2 - Electromagnetics Workshop – Week 2 Solutions Charge...

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Unformatted text preview: Electromagnetics Workshop – Week 2 Solutions Charge and Current Densities, Voltage Problem 1: Write an expression for the elemental charge , , or s v dq d dS dV ρ ρ ρ ′ ′ ′ ′ = l l in the appropriate coordinate system for each case below: a. A line charge of density 2cos φ ′ [C/m] on a ring of radius 2 [m] centered in the x-y plane ( z = plane) b. A surface charge of density 2 2cos cos θ φ ′ ′ [C/m 2 ] on a sphere of radius ½ [m] centered about the origin. c. A line charge of density ( 29 2 x ′ [C/m] on the line segment x y ′ ′ = , 0 1 x ′ ≤ ≤ in the z = plane. Use x ′ to parameterize the line segment. d. A surface charge of density 2 2 cos ρ φ ′ ′ [C/m 2 ] on a disk of radius 2 [m] centered about the origin. e. A volume charge of density ( 29 1.5 2 2 cos z ρ φ ′ ′ ′ [C/m 3 ] inside a circular cylinder of radius 2 [m] and height 1 [m]. f. A surface charge of density 2 2 cos r φ ′ ′ [C/m 2 ] on the circular cone 30 θ ′ = ° ....
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2 - Electromagnetics Workshop – Week 2 Solutions Charge...

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