CBSE 2023 · Region 4 · Set 1 · Q21 · 2 marks
A small magnetised needle $\displaystyle P$ is placed at the origin of $\displaystyle x-y$ plane with its magnetic moment pointing along the y -axis. Another identical magnetised needle $\displaystyle Q$ is placed in two positions, one by one. Case $\displaystyle 1$: at (a, $\displaystyle 0$) with its magnetic moment pointing along x -axis. Case $\displaystyle 2$ : at ( $\displaystyle 0, \mathrm{a}$ ) with its magnetic moment pointing along y -axis.(a)In which case is the potential energy of P and Q minimum ?(b)In which case is P and Q not in equilibrium ? Justify your answers.
A small magnetised needle $\displaystyle P$ is placed at the origin of $\displaystyle x-y$ plane with its magnetic moment pointing along the y -axis. Another identical magnetised needle $\displaystyle Q$ is placed in two positions, one by one. Case $\displaystyle 1$: at (a, $\displaystyle 0$) with its magnetic moment pointing along x -axis. Case $\displaystyle 2$ : at ( $\displaystyle 0, \mathrm{a}$ ) with its magnetic moment pointing along y -axis.
(a)
In which case is the potential energy of P and Q minimum ?
(b)
In which case is P and Q not in equilibrium ? Justify your answers.
Marking-scheme solution
(a) Potential energy is minimum in case $\displaystyle 2$, since Q is placed along the direction of P / stable equilibrium.
(b) P and Q are not in equilibrium in case 1. In this case Q is at the normal bisector of P /not in equilibrium.
Alternatively:(a) Since \(\displaystyle \mathrm{U}=-\mathrm{MB} \cos \theta\) and \(\displaystyle \theta=0^{\circ}\) so P.E. is minimum.
(b) Case $\displaystyle 1$, not in equilibrium, since \(\displaystyle \tau=\mathrm{MB} \sin \theta\) and \(\displaystyle \theta=90^{\circ}, \tau=\mathrm{MB}\). OR
(b) Since two needles are perpendicular they experience torque.
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CBSE Class 12 Physics past-paper question from the 2023board exam, with the answer as CBSE’s own marking scheme gives it. Where our answers come from.