Potential energy between electric dipoles

Question

Two dipoles are at an angle of 60 to each other. The distance between them is L. Electric field is perpendicular to the first dipole. The dipole moment of both the dipoles are P. The potential energy of the system is-

Answer 1

The electric field at dipole is

\(E_0 = \frac {KP}{L^3}\)

The potential energy of a dipole placed in an electric field is 

\(U = -\vec P .\vec E\)

\(U = -PE\, cos90° - PE \,cos 30° - \frac{KP^2}{L^3} cos60° \) 

\(U = - 0 - PE\times \frac{\sqrt 3}2 - \frac{KP^2}{L^3} \times \frac12\)

\(U = -\left[\frac{KP^2}{2L^3 } + \frac{\sqrt3}2PE\right]\)