Two thin rods of length L lie along the x-axis, one between x = a/2 and x = a/2 + L and the other between x = -a/2 and x = -a/2 - 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



(c) Show that if a » L. the magnitude of this force reduces to F = Q2/4πє0a2 (Hint: Use the expansion in (1 + z) = Z - z2 /2 + z3/3 - ..., valid for |z| « 1. Carry all expansions to at least order L2 / Ia2.) Interpret this result.

Transcribed Image Text:

(a + L)? Q? In 4me,L"a(a + 2L)