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Force between two aligned permanent dipoles

  • Thread starter overmage
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  • #1
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Homework Statement


Show that the force between two aligned permanent dipoles, a distance r apart, is attractive and varies as [tex]r^{-4}[/tex]

Length of dipole to be taken as d.


Homework Equations


None provided.

The Attempt at a Solution


I'm completely lost here and have no idea where to begin. My attempts at a solution have only led me to discover that somehow, energy of the dipole between two charged molecules is supposed to be E=[tex]\frac{p}{4\pi\epsilon_{0}r^{3}}[/tex] (where p = dipole moment = qd)

As to why this is so, I have no idea!

I've searched around these forums for similar problems. What is the electric field of a dipole and how do I derive it? I read that it's something to do with Taylor's Expansion on d/r. I realize I may sound like an idiot for asking such elementary questions, so i apologize.
 
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Answers and Replies

  • #2
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What do you mean by aligned? aligned how?

Also, thats not an energy you've written down, looks like the electric field to me! :D

The electric field **on axis** of a dipole is not too difficult to derive. (Off axis involves vectors and becomes more complicated) Assume the two charges that make up the dipole (+q and -q) lie on the z axis. Let +q lie at position z, and -q lie at position z+d.

You know what the potential due to a point charge is? You know that the potentials of the two charges will add? You can use a taylor approximation on the 1/(z+d) term to simplify the total potential. Then the electric field will be given by gradient of the total potential.
 

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