Figure shows a small magnetised needle $P$ placed at a point $O$. The arrow shows the direction of its magnetic moment. The other arrows show different positions (and orientations of the magnetic moment) of another identical magnetised needle $Q$.
$(a)$ In which configuration the system is not in equilibrium?
$(b)$ In which configuration is the system in $(i)$ stable, and $(ii)$ unstable equilibrium?
$(c)$ Which configuration corresponds to the lowest potential energy among all the configurations shown?
Figure shows a small magnetised needle $P$ placed at a point $O$. The arrow shows the direction of its magnetic moment. The other arrows show different positions (and orientations of the magnetic moment) of another identical magnetised needle $Q$.
$(a)$ In which configuration the system is not in equilibrium?
$(b)$ In which configuration is the system in $(i)$ stable, and $(ii)$ unstable equilibrium?
$(c)$ Which configuration corresponds to the lowest potential energy among all the configurations shown?
Potential energy of the configuration arises due to the potential energy of one dipole (say, $Q$ ) in the magnetic field due to other (P). Use the result that the field due to $P$ is given by the expression
$B _{ p }=-\frac{\mu_{0}}{4 \pi} \frac{ m _{ P }}{r^{3}}$
(on the normal bisector)
$B _{ p }=\frac{\mu_{0} 2}{4 \pi} \frac{ m _{ p }}{r^{3}}$ (on the axis)
where $m _{ p }$ is the magnetic moment of the dipole $P$. Equilibrium is stable when $m _{ 9 }$ is parallel to $B _{ p },$ and unstable when it is anti-parallel to $B _{ p }$ For instance for the configuration $Q _{3}$ for which $Q$ is along the perpendicular bisector of the dipole $P$, the magnetic moment of $Q$ is parallel to the magnetic field at the position $3 .$ Hence $Q _{3}$ is stable. Thus,
$(a)$ $PQ _{1}$ and $PQ _{2}$
$(b)$ (i) $PQ _{3}, PQ _{6}$ (stable); (ii) $PQ _{5}, PQ _{4}$ (unstable)
$(c)$ $PQ _{6}$
Similar Questions
Two identical bar magnets are held perpendicular to each other with a certain separation, as shown below. The area around the magnets is divided into four zones. Given that there is a neutral point it is located in
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- [KVPY 2014]
The small magnets each of magnetic moment $10 \,A-m^2$ are placed end-on position $0.1\,m$ apart from their centres. The force acting between them is....$N$
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$(a)$ Magnetic field lines show the direction (at every point) along which a small magnetised needle aligns (at the point). Do the magnetic field lines also represent the lines of force on a moving charged particle at every point?
$(b)$ Magnetic field lines can be entirely confined within the core of a toroid, but not within a straight solenoid. Why?
$(c)$ If magnetic monopoles existed, how would the Gauss’s law of magnetism be modified?
$(d)$ Does a bar magnet exert a torque on itself due to its own field? Does one element of a current-carrying wire exert a force on another element of the same wire?
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$(a)$ Magnetic field lines show the direction (at every point) along which a small magnetised needle aligns (at the point). Do the magnetic field lines also represent the lines of force on a moving charged particle at every point?
$(b)$ Magnetic field lines can be entirely confined within the core of a toroid, but not within a straight solenoid. Why?
$(c)$ If magnetic monopoles existed, how would the Gauss’s law of magnetism be modified?
$(d)$ Does a bar magnet exert a torque on itself due to its own field? Does one element of a current-carrying wire exert a force on another element of the same wire?
$(e)$ Magnetic field arises due to charges in motion. Can a system have magnetic moments even though its net charge is zero?
The diagram shows magnetic field lines. We move from above to below and back.Below shows the graph of variaton of magnetic flux with time. We will measure the flux of
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