Question

Relation between magnetic moment and angular velocity is
a) $M\propto \omega$
b) $M\propto {\omega }^2$
c) $M\propto \sqrt{\omega }$
d) None of the above

Answer 1

Hint:
Let us find the formula for the magnetic moment of any material. Magnetic moment is the product of the current passing through the material and the area of the material. As current is charge per unit time, and the time is related to angular velocity, we can relate the magnetic moment and the angular velocity.
Formula used:
$M=IA$

Complete answer:
let us find the formula of magnetic moment of a material,
$M=IA$
The current in the above formula is equal to,
$\begin{array}{rl}& I={\displaystyle \frac{q}{t}}\\ & \Rightarrow t={\displaystyle \frac{2\pi }{\omega }}\end{array}$
As we know the time period and the area,
$M=IA$
$M={\displaystyle \frac{q\omega A}{2}}$
$M\propto \omega$
So, the correct answer is “Option A”.

Additional Information:
The magnetic moment is a determination of its tendency to get arranged through a magnetic field. As we know every magnet will have two poles, south pole and the north pole, the magnetic moment can also be defined as the magnetic strength and orientation of a magnet or other object that produces a magnetic field. Many examples like permanent magnets, astronomical objects, loops of electric current, various molecules and elementary particles have magnetic moments. Magnetic moment is a vector quantity and it relates the torque of an object to the magnetic field. Magnetic moment is the product of current flowing through it and the area of the material.

Note:
Magnetic moment describes both magnitude and direction. It is a vector quantity. All metals don’t get attracted to magnets. Many of us think silver coloured objects get attracted to magnets, its false. Magnets can be made of many materials, not only iron. Magnetic strength depends on the size of the magnets.