Question

Two point dipoles of dipole moment $\overrightarrow{p_1}$ and $\overrightarrow{p_2}$ are at a distance $x$ from each other and $\overrightarrow{p_1}\left|\right|\overrightarrow{p_2}.$ The force between the dipoles is :

• A. $\frac{1}{4\pi {\epsilon }_0}\frac{4p_1{p}_2}{x^4}$
• B. $\frac{1}{3\pi {\epsilon }_0}\frac{8p_1{p}_2}{x^3}$
• C. $\frac{1}{4\pi {\epsilon }_0}\frac{6p_1{p}_2}{x^4}$
• D. $\frac{1}{4\pi {\epsilon }_0}\frac{8p_1{p}_2}{x^4}$

Answer 1

Answer: (C)

Given
Two parallel dipoles at distance $x$
Solution
Axial electric field of dipole P1
$E_{P_1}=\frac{2\ast P_1}{4\pi {ϵ}_0\ast x^3}$
Force on dipole $P_2$ due to electric field of $P_1$
$F=P_2\ast \frac{dE}{dx}$
$=P_2\ast \frac{d}{dx}\left(\frac{2P_1}{4\pi {ϵ}_1\ast x^3}\right)$
On solving
$F=-\left(\frac{6P_1{P}_2}{4\pi {ϵ}_0\ast x^4}\right)$