Question

Two point dipoles of dipole moment p1 and p2 are at a distance x from each other and p1||p2. The force between the dipoles is:

Answer 1

Two point dipoles of dipole moment p1 and p2 are at a distance x from each other and p1||p2. we have to find force between the dipoles .

first of all, find electric field at X distance from $P_1$ , $E=\frac{2kP_1}{x^3}$ [ it is axial electric field ]

now, force on $P_2$ due to electric field E, $F=P_2.\frac{dE}{dx}$

= $P_2\frac{d}{dx}\left(\frac{2kP_1}{x^3}\right)$

= $P_2\left(-\frac{6kP_1}{x^4}\right)$

= $-\frac{6kP_1P_2}{x^4}$

[ here negative sign indicates that force is acting opposite to direction of dipole]

hence, force between the dipoles is $-\frac{6kP_1P_2}{x^4}$