Potential energy of a dipole

in an external field E

 

1) Suppose there is a dipole of charges +q  &  -q

2) they are separated by a distance 2a.

3) Suppose at some moment the dipole making an angle q with the electric field E.




4) Due to the external electric field E the dipole experience a torque t

 

5) this torque is (as already proved)



Where E = electric field


P = dipole moment (2aq)


6) Now suppose, an external torque is applied just to stop the first former torque.

7) Then this torque new applied torque will be in opposite direction

8) Suppose this second external torque is applied just to rotate the dipole from an angle 


9) then work done by the torque for small angle of rotation is

Now putting the value of t from 2.31,





Now when