- #1

dreamspace

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## Homework Statement

So the problem revolves around a Linear Electric Quadrupole, with two positive charges on z-axis (in positions s and -s from origo) and two negative charges in origo.

1. Show that potential from a position R can be written as

2. The quadrupole moment can be written as

where

Show that

Show that the electric field of the linear quadrupole can be written as

We now change the Linear quadrupole out with a quadratic quadrupole

Show that the quadrupole moment can be written as

where

## Homework Equations

## The Attempt at a Solution

I've done number 1. It was pretty straight forward, and I did it with Law of Cosines and some series expansion, but I'm completely stuck at number 2.

After some googling, it seems that there's tensors involved in this one, but I can't remember the professor talking about tensors for more than maybe 1 min, with a very brief example on Ohms Law (I think).

I just can't figure out where to start, as I have no intuitive image of how tensors work, or how they're to be applied in this problem.

As for the electric field, it should just be the negative Gradient of the potential.

But again, I can't get my head around tensors, or how to derive them from the picture or equations I've been given.

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