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Unformatted text preview: ECE 329 Homework 4 Due: Sept 20 2010, 5PM 1. Maxwells equations for static electric fields In a region of free space that is currentfree and chargefree, is E = 2 x x + 2 sin( z ) y 2 z z a possible electrostatic field? Discuss. 2. Solving Poissons/Laplaces eq. and Boundary Conditions Depicted in the figure below is the cross sectional geometry of an infinitelylong cylindrical configuration of charge in free space. The circular cylindrical shell of inner radius a and outer radius b carries a uniformly distributed electric charge Q C/m. The cylindrical surface at r = b carries a uniformly distributed electric charge Q C/m, and the cylindrical surface at r = c carries a uniformly distributed electric charge 2 Q C/m. Given that the electrostatic potential is zero on the surface r = a , use Poissons equation to solve for the electrostatic potential V everywhere in space. Your result should be in terms of the geometric parameters of the cross sectional geometry, the permittivity of the free space and the charge density Q. (Hint: In view of the cylindrical symmetry of the charge density the electric field and the electrostatic potential are function of r only; furthermore, the electric field has only the radial component. Using the expressions for the gradient and the divergence in cylindrical coordinates (see Appendix B in Raos text), you should be able to show that the Laplacian of the electrostatic potential in cylindrical coordinates is given by: 2 V = 1 r r ( r V r ) + 1 r 2 ( 2 V 2 ) + 2 V z 2 ....
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 Spring '08
 Kim
 Electromagnet

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