Question
What is magnetisation ? Derive the relationship between magnetisation and magnetic intensity.
✓
Answer
→Magnetisation : "The net magnetic dipole moment per unit volume in a substance is called magnetisation."
→Magnetisation $\overrightarrow{ M }=\frac{\vec{m}_{\text {nes }}}{V}$
→Magnetisation is a vector quantity and its direction is taken in the direction of magnetic dipole moment.
→Its unit is $\frac{ A }{m}$ (or A.m ${ }^{-1}$ ) and dimensional formula is $L ^{--^m} A^1$.
→Consider a long solenoid of $n$ turns per unit length and carrying current I.
→The magnetic field in the interior of the solenoid,
$B _0=\mu_0 n I$
→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.
→This additional field $\overrightarrow{ B _m}$ is proportional to the magnetisation ( $\overrightarrow{ M }$ ) of the material.
$\begin{array}{l}
\therefore \overrightarrow{ B _m} \propto \overrightarrow{ M } \\
\therefore \overrightarrow{ B _m}=\mu_0 \overrightarrow{ M }
\end{array}$
→Substituting the value of $\overrightarrow{ B _m}$ from eq. (3) into eq. (2),
$\therefore \quad \vec{B}=\vec{B}_0+\mu_0 \overrightarrow{ M }$
→dividing the equation by $\mu_0$,
$\therefore \quad \frac{\vec{B}}{\mu_0}=\frac{\overrightarrow{B_0}}{\mu_0}+\vec{M}\\
but \frac{\overrightarrow{B_0}}{\mu_0}=\overrightarrow{ H }-$ Which is a vector quantity called magnetic intensity.$
\begin{array}{l}
\therefore \frac{\vec{B}}{\mu_0}=\vec{H}+\vec{M} \\
\therefore \vec{B}=\mu_0(\vec{H}+\vec{M})
\end{array}$
→Magnetic intensity $(\overrightarrow{ H })$ has same dimensions as $\overrightarrow{ M }$ and its unit is $\frac{ A }{m}$ (or A.m ${ }^{-1}$ ).
→Magnetisation $\overrightarrow{ M }=\frac{\vec{m}_{\text {nes }}}{V}$
→Magnetisation is a vector quantity and its direction is taken in the direction of magnetic dipole moment.
→Its unit is $\frac{ A }{m}$ (or A.m ${ }^{-1}$ ) and dimensional formula is $L ^{--^m} A^1$.
→Consider a long solenoid of $n$ turns per unit length and carrying current I.
→The magnetic field in the interior of the solenoid,
$B _0=\mu_0 n I$
→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.
→This additional field $\overrightarrow{ B _m}$ is proportional to the magnetisation ( $\overrightarrow{ M }$ ) of the material.
$\begin{array}{l}
\therefore \overrightarrow{ B _m} \propto \overrightarrow{ M } \\
\therefore \overrightarrow{ B _m}=\mu_0 \overrightarrow{ M }
\end{array}$
→Substituting the value of $\overrightarrow{ B _m}$ from eq. (3) into eq. (2),
$\therefore \quad \vec{B}=\vec{B}_0+\mu_0 \overrightarrow{ M }$
→dividing the equation by $\mu_0$,
$\therefore \quad \frac{\vec{B}}{\mu_0}=\frac{\overrightarrow{B_0}}{\mu_0}+\vec{M}\\
but \frac{\overrightarrow{B_0}}{\mu_0}=\overrightarrow{ H }-$ Which is a vector quantity called magnetic intensity.$
\begin{array}{l}
\therefore \frac{\vec{B}}{\mu_0}=\vec{H}+\vec{M} \\
\therefore \vec{B}=\mu_0(\vec{H}+\vec{M})
\end{array}$
→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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