Force between two unit pole strength placed at a distance of one metre is

Two magnetic lines intersect ? Why ?

$(a)$ What happens if a bar magnet is cut into two pieces: $(i)$ transverse to its length, $(ii)$ along its length?

$(b)$ A magnetised needle in a uniform magnetic field experiences a torque but no net force. An iron nail near a bar magnet, however, experiences a force of attraction in addition to a torque. Why?

$(c)$ Must every magnetic configuration have a north pole and a south pole? What about the field due to a toroid?

$(d)$ Two identical looking iron bars $A$ and $B$ are given, one of which is definitely known to be magnetised. (We do not know which one.) How would one ascertain whether or not both are magnetised? If only one is magnetised, how does one ascertain which one? [Use nothing else but the bars $A$ and $B$.]

Magnetic field intensity is defined as

The magnetic field due to a short magnet at a point on its axis at distance $X \,cm $ from the middle point of the magnet is $200 $ $Gauss$. The magnetic field at a point on the neutral axis at a distance $ X \,cm$  from the middle of the magnet is.....$Gauss$

The magnetic potential due to a magnetic dipole at a point on its axis situated at a distance of $20 \mathrm{~cm}$ from its center is $1.5 \times 10^{-5} \  \mathrm{Tm}$. The magnetic moment of the dipole is___________ $\mathrm{Am}^2$. (Given : $\frac{\mu_0}{4 \pi}=10^{-7} \  \mathrm{TmA}^{-1}$ )