Question

Figure shows a small magnetised needle P placed at a point O. The arrow shows the direction of its magnetic moment. Te other arrows show different positions (and orientations of the magnetic moment) of another identical magnetised needle Q.
In which configuration the system is not in equilibrium ?

Answer 1

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) = -(mu_(0))/(4pi) (m_(P))/(r^(3))` (on the normal bisector)
`B_(P) = (mu_(0)2)/(4pi) (m_(P))/(r^(3))` (on the axis)
where `m_(P)` is the magnetic moment of the dipole P.
Equilibrium is stable whem `M_(Q)` 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,
`PQ_(1)` and `PQ_(2)`