Jackson Electrodynamics Problem 2.3

[Locrian]

The problem and a solution can both be found here. In this problem there is a line charge and two conducting planes at the axis. You use the method of images to solve it. The first three parts are easy enough. The fourth asks what the electric field is far from the origin.

I do not know how to find that. I've found two separate solutions, both of which write the potential, wave hands, and promptly write the answer. The link above says "Here we simply need to Taylor expand the expression in (1)." I can do a simple Taylor expansion, so I have an idea what it looks like, but I have no clue what it has to do with this problem. The author's next two equations are just (1) multiplied out, with some jabber inbetween I can't make heads or tails of. Then they write the answer.

Could anyone help me along in how this answer is found? I have actually spent a great deal of time trying to figure out how this is solved, but I cannot seem to get the solution.

Thanks.

 

[Locrian]

Aha! There is a solution http://homerreid.ath.cx/~homer/physics/jackson/index.shtml that actually makes a bit of sense.

Still, if anyone has some comments on Taylor expansions I'd appreciate it. I do not understand how one would use a Taylor expansion in this problem.

 

[Meir Achuz]

That solultion is the Taylor series solution. It is a two dimension Taylor expansion in ${\vec r_0}/r$.

 

[Locrian]

That's almost exactly what the first link wrote. Unfortunately it is no help to me at all. If you know of a place that actually shows the problem being worked out in that manner please let me know.

Thanks for the response.

 

[Meir Achuz]

I meant to say that the steps in Homer's solution to part (d) is precisely a two dimensional Taylor expansion. It IS "the problem being worked out in that manner".