Question

Under what conditions, a magnet suspended in a uniform magnetic field will be in
i) Stable equilibrium and
ii) Unstable equilibrium

Answer 1

A magnet is metal that can produce a magnetic field. A magnet has two different poles, namely the North and the South Pole on two sides of the metal. These metals show a special property called the magnetic effect.
Formula used:
$\tau= MB sin(\theta)$ and $U=-MB cos(\theta)$

Complete answer:
We know that the magnetic field is an invisible force which is a vector that influences an electric charge and a few magnetic metals. Since it’s a vector clearly, it has both direction and magnitude. A magnet has two different poles, namely the North and the South Pole. Generally, the like poles attract, while the unlike poles repel. This is saying that, North Pole of one magnet repels from the north pole of another magnet, this is true for two South Pole also. However, if a North Pole of one magnet is brought near the south pole of another magnet, then they attract.
Let $M$ be the magnetic moment, making an angle $\theta$ with the axis. Then the magnetic field experienced by the magnet $B$ is given as $\tau= MB sin(\theta)$ and potential energy is given as $U=-MB cos(\theta)$
i) The magnet is said to be stable if the $\tau=0$ and $U$ is minimum. This occurs when the magnetic moment is parallel to the magnetic field, i.e. $\theta=0$
ii) The magnet is said to be unstable if the $\tau=0$ and $U$ is maximum. This occurs when the magnetic moment is acts in the opposite direction as to the magnetic field, i.e. $\theta=180$

Note:
There are two types of magnets on the basis of their magnetic strength namely the permanent and the temporary magnets. A permanent magnet produces a strong magnetic field always, whereas the magnetic field produced by a temporary magnet is short spanned and weak.