An electric dipole of length 4 cm, when placed with its axis making an angle of \( 60^\circ \) with a uniform electric field, experiences a torque of \( 4\sqrt{3}\,\mathrm{N\,m} \). If the dipole has charges of \( \pm 8\,\mathrm{nC} \), then the potential energy of the dipole in the electric field is:
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → \( -4\,\mathrm{J} \)
The torque on a dipole is \( \tau = pE\sin\theta \) and its potential energy is \( U = -pE\cos\theta \). The torque is used to find \( E \), and then \( U \) follows.
\( p = qL = 8\times10^{-9} \times 4\times10^{-2} = 3.2\times10^{-10}\,\mathrm{C\,m} \)
\( \displaystyle E = \frac{\tau}{p\sin60^\circ} = \frac{4\sqrt{3}}{3.2\times10^{-10} \times (\sqrt{3}/2)} = 2.5\times10^{10}\,\mathrm{N\,C^{-1}} \)
\( \displaystyle U = -pE\cos60^\circ = -(3.2\times10^{-10})(2.5\times10^{10})(0.5) = -4\,\mathrm{J} \)