The magnitude of torque acting on an electric dipole when placed at right angles to a uniform electric field is \( 2\sqrt{2}\times10^{-2}\,\mathrm{N\,m} \). Magnitude of the torque acting on the dipole when dipole moment makes 45° with electric field will be:
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → \( 2\times10^{-2}\,\mathrm{N\,m} \)
The torque on an electric dipole in a uniform field is \( \tau = pE\sin\theta \), where \( \theta \) is the angle between the dipole moment and the field. For the same p and E, the torque is proportional to \( \sin\theta \).
At right angles \( \theta = 90^\circ \), the torque is the maximum value \( pE \):
\( pE = 2\sqrt{2}\times10^{-2}\,\mathrm{N\,m} \)
\( \tau' = pE\sin45^\circ = 2\sqrt{2}\times10^{-2}\times\frac{1}{\sqrt{2}} = 2\times10^{-2}\,\mathrm{N\,m} \)