i need to show that the mutual energy between two dioples p1 and p2 (not necessarily parallel to eachother) is [tex] U=-\frac{p_1\cdot p_2}{|r|^3}-3\frac{(p_1\cdot r)(p_2\cdot r)}{|r|^5}[/tex](adsbygoogle = window.adsbygoogle || []).push({});

where r is the vector from p_1 to p_2. (the p's are moments of diople).

i tried using this equation: [tex]U=\int dV \rho_2 * \phi_1 [/tex]

and also this :[tex]\phi=\frac{p\cdot r}{|r|^3}[/tex]

(phi is the potential and rho is the density).

[tex]\rho_2=-1/4\pi\nabla^2\phi_2=-1/4\pi[\frac{1}{|r|^2}@/@r(r^2@\phi/@r)+\frac{1}{|r|^2*sin(\theta)}@/@\theta(sin(\theta)@\phi/@\theta)][/tex]

where @ stands for peratial derivative, but i didnt get to the desired answer.

any pointers?

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# Homework Help: Mutual energy of two dipoles.

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