MAGNETISM AND MATTER — Physics STD 12 Science — Question
Gujarat BoardEnglish MediumSTD 12 SciencePhysicsMAGNETISM AND MATTER2 Marks
Question
What is magnetisation ? Derive the relationship between magnetisation and magnetic intensity.
✓
Answer
$\rightarrow$ Magnetisation : "The net magnetic dipole moment per unit volume in a substance is called magnetisation."
$\rightarrow$Magnetisation $\overrightarrow{ M }=\frac{\vec{m}_{\text {nes }}}{V}$
$\rightarrow$Magnetisation is a vector quantity and its direction is taken in the direction of magnetic dipole moment.
$\rightarrow$Its unit is $\frac{ A }{m} \ ($or $A.m { }^{-1})$ and dimensional formula is $L ^{--^m} A^1$.
$\rightarrow$Consider a long solenoid of $n$ turns per unit length and carrying current $I$.
$\rightarrow$The magnetic field in the interior of the solenoid,
$B _0=\mu_0 n I$
$\rightarrow$If the interior of the solenoid is filled with a material having non $-$ zero magnetisation, magnetic field $\left( B _m\right)$ is generated due to this core material inside the solenoid.
Therefore, the net field in the interior of the solenoid is equal to the vector addition of both the magnetic fields.
$\therefore \vec{B}=\overrightarrow{B_0}+\overrightarrow{B_m}$
Where $\overrightarrow{ B }_m$ is the field contributed by magnetic core.
$\rightarrow$This additional field $\overrightarrow{ B _m}$ is proportional to the magnetisation $( \overrightarrow{ M })$ of the material.
$\therefore \overrightarrow{ B _m} \propto \overrightarrow{ M }$
$\therefore \overrightarrow{ B _m}=\mu_0 \overrightarrow{ M }$
$\rightarrow$Substituting the value of $\overrightarrow{ B _m}$ from eq. $(3)$ into eq. $(2),$
$\therefore \vec{B}=\vec{B}_0+\mu_0 \overrightarrow{ M }$
$\rightarrow$dividing the equation by $\mu_0,$
$\therefore \frac{\vec{B}}{\mu_0}=\frac{\overrightarrow{B_0}}{\mu_0}+\vec{M}$
but $\frac{\overrightarrow{B_0}}{\mu_0}=\overrightarrow{ H }-$ Which is a vector quantity called magnetic intensity.
$\therefore \frac{\vec{B}}{\mu_0}=\vec{H}+\vec{M}$
$\therefore \vec{B}=\mu_0(\vec{H}+\vec{M})$
$\rightarrow$Magnetic intensity $(\overrightarrow{ H })$ has same dimensions as $\overrightarrow{ M }$ and its unit is $\frac{ A }{m} \ ($or $A.m { }^{-1} )$.
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