• # question_answer An electric dipole of length 1 cm is placed with axis making an angle of $30{}^\circ$ 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)  $-0.245$ J                    B)  $-2.45\times {{10}^{-4}}$ J C)  $-0.0245$ J                  D)  $-24.5\times {{10}^{-4}}$ J

Torque $\tau \,=pE\,\sin \theta \,\Rightarrow \,P=\frac{\tau }{E\sin \theta }$Potential energy $U=-pE\cos \theta \,=\frac{-\tau }{E\,\sin \,\theta }.\,E\cos \theta$ $=\frac{-\tau }{E\sin \theta }\,=\frac{-10\sqrt{2}}{{{10}^{4}}\,\tan {{30}^{0}}}\,=-24.5\times {{10}^{-4}}J$