Question

An electric dipole of length $ 1 \,cm $ is placed with the axis making an angle of $ {{30}^{o}} $ to an electric field of strength $ {{10}^{4}}N{{C}^{-1}} $ . If it experiences a torque of $ 10\sqrt{2}Nm, $ the potential energy of the dipole is

• A. $ 0.245\text{ }J $
• B. $ 2.45\times {{10}^{-4}}J $
• C. $ 0.0245\text{ }J $
• D. $ 245.0\text{ }J $
• E. $ 24.5\times {{10}^{-4}}J $

Answer 1

Answer: (E)

Torque, $ \tau =pE\sin \theta $ or $ P=\frac{\tau }{E\sin \theta } $
Potential energy, $ U=pE\cos \theta $
$ =\frac{\tau }{E\sin \theta }.E\cos \theta $
$ =\frac{\tau }{E\tan \theta }=\frac{10\sqrt{2}}{{{10}^{4}}\tan {{30}^{o}}} $
$ =24.5\times {{10}^{-4}}J $