physics-class-12-unit-05-chapter-03-magnetization-and-application-of-amperes-law-l-3-3-sqys08elvkw

### <Success style="font-size:25px"> Magnetization And Application Of Amperes Law L-3 </Success>
### <primary style="font-size:24px"> Magnetization </primary>
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- Magnetized material consists of a large number of tiny magnetic dipoles, and these magnetic dipoles then generate their own magnetic field.

- $\vec M$ : Magnetic dipole moment per unit volume.

- Equivalent to a surface current per unit length.

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<footer style = "font-size: 18px"> $\rightarrow$ Magnetization and Application of Ampere's law $\rightarrow$ <span style = "color:blue"> Magnetization </span> $\rightarrow$ Magnetic Moment $\rightarrow$ Ampere's Law </footer>

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- $ \oint \vec{B} \cdot \overrightarrow{d l}=\mu_0 I_{enc} $

- $ I_ {enc} = N I l + M l $

- $ \oint \vec{B} \cdot \overrightarrow{d l}=\mu_0 (N I l + M l) $

- $ \oint \vec{M} \cdot \vec{d l} = M l $

- $ \oint \frac{\vec{B}}{\mu_0} \cdot \vec{d l} = N I l+\oint \vec{M} \cdot \overrightarrow{d l}$

- N : Number of turns per unit length

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<footer style = "font-size: 18px">Magnetization and Application of Ampere's law $\rightarrow$ Magnetization $\rightarrow$ <span style = "color:blue"> Magnetic Moment </span> $\rightarrow$ Ampere's Law $\rightarrow$ Magnetic Susceptibility </footer>

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- $ \oint\left(\frac{\vec{B}}{\mu_0}-\vec{M}\right) \cdot \vec{d l}=N I l $

- $ \vec{H}=\frac{\vec{B}}{\mu_0}-\vec{M} $

- $ \oint \vec{H} \cdot \vec{d l} = N I l =I_{f,_{enc}} $

- $ I_{f._{enc}}$ = Free current enclosed by the loop

- $ \oint \vec{H} \cdot \vec{d l} = I_{f,_{enc}}$

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<footer style = "font-size: 18px">Magnetization $\rightarrow$ Magnetic Moment $\rightarrow$ <span style = "color:blue"> Ampere's Law </span> $\rightarrow$ Magnetic Susceptibility $\rightarrow$ Permeability </footer>

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### <primary style="font-size:24px"> Permeability </primary>
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- $\vec{H} =\frac{\vec{B}}{\mu_0}-\vec{M} $

- $\vec{B} =\mu_0(\vec{H}+\vec{M}) $

- $\vec{M} =\chi_m \vec{H}$

- $\vec{B} =\mu_0\left(1+\chi_m\right) \vec{H} =\mu {\vec{H}} $

- $\mu  =\mu_0\left(1+\chi_m\right)$

- $\mu_0$ : Permeability of free space

- $\mu$ : Permeability of the medium

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<footer style = "font-size: 18px">Ampere's Law $\rightarrow$ Magnetic Susceptibility $\rightarrow$ <span style = "color:blue"> Permeability </span> $\rightarrow$ Diamagnetic and Paramagnetic Material $\rightarrow$ Relative Permeability </footer>

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### <primary style="font-size:24px"> Diamagnetic and Paramagnetic Material </primary>
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- For diamagnetic and paramagnetic material, $\left|\chi_m\right| \lll 1 $

- $\mu \simeq \mu_0$

- Diamagnetic: $\chi_m<0 \Rightarrow \mu \leqslant \mu_0$

- Paramagnetic: $\chi_m>0 \Rightarrow \mu \geq \mu_0$

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<footer style = "font-size: 18px">Magnetic Susceptibility $\rightarrow$ Permeability $\rightarrow$ <span style = "color:blue"> Diamagnetic and Paramagnetic Material </span> $\rightarrow$ Relative Permeability $\rightarrow$ Diamagnetic Materials </footer>

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### <primary style="font-size:24px"> Diamagnetic Materials </primary>
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- $\chi_m$ For diamagnetic & paramagnetic materials

| Diamagnetic | $\chi_m$                | 
| --------    | --------                |
| Bismath     | -$16.4 \times 10^{-5}$  | 
| Copper      | -$0.9 \times 10^{-5}$   | 
| Diamond     | -$2.2 \times 10^{-5}$   | 
| Gold        | -$3.5 \times 10^{-5}$   | 
| Silver      | -$2.4 \times 10^{-5}$   | 
| Water       | -$0.9 \times 10^{-5}$   |

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<footer style = "font-size: 18px">Diamagnetic and Paramagnetic Material $\rightarrow$ Relative Permeability $\rightarrow$ <span style = "color:blue"> Diamagnetic Materials </span> $\rightarrow$ Paramagnetic Materials $\rightarrow$ Example </footer>

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| Paramagnetic | $\chi_m$                 | 
| --------     | --------                 |
| Aluminium    |  2.1 $\times 10^{-5}$    | 
| Platinum     | 2.6 $\times 10^{-5}$     | 
| Magnesium    | 1.2 $\times 10^{-5}$     | 
| Tungsten     | 6.8 $\times 10^{-5}$     | 
| Uranium      | 40 $\times 10^{-5}$      | 
| Oxygen       | 190 $\times 10^{-8}$     | 
| Sedolinium   |4.8 $\times 10^{-2}$      |

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<footer style = "font-size: 18px">Relative Permeability $\rightarrow$ Diamagnetic Materials $\rightarrow$ <span style = "color:blue"> Paramagnetic Materials </span> $\rightarrow$ Example $\rightarrow$ Magnetic Susceptibility </footer>

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### <primary style="font-size:24px"> Example </primary>
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- When you place a medium in a magnetic field, external magnetic field magnetizes the medium then generates its magnetic field and the total magnetic field gets altered because of magnetization.

- N : Number of turns per unit length

- I : Current through the wire

- $\oint \vec H. \vec {d l}$ = $I_ {f_{enc}}$

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<footer style = "font-size: 18px">Diamagnetic Materials $\rightarrow$ Paramagnetic Materials $\rightarrow$ <span style = "color:blue"> Example </span> $\rightarrow$ Magnetic Susceptibility $\rightarrow$ Magnetic Intensity </footer>

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### <primary style="font-size:24px"> Magnetic Susceptibility </primary>
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- $ \oint \vec{H} \cdot \overrightarrow{d L}=I_{f,_{enc}} $

- $ \vec{H}=\frac{\vec{B}}{\mu_0}-\vec{M} $

- $ \vec{B}=\mu_0\left(1+\chi_m\right) \vec{H}$

- **For path $C_1$**

- $ H \cdot l = N.I.l $

- $H = N I$ 
 
- $ \vec{H} = N I \hat{k}$

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<footer style = "font-size: 18px">Paramagnetic Materials $\rightarrow$ Example $\rightarrow$ <span style = "color:blue"> Magnetic Susceptibility </span> $\rightarrow$ Magnetic Intensity $\rightarrow$ Relationship between Permeability and Magnetic Susceptibility </footer>

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- **For path $C_2$**

- $ \oint \vec{H} \cdot \overrightarrow{d \ell}=I_{f,_{enc}} $

- $ H^{\prime} \ell=N I \ell $

- $\Rightarrow \quad  H^{\prime}=N I $

- $ \overrightarrow{H^{\prime}}=N I \hat{k}=\vec{H}$

- $\vec{H}=N I \hat{k}$ Everywhere within the solenoid.

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<footer style = "font-size: 18px">Example $\rightarrow$ Magnetic Susceptibility $\rightarrow$ <span style = "color:blue"> Magnetic Intensity </span> $\rightarrow$ Relationship between Permeability and Magnetic Susceptibility $\rightarrow$ Magnetic Moment </footer>

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### <primary style="font-size:24px"> Relationship between Permeability and Magnetic Susceptibility </primary>
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- $\vec{B}=\mu_0\left(1+\chi_m\right) \vec{H}$

- **Reason I**

- ${\chi_m}=0 $

- $ \vec{B}=\mu_0 \vec{H}  =\mu_0 N I \hat{k}$

- **Reason II**

- $\vec{B} =\mu_0\left(1+\chi_m\right) \vec{H} $

- $ =\mu_0\left(1+\chi_m\right) N I \widehat{k}  =\mu N I \hat k$

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<footer style = "font-size: 18px">Magnetic Susceptibility $\rightarrow$ Magnetic Intensity $\rightarrow$ <span style = "color:blue"> Relationship between Permeability and Magnetic Susceptibility </span> $\rightarrow$ Magnetic Moment $\rightarrow$ Coil Paramagnetic </footer>

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- $\vec M = \chi_m \vec H$

- = $\chi_m N I \hat k$

- Diamagnetic core

- Paramagnetic core

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<footer style = "font-size: 18px">Magnetic Intensity $\rightarrow$ Relationship between Permeability and Magnetic Susceptibility $\rightarrow$ <span style = "color:blue"> Magnetic Moment </span> $\rightarrow$ Coil Paramagnetic $\rightarrow$ Primary Class of Magnetic Materials </footer>

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### <primary style="font-size:24px"> Coil Paramagnetic </primary>
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- In a diamagnetic materials magnetization is downward, because of bound  carrying conductor and so the magnetic field inside the material is slightly less than the magnetic field outside.

- In paramagnetic materials the magnetization has the same direction and hence produces the magnetic field in the same direction as the coil.

- The magnetic field inside the paramagnetic material is slightly more than the magnetic field outside.

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<footer style = "font-size: 18px">Relationship between Permeability and Magnetic Susceptibility $\rightarrow$ Magnetic Moment $\rightarrow$ <span style = "color:blue"> Coil Paramagnetic </span> $\rightarrow$ Primary Class of Magnetic Materials $\rightarrow$ Diamagnetic Materials </footer>

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### <primary style="font-size:24px"> Diamagnetic Materials </primary>
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- No intrensic dipole moment of constituent atoms.

- Dipoles induceds by the external magnetic field.

- Induced dipoles directent opposite to external applied magnetic field.

- Magnetization disappears when the external field is removed.

- Pushed from region of high field to smaller magnetic field in an inhomogenous field.

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<footer style = "font-size: 18px">Coil Paramagnetic $\rightarrow$ Primary Class of Magnetic Materials $\rightarrow$ <span style = "color:blue"> Diamagnetic Materials </span> $\rightarrow$ Thank You $\rightarrow$  </footer>