Question

Two point dipoles of dipole moment $\underset{P_1}{\overset{}{\to }}and\underset{P_2}{\overset{}{\to }}$ are at a distance x from each other and $\underset{P_1}{\overset{}{\to }}\parallel \underset{P_2}{\overset{}{\to }}$ The force between the dipoles is:

• A. $\frac{1}{4\pi e_0}\frac{4p_1{p}_2}{x^4}$
• B. $\frac{1}{4\pi e_0}\frac{3p_1{p}_2}{x^3}$
• C. $\frac{1}{4\pi e_0}\frac{6p_1{p}_2}{x^4}$
• D. $\frac{1}{4\pi e_0}\frac{8p_1{p}_2}{x^4}$

Answer 1

The correct option is C $\frac{1}{4\pi e_0}\frac{6p_1{p}_2}{x^4}$

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 P2 due to electric field of P1

$F=P_2\ast \frac{dE}{dx}$

=$P_2\ast \frac{d}{dx}\left(\frac{2P_1}{4\pi {ϵ}_0\ast x^3}\right)$

On solving

$F=-\left(\frac{6P_1{P}_2}{4\pi {ϵ}_0\ast x^4}\right)$

The correct option is C