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Problem Set 2 Solutions

# Problem Set 2 Solutions - MASSACHUSETTS INSTITUTE OF...

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MASSACHUSETTS INSTITUTE OF TECHNOLOGY Department of Physics 8.02 Fall 2007 Problem Set 2 Solutions Problem 1: Closed Surfaces Four closed surfaces, S 1 through S 4 , together with the charges –2 Q , Q , and – Q are sketched in the figure at right. The colored lines are the intersections of the surfaces with the page. Find the electric flux through each surface. By Gauss’s Law, the flux through the closed surfaces is equal to the charge enclosed over ε 0 . So, 1 2 3 4 0 0 0 S S S S 2 ; 0; ; Q Q ε ε Φ = − Φ = Φ = − Φ = Problem 2: Field on Axis of a Line Charge A wire of length has a uniform positive linear charge density and a total charge . Calculate the electric field at a point located along the axis of the wire and a distance from one end: l Q P a a. Give an integral expression for the electric field at point P in terms of the variables used in the above figure ( ) 2 ˆ a l e dx k a x λ + = − E i b. Evaluate this integral. 1 1 1 ˆ ˆ ˆ ˆ ( ) ( ) a l e e e e l Q k k k k a x a l a a a l a a l λ λ λ + = = = = − + + E i i i i + c. In the limit that the length of the rod goes to zero, does your answer reduce to the right expression? 2 ˆ In the limit that goes to zero, our expression becomes , as we desire. e Q l k = E i a G PS02 Solution - 1

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