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MIT6_013S09_pset02

# MIT6_013S09_pset02 - MASSACHUSETTS INSTITUTE OF TECHNOLOGY...

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MASSACHUSETTS INSTITUTE OF TECHNOLOGY Department of Electrical Engineering and Computer Science 6.013 – Electromagnetics and Applications Problem Set 2 (five problems) Suggested Reading: Course notes (Staelin) Sections 2.1-2.3.4, 2.4, 2.7.1-2.7.3, 3.2.1-3.2.2, Appdx. C. Problem 2.1 Assume the “Whatever” vector W(x,y,z) = ˆ ˆ . xsin y + yy (a) If an electric displacement vector D = W, what is the charge density ρ (x,y,z) [C/m 3 ]? (b) If the magnetic field H = W, what is the current density J(x,y,z) [A/m 2 ], assuming H is physically possible? (c) Does the magnetic field B = W satisfy all of Maxwell’s equations? If not, which one is violated? Problem 2.2 If the electric field E(t) = R e {E e j ω t } where E is a phasor , then what is E(t) if: (a) E = 1 - j (b) E = e j π /4 - 1 (c) E = j x ˆ + (1 - j) y ˆ (d) What is the complex vector E if E(t) = x ˆ cos ω t + y ˆ sin( ω t + π /4)? [Hint: E(t) = cos ω t for the case E = 1] Continued on next page - 1 - 2/9/09

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Problem 2.3 (a) What is the frequency f (Hz) of the wave having the magnetic field: H = x
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