(adsbygoogle = window.adsbygoogle || []).push({}); [SOLVED] General questions in E&M

I have a few questions regarding some concepts I'd like to clear up in my upper level undergraduate E&M course. I have a test tomorrow, and my professor is big on essay questions explaining the theory behind our current material. So, I'm going to write down the concepts I'm not clear on, and then try to explain them best I can. I figure that even if nobody replies I can at least try to straighten some things out on my own by writing them down. PLEASE say something if I'm wrong or if I left something out. Here I go:

1) For a given charge distribution, what are the physical conditions required in order for both the monopole moment and dipole moment to be zero? (i.e., if you have a quadripole or octipole, and you tried to calculate the potential of the charge distribution due to a monopole or dipole, why would it be equal to zero?)

The only physical significance I can think of deals with the nature of the answer from multipole expansions - they areapproximations. The first non-zero term in the sum dominates, and each subsequent term merely adds precision. So, if we have a quadripole (n=2), we know that the potential must fall off at a rate of 1/r^2. So, the first term in the sum MUST be equal to zero in order for this to be true:

[tex]V(r)= \sum_{n=0}^{\infty}{\frac{1}{r'^{n+1}}\int{(r')^nP_n(cos(\theta))\roe(r')d\tau}}

[/tex]

Are there any other physical dependents?

2) What conditions are necessary to allow the use of Laplace's equation instead of Poisson's equation in the determination of the electric potential?

The only condition I can think of is that the charge in the area you are measuring must be zero...since Laplace's equation IS Poisson's equation with a charge density equal to zero. Am I missing something?

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# Homework Help: General questions in E&M

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