I am looking for an equation that gives me the potential energy of the interaction between two parallel dipoles.
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$\begingroup$ This is pretty much formula based. Find the field due to one dipole near the other, then use $U=-\vec p \cdot \vec E$ $\endgroup$– udiboy1209Commented Jul 24, 2013 at 11:15
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3$\begingroup$ I think, according to homework policy, this question is off-topic. $\endgroup$– MostafaCommented Jul 24, 2013 at 11:18
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1 Answer
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Hint:
Interaction energy of two dipoles :
$$U=\frac{1}{4\pi \epsilon_0r^3}\left( \mathbf{p}_1.\mathbf{p}_2-3\left ( \mathbf{p}_1.\hat r )(\mathbf{p}_2.\hat r\right) \right)$$
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1$\begingroup$ Could you explain what is the meaning of $\hat r$? $\endgroup$ Commented Nov 14, 2018 at 14:28
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1$\begingroup$ It's the unit vector in direction of $\vec{r}$, i.e. $\hat{r}=\frac{\vec{r}}{r}$. $\endgroup$ Commented Oct 13, 2020 at 20:38
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$\begingroup$ Do you have any reference for this formula? Any book? $\endgroup$ Commented Mar 12, 2021 at 18:55
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1$\begingroup$ @user171780 See problem 4.8 (p. 165) in Griffiths Introduction to Electrodynamics (3rd ed). $\endgroup$– MostafaCommented Mar 12, 2021 at 21:46
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$\begingroup$ Not sure why you call this a "hint". $\endgroup$ Commented Oct 8, 2021 at 21:41