the flux of a vector filed K(r) = 10 e − 2 z ( r r + z ) out of the entire surface of the cylinder r = 1, 0 ≤ z ≤ 1 . Confirm the result using the divergence theorem? (6 marks) ====================================================================== Some useful relations: 1234- A . (B × C) = B . (C × A) = C . (A × B) 1∂ 1 ∂Aφ ∂Az ∇. A = + (rAr ) + (Cylindrical) r ∂r r ∂φ ∂z ∂Ay ∂Az ∂A + ∇. A = x + (Cartesian) ∂x ∂y ∂z ∧ ∂A ∧ ∂A ∧ ∂A ∇A= x (Cartesian) +y +z ∂x ∂y ∂z www.Husni.net ...
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This note was uploaded on 04/02/2012 for the course ENGINEERIN 110409221 taught by Professor Omarsarayra during the Spring '12 term at Hashemite University.

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