The relative magnetic permeability of a magnetic material is 800. Identify the nature of magnetic material and state its two properties.

Two identical bar magnets $P$ and $Q$ are placed in two identical uniform magnetic fields as shown in Figure. Justify that both the magnets are in equilibrium. Which one of these is in stable equilibrium? Give reasons for your answer.

A small magnet of magnetic moment $M$, is placed at a distance $r$ from the origin $O$ with its axis parallel to $x$-axis as shown in Figure. A small coil, of one turn, is
placed on the $x$-axis, at the same distance from the origin, with the axis of the coil coinciding with $x$-axis. For what value of current in the coil does a small magnetic needle, kept at origin, remains undeflected? What is the direction of current in the coil?

Two identical short magnets $a$ and $b$ of magnetic moments $m$ each are placed at a distance $d$ with their axes perpendicular to each other, as shown in Figure. Find the magnetic field at a point $P$ midway between the two dipoles.

Two magnets of magnetic moments $M$ and $M\sqrt{3}$ are joined to form a cross. The combination is suspended in a uniform magnetic field $B$. The magnetic moment $M$ now makes an angle $\theta$ with the field direction. Find the value of angle $\theta$.