exam 1 fall 2000

# exam 1 fall 2000 - Problem 1(25 pts A cylindrical column of...

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3 Problem 1 (25 pts) A cylindrical column of uniform charge density 0 v ρ [C/m 3 ] is shown below. The column is rotating at a constant angular speed of 0 ϖ [radians/s] in the counterclockwise direction. Recall that the speed at any distance from the z axis is given by 0 ϖ ρ [m/s]. a) Determine the current density vector J at any point inside the column. Express your answer in cylindrical coordinates. b) Find the total current that crosses through the surface S shown below, in the direction out of the paper . This surface is one meter high in the z direction, and has width a , running from the z axis to the edge of the column. x z S a 1 z x y 0 0 v a

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5 Problem 2 (25 pts ) a) Consider a slab of charge of thickness h , located between / 2 z h = - and / 2 z h = + . Within the slab there is a volume charge density v z ρ = [ 3 C/m ]. The slab is infinite in the x and y directions. Find the electric field vector in all regions: / 2 z h < - , / 2 / 2 h z h - < < , and / 2 z h . b)
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exam 1 fall 2000 - Problem 1(25 pts A cylindrical column of...

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