Two point dipoles of dipole moment p1 and p2


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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:

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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}


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