MASSACHUSETTS INSTITUTE OF TECHNOLOGY Department of Physics 8.02 Fall 2007 Problem Set 2 Solutions Problem 1: Closed Surfaces Four closed surfaces, S1through S4, together with the charges –2Q, 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 ε0. So, 1234000SSSS2;0;;QQεεΦ= −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: lQPaa.Give an integral expression for the electric field at point Pin terms of the variables used in the above figure ()2ˆaledxkaxλ+′= −′∫Eib.Evaluate this integral. 111ˆˆˆˆ()()aleeeelQkkkkaxalaa ala alλλλ+⎡⎤−⎡⎤==−== −⎢⎥⎢⎥′++Eiiii+⎣⎦⎣⎦c.In the limit that the length of the rod goes to zero, does your answer reduce to the right expression? 2ˆIn the limit that goes to zero, our expression becomes , as we desire.eQlk⎛⎞=−⎜⎟Eia⎝⎠GPS02 Solution - 1
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