ECE309-2008-hw4

ECE309-2008-hw4 - ECE 309 Electromagnetic Fields University...

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Unformatted text preview: ECE 309 Electromagnetic Fields University of Virginia Fall 2008 Homework # 4 Energy, Conductors, and Polarization Due: Wednesday, September 24 1. Find the energy stored in a uniformly charged solid sphere of radius R and total charge q . Find the energy in three different ways : (a) Use the expression relating energy to charge and potential, U = 1 2 Z V dv (b) Use the expression relating energy to the electric field (dont forget to integrate over all space !), U = 2 Z all space ~ E ~ E dv (c) Find the energy it takes to assemble the sphere, layer by layer, each time bringing in an infinitesimal charge dq from far away and smearing it uni- formly over the surface, thereby increasing the radius. How much work does it take to build up the radius by amount dr ? Integrate this to find the work necessary to put together the entire sphere of radius R and total charge q . 2. Two spherical cavities, of radii a and b , are hollowed out from the interior of a (neutral) conducting sphere of radius...
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This note was uploaded on 10/16/2010 for the course ECE 309 taught by Professor Weikle during the Spring '08 term at UVA.

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ECE309-2008-hw4 - ECE 309 Electromagnetic Fields University...

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