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Question

Figure 3.118 shows two dipole moments parallel to each other and placed at a distance x apart. What is the magnitude of force of interaction? What is the nature of force, attractive or repulsive?
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Solution

Potential energy of dipole system


$$\displaystyle U = -\bar{p_2}. \vec{E_{21}} = - p_2 \frac{1}{4 \pi \varepsilon_0} \frac{p_1}{x^3} cos \pi$$


$$E_{21}$$ is the field due to $$p_1  at p_2$$ as shown.


$$\displaystyle U = \frac{1}{4 \pi \varepsilon_0}\frac{p_1 p_2}{x^3}$$


$$\displaystyle F = -\frac{\partial U}{\partial x} = \frac{3}{4 \pi \varepsilon_0} \frac{p_1 p_2}{x^4}$$


F comes out to be positive, so it is a repulsive force


Physics
NCERT
Standard XII

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