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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 -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 %3D || X = Q? In La(a + 2L), (a + L)? F = (c) Show that if a » L, the magnitude of this force reduces to F = Q²/4€0a². (Hint: Use the expansion In(1 + z) = z – z²/2 + z³/3 least order L²/a².) Interpret this result. - .. , valid for |z| « 1. Carry all expansions to at -

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 -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 %3D || X = Q? In La(a + 2L), (a + L)? F = (c) Show that if a » L, the magnitude of this force reduces to F = Q²/4€0a². (Hint: Use the expansion In(1 + z) = z – z²/2 + z³/3 least order L²/a².) Interpret this result. - .. , valid for |z| « 1. Carry all expansions to at -

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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 Q? (a + L)? F = In 4TEOL2La(a + 2L). (c) Show that if a » L, the magnitude of this force reduces to F = Q²/4T€0ª². (Hint: Use the expansion In(1 + z) = z – z²/2 + z³/3 – least order L2/a².) Interpret this result. - valid for z « 1. Carry all expansions to at
Transcribed Image Text: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 Q? (a + L)? F = In 4TEOL2La(a + 2L). (c) Show that if a » L, the magnitude of this force reduces to F = Q²/4T€0ª². (Hint: Use the expansion In(1 + z) = z – z²/2 + z³/3 – least order L2/a².) Interpret this result. - valid for z « 1. Carry all expansions to at
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