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Unformatted text preview: EE101
1/6/10 Homework #1 Engineering Electromagnetics Winter 2010 D u e : W e d n esd a y J a n 13 2 : 00 P M Hand in to the TA at beginning of class. No late homework is accepted (see grading policy posted on web). If you cannot make it to class, you must slip the HW under my door before the due time. P r ob l e m #1 P r o b l e m #2 P r o b l e m #3 (10 points) (10 points) (10 points) Ulaby 3.41 Ulaby 3.45 Ulaby 3.48 P r ob l e m #4 (20 points) Show that ( F ) 0 where F (x,y,z) is an vector function, Assume that mixed second order partial derivatives are independent of the order of differentiation. For example P r o b l e m #5 (30 points) 2 Fx 2 Fx . xy yx A metal sphere of radius R1, carrying charge Q , is surrounded by a thick concentric metal shell (inner radius a, outer radius b). The shell carries no net charge. (a) Find the surface charge density s at R1, at a , and at b. Make a rough sketch. (b) Find the E-field in all 4 regions. (c) Find the potential at the center, using infinity as a reference. Sketch the potential versus R. (d) Now the outer surface is touched to a grounding wire, which lowers its potential to zero (same as at infinity). How do your answers to (a) and (b) and (c) change? P r ob l e m #6 (20 points) (a) Using Gauss’s Law and symmetry arguments, find the electrostatic E-field as a function of position for an infinite uniform plane of charge. Let the charge lie in the yz-plane and denote the charge per unit area by ρs. (b) Repeat part (a) for an infinite slab of charge parallel to the yz plane, whose density is b x b 0 given by ( x ) . 0, x b ρ0 is a charge density per unit volume. Make sure you give the field for all values of x, and don’t forget the direction. Page 1 of 1 ...
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