Question

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. In which configuration the system is in stable equilibrium?

Answer 1

In this question we will use the relation between magnetic moment, magnetic field and the angle, by observing the diagram we will get the required result. Further, we will discuss the basics of magnetic field and rules to find the magnetic field direction.

Formula used:
$\tau = MB\sin \theta$

Complete step-by-step answer:
Here, first we have to check direction of magnetic field due to P at all points and then check the angle between magnetic moments and direction of magnetic field.
We have
$\tau = MB\sin \theta$
For a stable equilibrium,
$\theta = 0$
Putting this value of the angle, in the above equation, we get:
$\tau = 0$
Therefore, when we observe from the diagram, $P{Q_3}$and $P{Q_6}$ are the two configurations, which will give us the stable equilibrium.

Additional Information: A magnetic field B can be defined as a vector field that tells the magnetic influence on moving electric charges, electric currents, and magnetized materials. Also, we should know that a charge that is moving in a magnetic field experiences a force that is perpendicular o its town velocity and to the magnetic field.
We know that Fleming's left-hand rule gives the direction of magnetic force acting on a conductor whereas; Fleming’s right-hand rule gives us the direction of induced current.
Fleming’s right-hand rule can be understood as: from this rule, if we Stretch the thumb, forefinger and middle finger of our right hand such that they are mutually perpendicular to each other

. Here, if the forefinger point indicates the direction of the magnetic field and the thumb indicates the direction of motion of the conductor, then the middle finger will indicate the direction of induced current in the conductor.
Fleming’s left-hand rule: from this rule if we Stretch our thumb, forefinger and middle finger of the left hand such that all these fingers are mutually perpendicular to each other.

So, if the forefinger points in the direction of the magnetic field and the middle finger indicates the direction of the current, then the thumb will indicate the direction of motion or the force on the conductor.

Note: Do remember the rules because both the rules tell the different fields. Further, we need to notice the direction of the magnetic field i.e., whether the field is inward or outward. All the three fingers should be placed perpendicular to each other.