Define the intensity of magnetic field.

$(a)$ 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?

A bar magnet having centre $O$ has a length of $4 $ $cm. $ Point $P_1$ is in the broad side-on and $P_2 $ is in the end side-on position with $OP_1 = OP_2 = 10$ metres. The ratio of magnetic intensities $H$ at $P_1$ and $P_2$ is

In which direction does a free hanging magnet get stabilized ? Explain.

Assertion : The poles of magnet can not be separated by breaking into two pieces.

Reason : The magnetic moment will be reduced to half when a magnet is broken into two equal pieces.

What is the magnitude of the equatorial and axial fields due to a bar magnet of length $5.0 \;cm$ at a distance of $50\; cm$ from its mid-point? The magnetic moment of the bar magnet is $0.40\; A m ^{2}$.