Am electric dipole is placed in a uniform electric field .
(i) Show that no traslatory force acts on it .
(ii) Derive an expression for the torque acting on it.
(iii) Find work done in rotating the dipole through `180^(@)`.

Explanation

Electric dipole of charges + q and - q separated by distance 2a is shown in figure.

It is placed in a uniform electric field at an angle `theta` with it.
(i) Force on charge `+q,F_(1)=qvecE` , in the direction of `vecE`.
Force on charge `-q,F_(2)=-qvecE`, in the opposite direction of E.
`therefore` Net translatory force on dipole `=F_(1)+F_(2)`
`=+qvecE-qvecE=0`
Hence , no translatory force acts on it.
(ii) But the two equal parallel and unlike forces form a couple in which a torque is given by
`tau="Force"xx` perpendicular distance between the two forces
`=qExx2asintheta`
`tau=pEsintheta`
where , `p=qxx2a=` dipole moment
(iii) Work done in rotating the dipole through `180^(@)` is
`W=intdW`
`=int_(0^(@))^(180^(@))tau d theta=pEint_(0^(@))^(180^(@))sin theta d theta`
`=pE[-costheta]_(0^(@))^(180^(@))`
`=pE[cos180^(@)-cos0^(@)]`
`=pE[1+1]=2pE`