A) \[5\times {{10}^{-6}}Nm\]
B) \[\frac{1}{2}\times {{10}^{-5}}Nm\]
C) \[5\sqrt{3}\times {{10}^{-6}}Nm\]
D) Data is insufficient
Correct Answer: A
Solution :
The magnet in a magnetic field experiences a torque which rotates the magnet to a position in which the axis of the magnet is parallel to the field. \[\tau =MB\text{ }sin\,\theta \] where, M is magnetic dipole moment, B the magnetic field and 9 the angle between the two. Given, \[{{\tau }_{1}}={{10}^{-5}}Nm,{{\theta }_{1}}=90{}^\circ ,{{\theta }_{2}}=30{}^\circ ,\] \[{{\tau }_{1}}=MB\sin 90{}^\circ \] ...(i) \[{{\tau }_{2}}=MB\sin 30{}^\circ \] ...(ii) Dividing Eq. (i) by Eq. i(ii), we get \[\frac{{{\tau }_{1}}}{{{\tau }_{2}}}=\frac{{{10}^{-5}}}{{{\tau }_{2}}}=\frac{1}{1/2}\] \[\Rightarrow \] \[{{\tau }_{2}}=\frac{{{10}^{-5}}}{2}\] \[=\frac{10}{2}\times {{10}^{-6}}\] \[=5\times {{10}^{-6}}Nm\]
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