$(a)$ 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 of length $10 \,cm$  and having the pole strength equal to $10^{-3}$ weber is kept in a magnetic field having magnetic induction $ (B)$  equal to $4\pi \times {10^{ – 3}}$ Tesla. It makes an angle of $30°$  with the direction of magnetic induction. The value of the torque acting on the magnet is

Which statement is correct 

Points $A$ and $B$ are situated perpendicular to the axis of a $2\,cm$  long bar magnet at large distances $X$ and $3X$  from its centre on opposite sides. The ratio of the magnetic fields at $ A$ and $B$  will be approximately equal to

The distance between the poles of a horse shoe magnet is $0.1\, m$ and its pole strength is $0.01\, amp-m$. The induction of magnetic field at a point midway between the poles will be