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Unformatted text preview: EE1 Spring 2008 Homework #4 Solutions 1) An electron beam shaped like a circular cylinder of radius r carries a charge density given by: v = ( 1 + r 2 )( C m 3 ) where is a positive constant and the beams axis is coincident with the zaxis. a) Determine the total charge contained in the length L of the beam. This can be determined by evaluating the volume integral of the volume charge density with the volume of the cylinder. Z v v dV = Lln (1 + r 2 ) . b) If the electrons are moving in the +z direction with uniform speed u, determine the magnitude and direction of the current crossing the zplane. Multiplying the charge density by the speed will result in the current density of the electron beam. J = v u A simple surface integral can then determine the current I crossing the zplane. I = Z J d S I = u ln (1 + r 2 ) The current is traveling in the z direction. 1 2) A coaxial conductor has radii a = 0.8 mm and b = 3 mm and a polystyrene dielectric for which r = 2 . 56. If P = 2 r r ( nC/m 2 ) in the dielectric, find: a) D and E as functions of r.a) D and E as functions of r....
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 Spring '08
 Joshi

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