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?

Answer 1

Potential energy of dipole system

$U=-\overline{p_2}.\overrightarrow{E_{21}}=-p_2\frac{1}{4\pi {\epsilon }_0}\frac{p_1}{x^3}cos\pi$

$E_{21}$ is the field due to $p_{1}at{p}_2$ as shown.

$U=\frac{1}{4\pi {\epsilon }_0}\frac{p_1{p}_2}{x^3}$

$F=-\frac{\partial U}{\partial x}=\frac{3}{4\pi {\epsilon }_0}\frac{p_1{p}_2}{x^4}$

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