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Note for ECE 2317 with Professor Jackson at UH Workshop Solutions Dielectrics

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This 4 page Class Notes was uploaded by an elite notetaker on Friday February 6, 2015. The Class Notes belongs to a course at University of Houston taught by a professor in Fall. Since its upload, it has received 17 views.

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Date Created: 02/06/15
Electromagnetics Workshop Solutions Electric Potential Problem 1 A disk 0 S p S a z 0 0 S S 27239 carries a surface charge density p p50 p2 a2 Find 00z in free space Assume oo 0 Solution 27 a p p p3 q J47r80R dS 478012 dpd S 00 a 3 q dp 65122Z3a2 222W Electromagnetics Workshop Solutions Electric Potential Problem 2 A line charge in free space with a constant charge density pl forms a quarter circle of radius a that lies in the x y plane with the center of curvature at the origin as shown Find the potential at a point P on the zaXis Assume that the potential is zero at the origin Z P p1 Solution p a 7r2 61 p a 00z l 47 50 I czzz2 850xlczzz2 This is the potential along the zaXis with respect to in nity To change the reference to z 0 we can just subtract the potential at z 0 with respect to in nity pza 00z qgt000 88 V Electromagnetics Workshop Solutions Electric Potential Problem 3 A regular hexagon of charge with line charge density pl exists in the x y plane centered around the origin The hexagon is inscribed within a circle of radius a a Find the potential due to this charge distribution along the zaxis assuming the reference is at in nity where the potential is zero b Repeat a assuming the reference is at the origin where the potential is 5 V S olution Since the hexagon is regular it can be split up into six equilateral triangles Hence the sides of a3 the triangles are of length a The height of each triangle is Since the charge density is uniform we can deduce that the electric field and hence the potential will be equally affected by each of the six sides of the hexagon Hence using superposition aZ d ltZgt647flg I 2y 2 0 02 mg2 y39 z2 Z 3p m aZazz2 V 27 50 a2xazz2 03i1n3c 5 2 C 5 3i1n3 27139 so 27139 so z 3p m 612 612ZZ 27 50 3 a2a2zz 5 V Electromagnetics Workshop Solutions Electric Potential Problem 4 A hollow cylinder of surface charge p5 sin2 Cmz is centered at the origin a Find the potential due to this cylinder at point P00z Assume oo 0 Validate this assumption by evaluating your answer in the limit as z gt oo b Find the electric eld at point P00z by taking the gradient of the potential c Find the electric eld at point P00z using Coulomb s law and compare with the answer in part b S olution hZ a if 2 sin2 39d 39dz39 a J 0132 J dZ39 a 1n zh2lazzh22 V 4780 412 0 a2 z z392 480 412 laz z z392 450 z h2quota2 z h22 lim zh21 a2zh22 1 lim zilnl0 2 2 z h21lazz h22 2 450

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