- #1

raintrek

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## Homework Statement

Consider two dipoles with moments u1 and u2 arranged as in the following diagram. Each dipole is depicted as two charges of equal magnitude separated by a distance d. The centre-to-centre separation of the two dipoles is the distance r. The line joining the two dipole centres makes an angle theta with the lower dipole (ie. q1 and -q1). Derive an expression in terms of u1, u2, theta and r which describes the potential energy of interaction of these two dipoles which is valid when d<<r. In the spirit of the hint below, your answer should not consider any (d/r)^n terms where n is greater than 2:

http://ds9.trekcore.com/dipole.JPG [Broken]

Hint:

[tex]\frac{1}{\sqrt{1-ax}}\approx1+\frac{1}{2}ax+\frac{3}{8}a^{2}x^{2}[/tex]

## Homework Equations

[tex]U(r)=\frac{kQQ}{r}[/tex]

## The Attempt at a Solution

I've been trying to solve this for the past hour without any luck. It centers around getting an expression for the separation between q1 and -q2, and -q1 and q2. I'm fairly certain the expression should be from Pythagoras given the hint (ie, I need to take a square root of r at some point), but I can't find one which involves d/r as also specified in the hint. If anyone could offer any pointers, I'd be most appreciative. Thanks!

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