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mmpstudent

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## Homework Statement

The problem has six charges that are at the corners of a regular hexagon in the xy plane, each charge a distance a from the origin. I have already solved for the electric fields in the x and y direction and now am trying to apply an approximation for the field on the x-axis at where x>>a. the field along the x-axis is

[itex]E_{x}= \displaystyle\sum_{n=1}^{6} \frac{x-acos\frac{k\pi}{3}}{[x^{2}-2axcos\frac{k\pi}{3}+a^{2}]^{3/2}}[/itex]

I am supposed to use a power series in the small quantity a/x using the method of taylor series to get to

[itex]E_{x}= \frac{1}{4\pi\epsilon_{0}}[{\frac{6q}{x^{2}}+\frac{9qa^{2}}{2x^{4}}}][/itex]

I haven't done this level math in a long time and I am sure that it is not too difficult, but I don't know what it means in the small quantity a/x. Do I just set x>>a in the efield equation and go about my business, if so, I don't understand where the a^2 term comes from in the numerator.

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