Two short magnets with their axes horizontal and perpendicular to the magnetic meridian are placed with their centres $40\, cm$  east and $ 50\,cm$  west of magnetic needle. If the needle remains undeflected, the ratio of their magnetic moments ${M_1}:{M_2}$ is

$(a)$ 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 $B$.]

Two identical bar magnets are held perpendicular to each other with a certain separation, as shown below. The area around the magnets is divided into four zones. Given that there is a neutral point it is located in

Two short bar magnets oflength $1\ cm$ each have magnetic moments $1.20\ Am^2$ and $1.00\ Am^2$ respectively. They are placed on a horizontal table parallel to each other with their $N$ poles pointing towards the South. They have a common magnetic equator and are separated by a distance of $20.0\ cm$. The value of the resultand horizontal magnetic induction at the mid-point $O$ of the line joining their centres is close to  (Horizontal component of earth.s magnetic induction is $3.6 \times  10^{-5}$ $Wbm^{-2}$  )

Two identical bar magnets are fixed with their centres at a distance $d$ apart. A stationary charge $Q$ is placed at $P$ in between the gap of the two magnets at a distance $D$ from the center $O$ as shown in the figure. The force on the charge $Q$ is