Question

A bar magnet of magnetic moment $\overrightarrow{M}$ is placed in the magnetic field $\overrightarrow{B}$. The torque exerted on it is:
A. $\overrightarrow{M}.\overrightarrow{B}$
B. $-\overrightarrow{M}.\overrightarrow{B}$
C. $\overrightarrow{M}\times \overrightarrow{B}$
D. $-\overrightarrow{B}.\overrightarrow{M}$

Answer 1

Hint: A bar magnet produces a magnetic field of its own and the strength of the field depends upon the pole strength of the magnet. A bar magnet has two poles and monopoles cannot exist. A magnetic dipole can be understood as two equal and opposite magnetic poles separated by some distance. And for such a dipole there exists a magnetic dipole moment.

Complete answer:
The magnetic dipole moment can be defined as the product of the pole strength of either of the poles with the length of the bar magnet. Mathematically we can write as, $\overrightarrow{M}=\overrightarrow{m}\times 2\overrightarrow{l}$
It is a vector quantity.Also, if a magnetic dipole is placed in an external magnetic field making some angle with it, then experiences a torque which is given by,
$\therefore \overrightarrow{\tau }=\overrightarrow{M}\times \overrightarrow{B}$

So, the correct option is C.

Additional information:
A magnetic moment is a quantity that represents the magnetic strength and orientation of a magnet or any other object that produces a magnetic field. More precisely, a magnetic moment refers to a magnetic dipole moment, the component of the magnetic moment that can be represented by a magnetic dipole. A magnetic dipole is a magnetic north pole and a magnetic south pole separated by a small distance.

Magnetic dipole moments have dimensions of current times area or energy divided by magnetic flux density. The unit for dipole moment in meter–kilogram– second–ampere is ampere-square meter. The unit in centimeter–gram–second electromagnetic system, is the erg (unit of energy) per gauss (unit of magnetic flux density). One thousand ergs per gauss equal to one ampere-square meter.

Note: Since, magnetic dipole moment is given as the cross product of pole strength and the length, it is a vector quantity. Same goes for the torque which is given by the cross product too. Torque can be understood as the force which acts on the body and the body has the tendency to start rotating about some axis.Torque is also called as the moment of force.The moment of force is a measure of the ability of the force acting on a particular body to rotate it around a given axis.