A magnet of magnetic moment \( 50\hat{\imath}\,\mathrm{A\,m^{2}} \) is placed along \( x \)-axis in a magnetic field \( \vec{B}=(0.5\hat{\imath}+3.0\hat{\jmath})\,\mathrm{T} \). The torque on the magnet is
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → \( 150\hat{k}\,\mathrm{Nm} \)
A magnet of moment \( \vec{m} \) in a uniform field \( \vec{B} \) experiences a torque \( \vec{\tau} = \vec{m}\times\vec{B} \). Only the part of the field perpendicular to the moment produces a torque.
\( \displaystyle \vec{\tau} = 50\hat{\imath}\times(0.5\hat{\imath}+3.0\hat{\jmath})\,\mathrm{N\,m} \)
\( \displaystyle \vec{\tau} = 25\,(\hat{\imath}\times\hat{\imath}) + 150\,(\hat{\imath}\times\hat{\jmath})\,\mathrm{N\,m} \)
Using \( \hat{\imath}\times\hat{\imath} = 0 \) and \( \hat{\imath}\times\hat{\jmath} = \hat{k} \):
\( \displaystyle \vec{\tau} = 150\hat{k}\,\mathrm{N\,m} \)
Note: A similar question was also asked in CUET (UG) 2023 on 27-05-2023 (Slot 3).