An electric dipole of length 2 cm is placed at an angle of \( 30^\circ \) with an electric field \( 3 \times 10^{5}\,\mathrm{N\,C^{-1}} \). If the dipole experiences a torque of \( 9 \times 10^{-3}\,\mathrm{N\,m} \), the magnitude of either charge of the dipole is
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → \( 3\,\mu\mathrm{C} \)
The torque on an electric dipole in a uniform field is \( \tau = p\,E\sin\theta \), and the dipole moment is \( p = q \times 2a \), where \( 2a \) is the length of the dipole.
\( 2a = 2\,\mathrm{cm} = 0.02\,\mathrm{m} \)
\( \displaystyle q = \frac{\tau}{(2a)\,E\sin\theta} = \frac{9\times10^{-3}}{0.02 \times 3\times10^{5} \times 0.5} \)
\( \displaystyle q = \frac{9\times10^{-3}}{3\times10^{3}} = 3\times10^{-6}\,\mathrm{C} = 3\,\mu\mathrm{C} \)