physics-class-12-unit-05-chapter-02-magnetization-magnetism-and-matter-l-2-3-3104jb0g2ng

### <Success style="font-size:25px"> Magnetization Magnetism And Matter L-2 </Success>
### <primary style="font-size:24px"> Magnetic Field due to Dipole Moments </primary>
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- Magnetic dipole having a magnetic moment m.

- $\vec{m}=I \vec{A}$

- Magnetic fields due to a dipoles, for field along axis.

- $\vec{B}=\frac{\mu_0 \vec{m}}{2 k x^2}$  ; $\quad x \gg R $

- Field in the plane

- $\vec{B}=-\frac{\mu_0 \vec{m}}{4 \pi x^2} ; \quad x \gg c $

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<footer style = "font-size: 18px"> $\rightarrow$ Magnetization Magnetism and Matter $\rightarrow$ <span style = "color:blue"> Magnetic Field due to Dipole Moments </span> $\rightarrow$ Torque on a Dipole $\rightarrow$ Example </footer>

### <Success style="font-size:25px"> Magnetization Magnetism And Matter L-2 </Success>
### <primary style="font-size:24px"> Torque on a Dipole </primary>
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- Torque on a dipole due to an external magnetic field B.

- $\vec \tau = \vec m \times \vec B$

- Potential energy of the dipole in an external field

- U = - $\vec m . \vec B$

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<footer style = "font-size: 18px">Magnetization Magnetism and Matter $\rightarrow$ Magnetic Field due to Dipole Moments $\rightarrow$ <span style = "color:blue"> Torque on a Dipole </span> $\rightarrow$ Example $\rightarrow$ Torque on the Loop </footer>

### <Success style="font-size:25px"> Magnetization Magnetism And Matter L-2 </Success>
### <primary style="font-size:24px"> Example </primary>
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- Radius  $R=5 \mathrm{cm}$

- Current $I=5 \mathrm{A}$

- Magnetic field  $B=0.1 \mathrm{K}$

-  Magnetic moment

- $\vec{m}  =I \vec{A} $

- $ =I \cdot \pi R^2 \hat{k} $

- $ =5 \times \pi \times 25 \times 10^{-4} \hat{k}$

- $ =1.25 \pi \times 10^{-2} \hat{k} A \cdot m^2$

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<footer style = "font-size: 18px">Magnetic Field due to Dipole Moments $\rightarrow$ Torque on a Dipole $\rightarrow$ <span style = "color:blue"> Example </span> $\rightarrow$ Torque on the Loop $\rightarrow$ Potential Energy Change </footer>

### <Success style="font-size:25px"> Magnetization Magnetism And Matter L-2 </Success>
### <primary style="font-size:24px"> Potential Energy Change </primary>
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- Initial P E = 0

- Final P E  =-$\vec{m} \cdot \vec{B}$

- =-m B

- $ =-1.25 \pi \times 10^{-1} \mathrm{J}$

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<footer style = "font-size: 18px">Example $\rightarrow$ Torque on the Loop $\rightarrow$ <span style = "color:blue"> Potential Energy Change </span> $\rightarrow$ Magnetization $\rightarrow$ Magnetic Moment of Atom </footer>

### <Success style="font-size:25px"> Magnetization Magnetism And Matter L-2 </Success>
### <primary style="font-size:24px"> Magnetic Moment of Atom </primary>
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- The model which was proposed by Niels Bohr in 1911.

- Velocity of electron $=v$

- Radius of the orbit  $=R$

- Time taken for one resolution of the electron T = $\frac {2\pi R }{v}$

- Number of revolution per unit time  =$\frac{1}{T}=\frac{v}{2 \pi R}$

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<footer style = "font-size: 18px">Potential Energy Change $\rightarrow$ Magnetization $\rightarrow$ <span style = "color:blue"> Magnetic Moment of Atom </span> $\rightarrow$ Magnetic Dipole Moment $\rightarrow$ Angular Momentum </footer>

### <Success style="font-size:25px"> Magnetization Magnetism And Matter L-2 </Success>
### <primary style="font-size:24px"> Bohr Magnetron </primary>
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- Unit of magnetic dipole moments

- $ m=\frac{e}{2 m_e} \cdot \frac{h}{2 \pi} $

- $=\frac{e h}{4 \pi m_e}$  Bohr magnetron

- $ m_{B} \approx 9.274 \times 10^{-24} \text { A.} m^2$

- We can associate with the orbital motion of the electron in an atom with an orbital dipole moment, which is represented by the Bohr magnetron.

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<footer style = "font-size: 18px">Magnetic Dipole Moment $\rightarrow$ Angular Momentum $\rightarrow$ <span style = "color:blue"> Bohr Magnetron </span> $\rightarrow$ Spin $\rightarrow$ Physical Picture of a Uniform Magnetic Medium </footer>

### <Success style="font-size:25px"> Magnetization Magnetism And Matter L-2 </Success>
### <primary style="font-size:24px"> Magnetic Dipole Moment </primary>
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- Cylindrical sample of area A and the charge t uniformly magnetized along its axis.

- Volume : A.t

- Magnetic dipole  moment of the sample = M .A.t

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<footer style = "font-size: 18px">Spin $\rightarrow$ Physical Picture of a Uniform Magnetic Medium $\rightarrow$ <span style = "color:blue"> Magnetic Dipole Moment </span> $\rightarrow$ Magnetic Dipole Moment $\rightarrow$ Solenoid </footer>

### <Success style="font-size:25px"> Magnetization Magnetism And Matter L-2 </Success>
### <primary style="font-size:24px"> Magnetic Dipole Moment </primary>
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- Magnetic dipole moment = I.A

- M.A.t = I A

- M = $\frac {I}{t}$

- Magnetization = current per unit length on the surface

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<footer style = "font-size: 18px">Physical Picture of a Uniform Magnetic Medium $\rightarrow$ Magnetic Dipole Moment $\rightarrow$ <span style = "color:blue"> Magnetic Dipole Moment </span> $\rightarrow$ Solenoid $\rightarrow$ Magnetic Field </footer>

### <Success style="font-size:25px"> Magnetization Magnetism And Matter L-2 </Success>
### <primary style="font-size:24px"> Solenoid </primary>
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- Finitely long solenoid creates a uniform magnetic field within the solenoid.

- Outside the solenoid the magnetic field is 0.

- N turns per unit length

- I Current

- $\vec B = \mu_0 N I \hat K$ = 0 (outside)

- Current per unit length = N I

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<footer style = "font-size: 18px">Magnetic Dipole Moment $\rightarrow$ Magnetic Dipole Moment $\rightarrow$ <span style = "color:blue"> Solenoid </span> $\rightarrow$ Magnetic Field $\rightarrow$ Magnetic Field Inside Solenoid </footer>

### <Success style="font-size:25px"> Magnetization Magnetism And Matter L-2 </Success>
### <primary style="font-size:24px"> Magnetic Field </primary>
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- Current per unit length (M)

- A uniformly magnetized cylinder magnetized parallel to the axis is equivalent  to a solenoid.

- $\vec B$ =$ \mu_0 M \hat k$ = $\mu _0 \vec M$, (inside)

- $\vec B$ = 0, (outside)

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<footer style = "font-size: 18px">Magnetic Dipole Moment $\rightarrow$ Solenoid $\rightarrow$ <span style = "color:blue"> Magnetic Field </span> $\rightarrow$ Magnetic Field Inside Solenoid $\rightarrow$ Current Enclosed by Loop </footer>

### <Success style="font-size:25px"> Magnetization Magnetism And Matter L-2 </Success>
### <primary style="font-size:24px"> Magnetic Field Inside Solenoid </primary>
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- N turns / unit length carrying current I

- Magnetization $\vec M$

- $\vec B $(inside)

- $ \vec B = \mu_0 NI \hat k + \mu_0 \hat M$

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

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<footer style = "font-size: 18px">Solenoid $\rightarrow$ Magnetic Field $\rightarrow$ <span style = "color:blue"> Magnetic Field Inside Solenoid </span> $\rightarrow$ Current Enclosed by Loop $\rightarrow$ Thank You </footer>

### <Success style="font-size:25px"> Magnetization Magnetism And Matter L-2 </Success>
### <primary style="font-size:24px"> Current Enclosed by Loop </primary>
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- We define, $\vec H = \frac {\vec B} {\mu_0} - \vec M$

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

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

- $ I_{f_{enc}}$ = Free current enclosed by the loop of integration

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![image](https://temp-public-img-folder.s3.ap-south-1.amazonaws.com/sathee.prutor.images/subject-images/iitpal/image/physics-class-12-unit-05-chapter-02-magnetization-magnetism-and-matter-l-2_3-3104jb0g2ng-08.jpg)
![image](https://temp-public-img-folder.s3.ap-south-1.amazonaws.com/sathee.prutor.images/subject-images/iitpal/image/physics-class-12-unit-05-chapter-02-magnetization-magnetism-and-matter-l-2_3-3104jb0g2ng-09.jpg)

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<footer style = "font-size: 18px">Magnetic Field $\rightarrow$ Magnetic Field Inside Solenoid $\rightarrow$ <span style = "color:blue"> Current Enclosed by Loop </span> $\rightarrow$ Thank You $\rightarrow$  </footer>