Ve230_Homework_2

# 4 charges q q and q lie on the corners of an

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4) Charges Q , Q , and q lie on the corners of an equilateral triangle with sides of length a . (a) What is the force on the charge q ? (b) What must q be for E to be zero half-way up the altitude at P?

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5) Find the electric field along the z-axis due to four point charges q placed along the vertices of a square with side of length a in the xy plane centered at the origin when: (a) the charges have the same polarity, q 1 = q 2 = q 3 = q 4 = q (b) the charges alternate in same polarity, q 1 = q 3 = q q 2 = q 4 = q (c) the charges are q 1 = q 2 = q q 3 = q 4 = q 6) Find the total charge in each of the following distributions where a is a constant parameter: (a) An infinitely long line charge with density: λ z ( ) = λ 0 e z / a (b) A spherically symmetric volume charge distributed over all space ρ r ( ) = ρ 0 1 + r a ( ) 4 (c) An infinite sheet of surface charge with density σ x , y ( ) = σ 0 e x / a 1 + y b ( ) 2 7) An infinitely long hollow semi-cylinder of radius R carries a uniform surface charge distribution σ 0 . (a) What is the electric field along the axis of the cylinder? (b) Use the results of (a) to find the electric field along the axis due to a semi-cylinder of volume charge density ρ 0 . (c) Repeat (a) and (b) to find the electric field at the center of a uniformly surface or volume charged hemisphere.
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• Summer '13
• BenjaminYellen
• Charge, Electric charge, Fundamental physics concepts, charge density

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