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. $\frac{1}{4\pi\varepsilon_{0}} \frac{4p_{1}p_{2}}{x^{4}}$
• B. $\frac{1}{3\pi\varepsilon_{0}} \frac{8p_{1}p_{2}}{x^{3}}$
• C. $\frac{1}{4\pi\varepsilon_{0}} \frac{6p_{1}p_{2}}{x^{4}}$
• D. $\frac{1}{4\pi\varepsilon_{0}} \frac{8p_{1}p_{2}}{x^{4}}$

Answer 1

Answer: (C)

Given
Two parallel dipoles at distance $x$
Solution
Axial electric field of dipole P1
$E _{ P _{1}}=\frac{2 * P _{1}}{4 \pi \epsilon_{0} * x ^{3}}$
Force on dipole $P _{2}$ due to electric field of $P _{1}$
$F = P _{2} * \frac{ dE }{ dx }$
$= P _{2} * \frac{ d }{ dx }\left(\frac{2 P _{1}}{4 \pi \epsilon_{1} * x ^{3}}\right)$
On solving
$F =-\left(\frac{6 P _{1} P _{2}}{4 \pi \epsilon_{0} * x ^{4}}\right)$