Question

A bar magnet of magnetic moment $M$ is placed in the magnetic field $B$. The torque acting on the magnet will be:
\[\begin{align}
  & A.M\times B \\
 & B.M-B \\
 & C.\dfrac{1}{2}M\times B \\
 & D.M+B \\
\end{align}\]

Answer 1

Hint: Here the torque acting is to be found which is equivalent to the moment of deflecting a couple. First of all write the basic equation of torque experienced. And then substitute the force experienced with
\[F=iBl\]
And also the perpendicular distance should be substituted by the equation,
\[d=b\sin \theta \].
Find out the relation between the magnetic moment as well as the magnetic field with the torque and arrive at the answer.

Complete answer:
Here we can see that the torque acting is to be found which is equivalent to the moment of deflecting a couple. Therefore the torque acting is given by the equation,

$\tau =force\times d$
Where force is given as,
$F={{F}_{1}}={{F}_{2}}$
And also $d$ is the perpendicular distance of travel.
As we know that the force acting is given by the formula,
$F=iBl$
Where $i$ be the current,$B$ is the magnetic field acting and $l$ is the length.
And also
$d=b\sin \theta $
Where $\theta $ is the angle and $b$ is the distance. Substituting this in the equation of torque,
$\tau =iBl\times b\sin \theta $
We know that the magnetic moment is given by the equation,
$M=ibl$
Substitute this in that equation will give,
$\tau =MBsin\theta $
This can be written in the form of the cross product,
$\tau =M\times B$

So, the correct answer is “Option A”.

Note:
The magnetic moment is given as a determination of a substance’s urge to be arranged in a magnetic field. Magnetic moments can be explained as the magnetic strength and orientation of a magnet or any other substance that creates a magnetic field. The magnetic moment abbreviated as $M$ is a vector quantity which helps to calculate the tendency of a body to interact with an external magnetic field. It is commonly used in NMR technology.