Two point charges \( \pm200\,\mu\mathrm{C} \) are placed at a distance of \( 2\,\mathrm{mm} \) from each other in uniform electric field of \( 10^{5}\,\mathrm{N/C} \) such that the line joining the negative to positive charge makes an angle \( 30^\circ \) with the field. The torque acting on the system is,
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → \( 0.02\,\mathrm{Nm} \)
The two charges form an electric dipole. In a uniform field the torque on a dipole is \( \tau = pE\sin\theta \), where \( \theta \) is the angle between the dipole moment (negative to positive charge) and the field.
\( q = 200\,\mu\mathrm{C} = 2\times10^{-4}\,\mathrm{C} \)
\( 2a = 2\,\mathrm{mm} = 2\times10^{-3}\,\mathrm{m} \)
\( \displaystyle p = q \times 2a = 2\times10^{-4} \times 2\times10^{-3} = 4\times10^{-7}\,\mathrm{C\,m} \)
\( \displaystyle \tau = pE\sin\theta = 4\times10^{-7} \times 10^{5} \times \sin30^\circ = 4\times10^{-2} \times 0.5 = 0.02\,\mathrm{N\,m} \)