Electrical Engineering 117A - Fall 1997 - Spanos - Midterm 2

Electrical Engineering 117A - Fall 1997 - Spanos - Midterm...

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EE117A SOLUTION-Fall1997 EE117A SOLUTION -- Fall1997 Electromagnetic Field and Waves Wed, Oct 29, 1997 Costas J. Spanos NOTE: This solution is from a student who got 30/30, 30/35, and 35/35, that is total 95 out of 100. PROBLEM 1 OF 3 (30 Points) State (in words) the Gauss theorem (7pts) The flux of electric field, if integrated over a surface that enclosed a volume, equals to the total of charge enclosed by that volume divided by the dielectric( E ) of material which E (of interest) is in. What is the differential form of Ampere theorem? (7pts) the cross product of gradient vector and H vector equals to J vector, that is gradient(Vector) X H(Vector) = J(Vector) What is an "irrotationl" field? (6pts) The Field F(Vector) is irrotational when the cross product of gradient(Vector) and F(Vector) equals to zero, that is gradient(Vector) X F(Vector) = 0. (This case is usually true for static E Field.) An infinite surface on the y-z plain has a charge density of 1 Cb/m 2 .
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