Two identical bar magnets with a length $10 \,cm $ and weight $50 \,gm$-weight are arranged freely with their like poles facing in a inverted vertical glass tube. The upper magnet hangs in the air above the lower one so that the distance between the nearest pole of the magnet is $3\,mm.$ Pole strength of the poles of each magnet will be…….$ amp × m$

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 $3.6 \times  10^{-5}$ $Wbm^{-2}$  )

A short bar magnet with its north pole facing north forms a neutral point at $P$ in the horizontal plane. If the magnet is rotated by $90^o$ in the horizontal plane, the net magnetic induction at $P$ is (Horizontal component of earth’s magnetic field = ${B_H}$)

A short bar magnet of magnetic movement $5.25 \times 10^{-2} \;J\, T ^{-1}$ is placed with its axis perpendicular to the earth's field direction. At what distance from the centre of the magnet, the resultant field is inclined at $45^{\circ}$ with earth's field on

$(a)$ its normal bisector and

$(b)$ its axis.

Magnitude of the earth's field at the place is given to be $0.42 \;G$. Ignore the length of the magnet in comparison to the distances involved.

When the $N-$pole of a bar magnet points towards the south and $S-$pole towards the north, the null points are at the