Two thin rods of length L lie along the x-axis, one between x=a/2 and x=a/2+L and...
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.
Part A
Calculate the electric field produced by the second rod at points along the positive x-axis.
Express your answer in terms of the variables x, a, L, Q and appropriate constants.
ANSWER:
| Ex = |
2kQL(12x+a?12L+2x+a) |
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Part B
Find the magnitude of the force that one rod exerts on the other.
Express your answer in terms of the variables x, a, L, Q and appropriate constants.
ANSWER:
| F = |
Part C
Assuming a?L, find the magnitude of this force reduces to. (Hint: Use the expansion ln(1+z)=z?z2/2+z3/3?...), valid for |z|?1. Carry all expansions to at least order L2/a2.)
Express your answer in terms of the variables a, Q and appropriate constants.
ANSWER:
| F = |
Part D
Interpret this result.
ANSWER:
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Two thin rods of length L lie along the
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