Question

Dipole is placed parallel to the electric field. If Q is the work done in rotating the dipole by 60?, then work done in rotating it by 180? is

• A. 2W
• B. 3W
• C. 4W
• D. W/2

Answer 1

Answer: (C)

A dipole placed in an external electric field is acted upon by a torque which tends to align the dipole in the direction of the field. Therefore, work must be done to change the orientation of the dipole against the torque. If dipole be rotated from an initial orientation $ \theta ={{\theta }_{1}} $ to final orientation $ \theta ={{\theta }_{2}} $ , the total work required is
$ W=\int_{{{\theta }_{1}}}^{{{\theta }_{2}}}{pE\,\,\sin \theta \,\,d\theta } $
$ W=pE[-cos\theta ]_{{{\theta }_{1}}}^{{{\theta }_{2}}} $ where $
p $ is dipole moment and $ E $ the electric field. In first case, $ W=pE(1-\cos {{60}^{o}}) $
$ W=pE\left( 1-\frac{1}{2} \right)=\frac{pE}{2} $
$ \Rightarrow $ $ pE=2W $ In second case, $ {{W}_{2}}=pE(1-\cos {{180}^{o}}) $ $ {{W}_{2}}=2W(1+1)=4W $