exam 1 spring 2001

exam 1 spring 2001 - The semicircle starts at = and ends at...

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Problem 1 (25 pts) A system of three charges is shown in the diagram below. Find the total force on the charge 3 q . 1 z x y 1 q (1,0,1) (0,1,0) (1,2,1) 2 q 3 q 1 2 3 1[ ] 2[ ] 3[ ] q C q C q C = = - =

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Problem 2 (25 pts) Given the electric flux density 2 2 2 2 ˆ ˆ ˆ 5cos ( ) 17 9 cos ( ) [ / ] C m φ ρ ρ φ = - + φ z find the net electric flux in the upward direction through the annulus shown in the figure ( a b ρ ). 2 z x y b a
Problem 3 (25 pts) A thin line charge of density 0 sin( ) ρ ρ φ = l is in the form of a semi-circle of radius a lying on the x-y plane with its center located at the origin.

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Unformatted text preview: The semicircle starts at = and ends at π = . Find the electric field vector E at a location z along the z-axis. 3 z x y a sin( ) = l Problem 4 (25 pts) Given the electric field ( 29 ( 29 ( 29 2 2 ˆ ˆ ˆ 3 4sin 2 1 [ / ] z V m φ φρ ρ = + + + + Eρ φ z find the result of the line integration B AB A V = ⋅ ∫ E d l by integrating along the path shown in the figure. 4 A 45 o 2 [m] 1 [m] B x y...
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