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. $\frac{3p_1{p}_2}{4\pi {ϵ}_0{x}^4}$
• B. $\frac{p_1{p}_2}{2\pi {ϵ}_0{x}^4}$
• C. $\frac{p_1{p}_2}{4\pi {ϵ}_0{x}^4}$
• D. $\frac{p_1{p}_2}{3\pi {ϵ}_0{x}^4}$

Answer 1

Answer: (A)

Let U = potential energy
$U=-p_2{E}_{21}=\frac{-p_2{p}_1}{4\pi {ϵ}_0{x}^3}cos180^{{}^{\circ }}$
$U=\frac{p_1{p}_2}{4\pi {ϵ}_0{x}^{\text{3}}}$
$\text{We know,}\text{ F}=-\frac{\text{d}\text{U}}{\text{d}\text{x}}=\frac{3p_1{p}_2}{4\pi {ϵ}_0{x}^4}$