physics-class-12-unit-06-chapter-02-faradays-law-of-induction-mutual-and-self-inductance-l-2-4-hqm0dbe-7sa

### <Success style="font-size:25px"> Faradays Law Of Induction Mutual And Self Inductance L-2 </Success>
### <primary style="font-size:24px"> Magnetic Flux </primary>
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* Magnetic Field B

* Magnetic flux

- $\Phi_B = B \times L$

* Rate of charge of flux = $\frac {\Phi _B}{dt}$

- = B L $\frac {dx}{dt}$ = B L v

* Induced emf $\varepsilon = \frac {\Phi_B}{dt}$ = - B L v

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<footer style = "font-size: 18px"> $\rightarrow$ Faradays Law of Induction Mutual and Self Inductance $\rightarrow$ <span style = "color:blue"> Magnetic Flux </span> $\rightarrow$ Magnetic Force $\rightarrow$ Example </footer>

### <Success style="font-size:25px"> Faradays Law Of Induction Mutual And Self Inductance L-2 </Success>
### <primary style="font-size:24px"> Magnetic Force </primary>
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- **Magnetic Force:**

- $\vec F_B = I \vec L \times \vec B$

- $F_B = I \vec L  \vec B$

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<footer style = "font-size: 18px">Faradays Law of Induction Mutual and Self Inductance $\rightarrow$ Magnetic Flux $\rightarrow$ <span style = "color:blue"> Magnetic Force </span> $\rightarrow$ Example $\rightarrow$ Magnetic Force on the Rod </footer>

### <Success style="font-size:25px"> Faradays Law Of Induction Mutual And Self Inductance L-2 </Success>
### <primary style="font-size:24px"> Example </primary>
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- B = 0.5 T

- L = 10 cm = 0.1m

- v = 2m/s

- R = 0.05 $\Omega$

* Induces emf $\tau$ = BLv

- = $0.5 \times 0.1 \times 2$ = 0.1 v

* Current in the loop  I =$ \frac {E}{R} = \frac {0.1}{0.05}$ = 2A

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<footer style = "font-size: 18px">Magnetic Flux $\rightarrow$ Magnetic Force $\rightarrow$ <span style = "color:blue"> Example </span> $\rightarrow$ Magnetic Force on the Rod $\rightarrow$ Eddy Current </footer>

### <Success style="font-size:25px"> Faradays Law Of Induction Mutual And Self Inductance L-2 </Success>
### <primary style="font-size:24px"> Application </primary>
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- Magnetic braking in trains

- Electric motor

- Induction Furnace

- Metal detector

- Undefinable effect

- Heating in transfarmer core
 
- Liminating the core

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<footer style = "font-size: 18px">Eddy Current $\rightarrow$ Lamination $\rightarrow$ <span style = "color:blue"> Application </span> $\rightarrow$ Inductance $\rightarrow$ Inductance </footer>

### <Success style="font-size:25px"> Faradays Law Of Induction Mutual And Self Inductance L-2 </Success>
### <primary style="font-size:24px"> Inductance </primary>
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- $ \vec{B}_ 1$ = $\frac{\mu_ {0} I_ {1}}{4 \pi} \oint_ {Loop^{\prime}} \frac{\vec {dl_1} \times \vec{r}}{r^2} $

- Flux length loop 2 =$\int_{Loop 2} \vec{B}_1 \cdot d \vec{A}_2 \propto I_1$

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<footer style = "font-size: 18px">Lamination $\rightarrow$ Application $\rightarrow$ <span style = "color:blue"> Inductance </span> $\rightarrow$ Inductance $\rightarrow$ Solenoid </footer>

### <Success style="font-size:25px"> Faradays Law Of Induction Mutual And Self Inductance L-2 </Success>
### <primary style="font-size:24px"> Inductance </primary>
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- $\phi_2 = M_2 , I_2$

- $M_{21}$ , constant of propotionality called mutual inductances.

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

### <Success style="font-size:25px"> Faradays Law Of Induction Mutual And Self Inductance L-2 </Success>
### <primary style="font-size:24px"> Solenoid </primary>
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* Two conical long clyinder

* Solenoid $S_1$

* Number of turn per unit length : $N_1$

* Radius of $r_1$

* Solenoid $S_2$

* Number of turn per unit length : $N_2$

* Radius of $r_2$

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

### <Success style="font-size:25px"> Faradays Law Of Induction Mutual And Self Inductance L-2 </Success>
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* Pass current $I_1$ through $S_1$

* Magnetic fields produced by $S_1$ = $\mu_0 N_1 I_1$

* Magnetic flux through each loop of $S_2$ = $\mu_0 N_1 I_1 \pi r_{1}^{2}$

* Flux thorugh length L of solenoid $S_2$ = $\mu_0 N_1 I_1 \pi r_{1}^{2} N_2 L$

- = $\mu_0 N_1 N_2 \pi r_{1}^{2} L I_1 $ = $M_{21} I_1$

- $M_{21}  = \mu_0 N_1 N_2 \pi r_{1}^{2} L  $
  
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<footer style = "font-size: 18px">Solenoid $\rightarrow$ Magnetic Field $\rightarrow$ <span style = "color:blue"> Magnetic Field </span> $\rightarrow$ Magnetic Flux $\rightarrow$ Mutual Inductance </footer>

### <Success style="font-size:25px"> Faradays Law Of Induction Mutual And Self Inductance L-2 </Success>
### <primary style="font-size:24px"> Magnetic Flux </primary>
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* Current $I_2$ through $S_2$

* Magnetic flux generated = $\mu_0 N_2 I_2$

* Flux through each loop of $S_1$ = $\mu_0 N_2 I_2 \pi r_{1}^{2}$

* Flux through a length L of $S_1$ = $\mu_0 N_2 I_2 \pi r_{1}^{2} N_1 L$

- = $\mu_0 N_1 N_2 \pi r_{1}^{2} L I_2$ = $M_{12} I_{2}$
 
 - $ M_{12} = \mu_0 N_1 N_2 \pi r_{1}^{2} L$

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<footer style = "font-size: 18px">Magnetic Field $\rightarrow$ Magnetic Field $\rightarrow$ <span style = "color:blue"> Magnetic Flux </span> $\rightarrow$ Mutual Inductance $\rightarrow$ Faraday's law </footer>

### <Success style="font-size:25px"> Faradays Law Of Induction Mutual And Self Inductance L-2 </Success>
### <primary style="font-size:24px"> Mutual Inductance </primary>
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* Current I through the into solenoid magnetic field , $B = \mu_o N_l I$

* Magnetic flux through the smaller solenoid = $\mu_o N_l I \pi r_{s}^{2} N_s L$

- = $\mu_o N_l N_s \pi r_{s}^{2} I L$

- M = $\mu_o N_l N_s \pi r_{s}^{2} L$

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<footer style = "font-size: 18px">Magnetic Field $\rightarrow$ Magnetic Flux $\rightarrow$ <span style = "color:blue"> Mutual Inductance </span> $\rightarrow$ Faraday's law $\rightarrow$ Self Inductance </footer>

### <Success style="font-size:25px"> Faradays Law Of Induction Mutual And Self Inductance L-2 </Success>
### <primary style="font-size:24px"> Faraday's law </primary>
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- According to Faraday's law changing current through loop 1 will induce an emf in loop 2.

- E =-$\frac{d \bar{\phi}_{2}}{d t} = -M \frac{d I_1}{d t}$

- ${\delta_2 = M I_1}$

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<footer style = "font-size: 18px">Magnetic Flux $\rightarrow$ Mutual Inductance $\rightarrow$ <span style = "color:blue"> Faraday's law </span> $\rightarrow$ Self Inductance $\rightarrow$ Self Inductance </footer>

### <Success style="font-size:25px"> Faradays Law Of Induction Mutual And Self Inductance L-2 </Success>
### <primary style="font-size:24px"> Self Inductance </primary>
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* Number of turns per unit length = N

* Current = I

* Magnetic field = $\mu_0 N I$

* Each loop of the solenoid, will have a flux, $\phi = \mu_0 N I \pi r^2$

* Total magnetic flux through a length l of the solenoid = $\phi N l$

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<footer style = "font-size: 18px">Mutual Inductance $\rightarrow$ Faraday's law $\rightarrow$ <span style = "color:blue"> Self Inductance </span> $\rightarrow$ Self Inductance $\rightarrow$ Property of Inductance </footer>

### <Success style="font-size:25px"> Faradays Law Of Induction Mutual And Self Inductance L-2 </Success>
### <primary style="font-size:24px"> Self Inductance </primary>
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- $\bar \phi = \phi N l$ = $ \mu_0 N I \pi r^2 N l$ = $ \mu_0 N^2 \pi r^2 N I$ = L I
 
-  L =  $ \mu_0 N^2 \pi r^2 l$  Self Inductances
 
 - **Generates:** 
 
-  EMF E = - $\frac {d\bar \phi}{dt}$
 
-   E = -L$\frac {dI}{dt}$
  
-   Back EMF

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<footer style = "font-size: 18px">Faraday's law $\rightarrow$ Self Inductance $\rightarrow$ <span style = "color:blue"> Self Inductance </span> $\rightarrow$ Property of Inductance $\rightarrow$ Example </footer>

### <Success style="font-size:25px"> Faradays Law Of Induction Mutual And Self Inductance L-2 </Success>
### <primary style="font-size:24px"> Example </primary>
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- Long solenoids

- N= 100 turns/cm

- R = 1.6 cm

- Self inductance per unit length

- L = $\mu_0 N^2 \pi r^2$ per unit length

- = $ 4 \pi \times 10^{-7} \times 10^{8} \times \pi (1.6)^2 \times 10^{-14} \times 1$ = 0.1 H/m
 
 - **H : HENRY** 
 
-  1H = 1 $\frac {T.m^2}{A}$

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<footer style = "font-size: 18px">Self Inductance $\rightarrow$ Property of Inductance $\rightarrow$ <span style = "color:blue"> Example </span> $\rightarrow$ Example $\rightarrow$ Thank You </footer>