physics-class-12-unit-04-chapter-05-magnetostatics-introduction-and-biot-savart-law-l-5-7-h-wv6dc7uxk

### <Success style="font-size:25px"> Magnetostatics Introduction And Biot Savart Law L-5 </Success>
### <primary style="font-size:24px"> Magnetic Field </primary>
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- **Magnetic Field $ \vec B$**

- $|\vec B| = B = \frac{| \vec{F_B}|}{qv}$

- **Vector Magnetic force**

- $\vec{F_B} = q(\vec v \times  \vec B)$

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<footer style = "font-size: 18px">Magnetostatics Introduction $\rightarrow$ Electric Field $\rightarrow$ <span style = "color:blue"> Magnetic Field </span> $\rightarrow$ Magnetic Force $\rightarrow$ Magnetic Force </footer>

### <Success style="font-size:25px"> Magnetostatics Introduction And Biot Savart Law L-5 </Success>
### <primary style="font-size:24px"> Magnetic Force </primary>
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- $\vec B = B \hat{j}$

- $\vec v = vsin\phi \hat{i} + v cos \phi \hat{j}$

- $\vec {F_B} = q(\vec v \times \vec B)$

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<footer style = "font-size: 18px">Magnetic Field $\rightarrow$ Magnetic Force $\rightarrow$ <span style = "color:blue"> Magnetic Force </span> $\rightarrow$ Example $\rightarrow$ SI Unit of Magnetic Field </footer>

### <Success style="font-size:25px"> Magnetostatics Introduction And Biot Savart Law L-5 </Success>
### <primary style="font-size:24px"> Example </primary>
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- $q=1 \mu C=10^{-6}C$

- $B = 10 \hspace{1 mm} mT$

- $ v = 10 \hspace{1 mm} m/s $

- $F = qvB$

- $=10^{-6}\times 10 \times 10 \times 10^{-3}$

- $=10^{-7}N$

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<footer style = "font-size: 18px">Magnetic Force $\rightarrow$ Magnetic Force $\rightarrow$ <span style = "color:blue"> Example </span> $\rightarrow$ SI Unit of Magnetic Field $\rightarrow$ SI Unit of Magnetic Field </footer>

### <Success style="font-size:25px"> Magnetostatics Introduction And Biot Savart Law L-5 </Success>
### <primary style="font-size:24px"> Magnetic Fields </primary>
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| Column 1 | Column 2 |
| -------- | -------- |
|Surface of mention stars    | $10^8T$     |
| Maglew Trains    | $5T$     |
| MRI machine    | $1T$     |
| Near a small has magnet    | $10^{-2}T$     |
| Earth's magnetic field    | $10^{-5}T$     |
| Interstellar space    | $10^{-10}T$     |

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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-04-chapter-05-magnetostatics-introduction-and-biot-savart-law-l-5_7-h-wv6dc7uxk-03.jpg)

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<footer style = "font-size: 18px">SI Unit of Magnetic Field $\rightarrow$ SI Unit of Magnetic Field $\rightarrow$ <span style = "color:blue"> Magnetic Fields </span> $\rightarrow$ Biot - Savart Law $\rightarrow$ Biot - Savart Law </footer>

### <Success style="font-size:25px"> Magnetostatics Introduction And Biot Savart Law L-5 </Success>
### <primary style="font-size:24px"> Biot - Savart Law </primary>
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- $d \vec{B}=\frac{\mu_0}{4 \pi}I\frac{\vec{dl}\times \vec{r}}{r^3}=\frac{\mu_0}{4 \pi}I\frac{\vec{dl}\times \hat{r}}{r^2}$

- $\frac{\mu_0}{4 \pi}$: Constant of proportionality

- $\mu_0:$ Permeability of free space

- $\frac{\mu_0}{4 \pi}=10^{-7} T.m/A$

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<footer style = "font-size: 18px">Magnetic Fields $\rightarrow$ Biot - Savart Law $\rightarrow$ <span style = "color:blue"> Biot - Savart Law </span> $\rightarrow$ Properties of Magnetic and Electric Field $\rightarrow$ Speed of Light in Terms of Permittivity and Permeability </footer>

### <Success style="font-size:25px"> Magnetostatics Introduction And Biot Savart Law L-5 </Success>
### <primary style="font-size:24px"> Properties of Magnetic and Electric Field </primary>
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- Both $\vec{E}$ and $\vec{B}$ fills are long range

- Both decrease as $1 / r^2$

- Both obey Principle of superposition

- $\vec{E}$ is produced by a ruler charge

- $\vec{B}$ is produced in a current element $I\vec{dl}$

- $\vec{E}$ is along the line joining the charge of p

- $\vec{B}$ is $\perp$ to the plane containing $\vec{r}$ and $I\vec{dl}$

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<footer style = "font-size: 18px">Biot - Savart Law $\rightarrow$ Biot - Savart Law $\rightarrow$ <span style = "color:blue"> Properties of Magnetic and Electric Field </span> $\rightarrow$ Speed of Light in Terms of Permittivity and Permeability $\rightarrow$ Magnetic field on the Axis </footer>

### <Success style="font-size:25px"> Magnetostatics Introduction And Biot Savart Law L-5 </Success>
### <primary style="font-size:24px"> Speed of Light in Terms of Permittivity and Permeability </primary>
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- $\vec{B}$ depends on angle between $I \vec{dl}$ and $\vec{r}$

- $\epsilon_0 \mu_0  = 4 \pi \epsilon_0 . \frac{\mu_0}{4 \pi} $

- $ =\frac{1}{9 \times 10^9} \times 10^{-7}=\frac{1}{9 \times 10^{16}}=\frac{1}{(3 \times 18^8)^2} $

- $ =\frac{1}{c^2}$

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<footer style = "font-size: 18px">Biot - Savart Law $\rightarrow$ Properties of Magnetic and Electric Field $\rightarrow$ <span style = "color:blue"> Speed of Light in Terms of Permittivity and Permeability </span> $\rightarrow$ Magnetic field on the Axis $\rightarrow$ Magnetic Field due to Wire </footer>

### <Success style="font-size:25px"> Magnetostatics Introduction And Biot Savart Law L-5 </Success>
### <primary style="font-size:24px"> Magnetic field on the Axis </primary>
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- **Magnetic field on the axis of a circular loop of current**

- $\vec{dB}=\frac{\mu_0}{4 \pi} I \frac{\vec{dl}\times \vec{r}}{r^3}$

- $(\vec{dl}\times \vec{r})=dl r$

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<footer style = "font-size: 18px">Properties of Magnetic and Electric Field $\rightarrow$ Speed of Light in Terms of Permittivity and Permeability $\rightarrow$ <span style = "color:blue"> Magnetic field on the Axis </span> $\rightarrow$ Magnetic Field due to Wire $\rightarrow$ Magnetic Field due to Wire </footer>

### <Success style="font-size:25px"> Magnetostatics Introduction And Biot Savart Law L-5 </Success>
### <primary style="font-size:24px"> Magnetic Field due to Wire </primary>
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- $r^2=R^2+z^2$

- $dB_z = \frac{\mu_0}{4 \pi}I \frac{dl r}{r^3}\cos \theta$

- $ \cos \theta=\frac{R}{r}$

- $d B_z=\frac{\mu_0 I}{4 \pi r^2} d l \frac{R}{r}$

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<footer style = "font-size: 18px">Speed of Light in Terms of Permittivity and Permeability $\rightarrow$ Magnetic field on the Axis $\rightarrow$ <span style = "color:blue"> Magnetic Field due to Wire </span> $\rightarrow$ Magnetic Field due to Wire $\rightarrow$ Magnetic Field at Axial Point </footer>

### <Success style="font-size:25px"> Magnetostatics Introduction And Biot Savart Law L-5 </Success>
### <primary style="font-size:24px"> Magnetic Field due to Wire </primary>
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- $ d B_z =\frac{\mu_0 I R}{4 \pi r^3}dl = \frac{\mu_0 I R}{4 \pi(R^2+z^2)^{3 / 2}} d l$

- $B_z = \frac{\mu_o I R}{4 \pi (R^2+z^2)^{3/2}}\oint dl = \frac{\mu_0 I R}{4 \pi (R^2+z^2)^{3/2}}.2 \pi R$

- $=\frac{\mu_0IR^2}{2(z^2+R^2)^{3/2}}$

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<footer style = "font-size: 18px">Magnetic field on the Axis $\rightarrow$ Magnetic Field due to Wire $\rightarrow$ <span style = "color:blue"> Magnetic Field due to Wire </span> $\rightarrow$ Magnetic Field at Axial Point $\rightarrow$ Magnetic Field Centre of the Loop </footer>

### <Success style="font-size:25px"> Magnetostatics Introduction And Biot Savart Law L-5 </Success>
### <primary style="font-size:24px"> Magnetic Field at Axial Point </primary>
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- $\vec{B}=\frac{\mu_0 I R^2}{2(z^2+R^2)^{3 / 2}} \hat{k}$

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<footer style = "font-size: 18px">Magnetic Field due to Wire $\rightarrow$ Magnetic Field due to Wire $\rightarrow$ <span style = "color:blue"> Magnetic Field at Axial Point </span> $\rightarrow$ Magnetic Field Centre of the Loop $\rightarrow$ Example </footer>

### <Success style="font-size:25px"> Magnetostatics Introduction And Biot Savart Law L-5 </Success>
### <primary style="font-size:24px"> Magnetic Field Centre of the Loop </primary>
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- At z = 0 (Centre of the loop)

- $\vec{B}=\frac{\mu_0 I}{2 R} \hat{K}$

- N - loop (closely around)

- $\vec{B}=\frac{\mu_0 N I}{2 R} \hat{k}$

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<footer style = "font-size: 18px">Magnetic Field due to Wire $\rightarrow$ Magnetic Field at Axial Point $\rightarrow$ <span style = "color:blue"> Magnetic Field Centre of the Loop </span> $\rightarrow$ Example $\rightarrow$ Problem </footer>

### <Success style="font-size:25px"> Magnetostatics Introduction And Biot Savart Law L-5 </Success>
### <primary style="font-size:24px"> Example </primary>
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- R = 20cm

- N = 100

- I = 5A

- $B=\frac{\mu_0 N I}{2 R} =\frac{4 \pi \times 10^{-7} \times 100 \times 5}{2 \times 0.2}$

- $\simeq 1.57 mT$

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<footer style = "font-size: 18px">Magnetic Field at Axial Point $\rightarrow$ Magnetic Field Centre of the Loop $\rightarrow$ <span style = "color:blue"> Example </span> $\rightarrow$ Problem $\rightarrow$ Thank You </footer>