Potential energy of electric dipole

*“ Potential energy of electric dipole”:
The energy possessed by the dipole due to its specific position in an uniform electric field is called potential energy. It is a scalar quantity. It is denoted by  U.

*Measurement —The work done in turning a dipole from Standard position to any other position is stored in dipole in the form of potential energy.

Consider and electric dipole AB made up of two point charges  -q and +q  having a dipole moment P.
 the dipole Axis making an angle Φ with direction of electric field

“standard position of dipole is the perpendicular position with respect to direction of electric field in which the potential energy of a dipole becomes zero”

let the work done against dipole torque τ = P·E sinθ  in turning a dipole by small angle dθ is dw·

work done = dipole torque × angular displacement
              dw = τ·dθ
              dw = P·Esinθ                        taking integration of both side in the limit  θ1 to θ2

∫w =∫θ1​θ2
​​pEsinθdθ

 
 ​W = - P·E [cosθ2 - cosθ1]            
 W = P·E [ cosθ1 - cosθ2]

If  θ1 = π/2     and    θ2 = θ
then  W =  P·E ( cosπ/2 - cosθ)
∴  W = P·E ( 0 - cosθ)
    W = - P·E cosθ

This work done is stored in dipole 
in the form of potential energy

∴  U = W
∴ U = -P·E cosθ