Question

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:

Essay answers are limited to about 500 words (3800 characters maximum, including spaces).

3785 Character(s) remaining

Answer 1

-a 2 fiuut Rod tgtし the terce dnet ane

a +L dx. 2pa 札 a. Q'파 (,h@+1)-In (a(q+x))) 2. 2L