Magnetisation & Magnetic Intensity 📘
1 ⭐ Magnetisation (M)
Every bit of matter contains tiny current loops (mostly orbiting electrons) that act like little magnets. When we add them all up inside a chunk of material, we get its magnetisation:
\[
M=\frac{m_{\text{net}}}{V}\tag{5.7}
\]
Here \(m_{\text{net}}\) is the net magnetic moment and \(V\) is the volume. \(M\) points in a specific direction and is measured in amperes per metre (A m−1). 😊 :contentReference[oaicite:0]{index=0}
2 🔌 Field inside a long solenoid
- Without any material core, the field is \[ B_0=\mu_0 n I \tag{5.8} \] where \(n\) = turns per metre and \(I\) = current.
- Put a magnetised material inside and the field grows: \[ B=B_0+B_m \tag{5.9} \] with the extra piece \[ B_m=\mu_0 M \tag{5.10} \]
More magnetisation ⇒ stronger total field! :contentReference[oaicite:1]{index=1}
3 💡 Magnetic Intensity (H)
We split the total field into an “external” part and the material’s own response by defining \[ \mathbf H=\frac{\mathbf B}{\mu_0}-\mathbf M \tag{5.11} \] so that \[ \mathbf B=\mu_0(\mathbf H+\mathbf M). \tag{5.12} \] Both \(H\) and \(M\) share the same units (A m−1). :contentReference[oaicite:2]{index=2}
4 🧲 Susceptibility & Permeability
External field tries to “align” the tiny magnets, giving the rule \[ M=\chi\,H \tag{5.13} \] where magnetic susceptibility \(\chi\) tells us how easily the material gets magnetised.
- If \(\chi\) > 0 but small ⇒ paramagnetic
- If \(\chi\) < 0 ⇒ diamagnetic
Plugging \(M=\chi H\) into \(B=\mu_0(H+M)\) gives
\[ B=\mu_0(1+\chi)H=\mu_0\mu_r H=\mu H,\tag{5.14–5.15} \]where
\[ \mu_r=1+\chi,\qquad \mu=\mu_0\mu_r. \]So knowing any one of \(\chi,\;\mu_r,\;\mu\) lets you find the other two. 👌 :contentReference[oaicite:3]{index=3}
5 📏 Worked Example (quick numbers)
Solenoid core with \(\mu_r=400\), 1000 turns m−1, current \(I=2\) A:
| Quantity | Answer |
|---|---|
| \(H = nI\) | \(2\times10^{3}\,\text{A m}^{-1}\) |
| \(B=\mu_r\mu_0H\) | \(1.0\;\text{T}\) |
| \(M=(\mu_r-1)H\) | \(\approx8\times10^{5}\,\text{A m}^{-1}\) |
| Magnetising current \(I_M\) | \(7.94\times10^{2}\,\text{A}\) |
Notice how a high-\(\mu_r\) material makes the same coil much stronger! 💥 :contentReference[oaicite:4]{index=4}
6 🏷️ Quick Classification of Materials
| Diamagnetic | Paramagnetic | Ferromagnetic | |
|---|---|---|---|
| \(\chi\) | −1 ≤ χ < 0 | 0 < χ < ε | χ ≫ 1 |
| \(\mu_r\) | 0 ≤ \(\mu_r\)< 1 | 1 < \(\mu_r\)< 1+ε | \(\mu_r\) ≫ 1 |
- Diamagnets drift toward weaker field regions – think of them as gently repelled. :contentReference[oaicite:5]{index=5}
- Paramagnets (small \(χ>0\)) lean toward stronger field, but only a little.
- Ferromagnets (huge \(χ\)) are the “strong” magnets you stick on the fridge.
7 🌟 High-Yield NEET Nuggets
- Definition alert: \(M=\dfrac{m_{\text{net}}}{V}\) – memorize it! :contentReference[oaicite:6]{index=6}
- Core booster: Extra field inside a solenoid is \(B_m=\mu_0 M\). :contentReference[oaicite:7]{index=7}
- Relation trio: \(M\), \(H\), and \(B\) connect via \(B=\mu_0(H+M)\). :contentReference[oaicite:8]{index=8}
- Shortcut: \(\mu_r=1+\chi\) – turns susceptibility into permeability at once. :contentReference[oaicite:9]{index=9}
- Material ID: Sign & size of \(χ\) instantly tells you dia/para/ferro. :contentReference[oaicite:10]{index=10}
Keep these ideas handy, and magnetic questions will feel like attraction at first sight 😉
