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Unformatted text preview: current element just to the left of the nearest one should contribute an upward component to the eld at P . The current elements are all equivalent, as is reected in the horizontal-translational symmetry built into this problem; therefore, all vertical components should cancel in pairs. The eld at P must be purely horizontal, as drawn. (b) The path used in evaluating H ~ B d~s is rectangular, of horizontal length x (the horizontal sides passing through points P and P respectively) and vertical size y &gt; y . The vertical sides have no contribution to the integral since ~ B is purely horizontal (so the scalar dot product produces zero for those sides), and the horizontal sides contribute two equal terms, as shown below. Amperes law yields 2 B x = x = B = 1 2 ....
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- Fall '08