EEE224_Fall10_ProblemSet1

EEE224_Fall10_ProblemSet1 - EEE-224 SUPPLEMENTARY PROBLEM...

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Unformatted text preview: EEE-224 SUPPLEMENTARY PROBLEM SET # 1 (Vector Calculus) Q.1) The temperature in an auditorium is given by T = x 2 + y 2 − z . A mosquito located at (1, 1, 2) in the auditorium desires to fly in such a direction that it will get warm as soon as possible. In what direction must it fly? Q.2) Evaluate ∇V , ∇ ⋅∇V and ∇ × ∇V if: (a) V = 3 x 2 y + xz (b) V = rz cos φ (c) V = 4 R 2 cos θ sin φ ˆ ˆ Q.3) Given that H = x 2 ax + y 2 a y , evaluate C ∫ H ⋅ dl , where C is along the curve y = x 2 from (0, 0) to (1, 1). ˆ ˆ Q.4) Let A = r sin φ ar + r 2 aφ . Evaluate C ∫ A ⋅ dl given that L is the contour of the following figure. b a ˆ ˆ ˆ Q.5) Verify the divergence theorem for the following field F = r 2 sin φ ar + z cos φ aφ + rzaz through the hollow cylinder defined by 2 ≤ r ≤ 3 , 0 ≤ z ≤ 5 . Q.6) Find the flux of the curl of field T = hemisphere R = 4, 0 ≤ z . 1 ˆ ˆ ˆ cos θ aR + R sin θ cos φ aθ + cos θ aφ through the R2 Textbook problems (Sadiku): Chapter 3 1 ...
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This note was uploaded on 01/07/2011 for the course EE 209 taught by Professor Alexander during the Spring '10 term at Middle East Technical University.

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