Consider the situation shown in the diagram, where A small magnetised needle A is placed at a centre marked, as O. The direction of its mangetic moment I s indicated by arrow. The other arrow show different position (and orientations of the magnetic moment) of antoher identical magnetised eedle X.
In which configuration the system is not in equlibrium?
(ii) In which configuration is the system in (a) stable and (b) unsable equilibrium
(iii) Which configuration corresponds to the lowest potentials energy among all the configuration shown

Explanation

Potential energy arises due to the PE of dipole X in magnetic field of A.
Magnetic field due to A.
On end position, `B_(A)=(mu_(0))/(4pi).(2M)/(r^(3)),along M`
On broadside position, `B_(P)=(mu_(0))/(4pi).(M)/(r^(3)),"opposite to M" `
The PE, U=-M.B =-MB cos `theta`
For stable equilibrium, U is minium i.e. `theta=0`
For unstable equillibrium, U is maximum i.e. `theta=180^(@)`
(i) In `X_(1) and X_(2)` when not in equilibrium
(ii) (a) `X_(5), X_(6)` in stable equilibrium and (b) `X_(4),X_(3)` in unstable equilibrium.
(iii) `X_(6)` corresponds to lowest PE,
`" " U=-MB cos theta`
`" " =-M.(mu_(0))/(4pi)(2M)/(r^3) cos 0^(@)=-(mu_(0).2M^(2))/(4pir^(3))=U_(mn)`