Question

drive an expression for energy stored in a dipole in uniform electric field

Answer 1

suppose an electric dipole of dipole moment (p) is placed along a direction making an angle Φ with the direction of and uniform electric field (E) then the torque acting on the dipole is given by

t=pE sin Φ

if the dipole is ratated through an infinitesimally small angle Φ, angainst the torque acting on it then the small work done is given by

dw=pdΦ=pE sinΦ

w=pE(cosΦ1- cosΦ2)

this work done is stored in the dipole in the form of its potential energy

therefore u=pE (cos 90°-cosΦ)

u=-pE cosΦ
u= -P.E