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I'm a physics tutor. This is not a homework problem. I'm unable to solve this problem.

The energy of electric interaction between these dipoles will be:

enter image description here

Choose the correct answer from:

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I tried taking P1=q1*d1 and P2=q2*d2 then calculated Potential energy between (q1,-q1), (q1,-q2), (q2,-q2), (-q1,q2) and used certain approximations but couldn't get to any of the results shown.

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2 Answers 2

up vote 1 down vote accepted

The answer is by assuming a short dipole.

There are many ways of going about this (I'm only giving hints to the full method). One is by splitting the lower dipole into parallel and perpendicular components(its a vector, we can do that). Now use the formulae for field from a dipole at axial and equatorial positions (equatorial is $\frac{kp}{r^3}$, axial is double that), and calculate the change in potential while moving two charges $\pm q$ from infinity to a distance $r \pm d$.

Or, you can directly apply the formula $V(r,\theta)=\frac{k\vec{p}\cdot\vec{r}}{r^3}$, on the two charges at $r\pm d$.

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You may use the electrostatic potential due to electric dipole $P_2$ (see, e.g., http://en.wikipedia.org/wiki/Dipole#Field_from_an_electric_dipole, although the system of units is different there) and find the energy of charges $+q_1$ at $r+d_1$ and $-q_1$ at $r$ under the condition that $d_1\ll r$.

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