Question

Find the force of interaction of two dipoles, if the two dipole moments are parallel to each other and placed at a distance $x$ apart

• A. $\frac{3 p_{1} p_{2}}{4 \pi \epsilon _{0} x^{4}}$
• B. $\frac{p_{1} p_{2}}{2 \pi \epsilon _{0} x^{4}}$
• C. $\frac{p_{1} p_{2}}{4 \pi \epsilon _{0} x^{4}}$
• D. $\frac{p_{1} p_{2}}{3 \pi \epsilon _{0} x^{4}}$

Answer 1

Answer: (A)

Let U = potential energy
$U=-p_{2}E_{2 1}=\frac{- p_{2} p_{1}}{4 \pi \epsilon _{0} x^{3}}cos180^{^\circ }$
$U=\frac{p_{1} p_{2}}{4 \pi \epsilon _{0} x^{\text{3}}}$
$\text{We know,}\textit{ F}=-\frac{\text{d} \textit{U}}{\text{d} \textit{x}}=\frac{3 p_{1} p_{2}}{4 \pi \epsilon _{0} x^{4}}$