Two thin rods of length L lie along the x-axis, one

Chapter 21, Problem 21.97

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Two thin rods of length L lie along the x-axis, one between x = 1 2 a and x = 1 2 a + L and the other between x = -1 2 a and x = -1 2 a - L. Each rod has positive charge Q distributed uniformly along its length. (a) Calculate the electric field produced by the second rod at points along the positive x-axis. (b) Show that the magnitude of the force that one rod exerts on the other is F = Q2 4pP0L2 ln c 1a + L22 a1a + 2L2 d (c) Show that if a W L, the magnitude of this force reduces to F = Q2>4pP0a2 . (Hint: Use the expansion ln11 + z2 = z - 1 2 z 2 + 1 3 z 3 - g, valid for 0z0 V 1. Carry all expansions to at least order L2>a2 .) Interpret this result.

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