Question

A bar magnet is cut into two equal halves by a plane parallel to the magnetic axis. From the given following physical quantities, which remains unchanged is

• A. pole strength
• B. magnetic moment
• C. intensity of magnetisation
• D. moment of inertia

Answer 1

The correct option is C intensity of magnetisation

$\text{Pole strength:}$

If $A$ is the cross-sectional area, $m$ is the pole strength and $l_{ef}$ is the magnetic length, then cutting along the axial line changes pole strength by $\frac{m}{2}$ and area as well to $\frac{A}{2}$.


$\text{Magnetic Moment:}$

The initial magnetic moment is given by, $M_i=m{l}_{ef}$

Final magnetic moment, $M_f=\frac{m{l}_{ef}}{2}$

$\Rightarrow M_f=\frac{M_i}{2}$

$\text{Intensity of magnetization:}$

It is a property which depends on the nature of the material and is given by formula,

$I=\frac{M}{V}$

Here, magnetic moment, $M\to \frac{M}{2}$ and volume, $V\to \frac{V}{2}$

$\therefore I_i=I_f$

$\text{Moment of inertia:}$

The moment of inertia is given by,

$\text{M.O.I=mass}\times K^2$

Here, on cutting the magnet, mass as well as radius of gyration $K$ are changing. Thus, moment of inertial will also change.

Hence, option $\left(C\right)$ is correct.