EEE303_hw1 - EEE-303 HOMEWORK # 1 (Due: 8th of October,...

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EEE-303 HOMEWORK # 1 (Due: 8 th of October, class hour) 1) Check whether the following fields satisfy Maxwell’s equations. Assume that the fields exist in charge-free regions. (Note: r and R are in cylindrical and spherical coordinates, respectively.) (a) () ˆ 40sin 10 z At ω =+ x a (b) 10 ˆ cos 2 B tr a r φ =− (c) 2 cos ˆˆ 3c o t s i n r Cr a a r t ⎛⎞ ⎜⎟ ⎝⎠ (d) 1 ˆ sin sin 5 Dt R a R θ θω 2) In a charge-free region for which 0 σ = , 0 r ε εε = , and 0 μ = , 9 ˆ 5cos 10 4 A/m z Ht y a , find: (a) d J and D , (b) r . 3) Suppose that the following H-field exists in a source-free vacuum region: ( ) ()( ) 00 sin cos cos sin x z HE x t z a E x t z a β α αω μω (a) Use Ampere’s law to find the E associated with the H-field. (b) By substituting the E found in part (a) into Maxwell’s curl- E equation, show that these E- and H-fields are valid only when 22 2 βμ += (c) Prove that these E- and H-fields also satisfy Maxwell’s divergence equations. 4) In a region where 1 rr = = and 0 = , the retarded potentials are given by V and Vx zc t ˆ z z Ax t a c Wb/m, where 1/ c με = . (a) Show that V t
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This note was uploaded on 03/14/2010 for the course EE 303 taught by Professor Fatihcanatan during the Fall '09 term at Middle East Technical University.

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