3209-2009-Solutions4 - ECE 3209 Electromagnetic Fields...

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Unformatted text preview: ECE 3209 Electromagnetic Fields University of Virginia Fall 2009 Homework # 4 Solutions 1. Two spherical conductors separated by a long wire. If the spheres are separated by enough distance, then the charge distribution on one will not influence that on the other and the charge on each sphere will be uniformly distributed around each surface. Thus, if the charge on sphere a is q a and that on sphere b is q b , the potential of each (with reference point at infinity) will be, a = q a 4 a , b = q b 4 b If the potential of the spheres is the same, then a = b , so that q a a = q b b Since the total charge is q = q a + q b , we have q a = a a + b q, q b = b a + b q Note that if a b , then q a q and q b , that is, most of the charge resides on the sphere with smaller radius. Consequently, the field surrounding that sphere is much stronger. A lightning rod relies on a very sharp tip (which can be thought of as a sphere with very small radius) to create a large electric field. The idea is that the air will breakdown near this sharp tip first, causing lightning to strike it rather than the structure to which it is attached. 2. Dipole antenna....
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This note was uploaded on 10/16/2010 for the course ECE 309 taught by Professor Weikle during the Fall '08 term at UVA.

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3209-2009-Solutions4 - ECE 3209 Electromagnetic Fields...

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