An electric dipole is placed at an angle of \( 30^\circ \) with an electric field of intensity \( 3 \times 10^{5}\,\mathrm{N/C} \). It experiences a torque equal to 6 N m. If the dipole length is 2 cm, the value of charge will be
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → \( 2 \times 10^{-3}\,\mathrm{C} \)
The torque on a dipole in a uniform field is \( \tau = pE\sin\theta \), with the dipole moment \( p = q \times (2a) \), where \( 2a \) is the dipole length.
\( \displaystyle \tau = q\,(2a)\,E\sin\theta \;\Rightarrow\; q = \frac{\tau}{(2a)\,E\sin\theta} \)
\( 2a = 2\,\mathrm{cm} = 0.02\,\mathrm{m} \)
\( \sin 30^\circ = 0.5 \)
\( \displaystyle q = \frac{6}{0.02 \times 3\times10^{5} \times 0.5} = \frac{6}{3000} = 2\times10^{-3}\,\mathrm{C} \)