physics-class-12-unit-04-chapter-01-force-and-torque-due-to-magnetic-field-l-1-7-ustrwp959qu

### <Success style="font-size:25px"> Force And Torque Due To Magnetic Field L-1 </Success>
### <primary style="font-size:24px"> Force on a Current Carrying Conductor </primary>
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- $\vec{F}_B=q(\vec{v} \times \vec{B})$

- Drift velocity of the charge $\Rightarrow v$

- Force on each charge  $=q v B$

- Charge density (charge number / unit volume) $=n$

- Volume = A.l

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<footer style = "font-size: 18px"> $\rightarrow$ Force and Torque due to Magnetic Field $\rightarrow$ <span style = "color:blue"> Force on a Current Carrying Conductor </span> $\rightarrow$ Charge Per Unit Length $\rightarrow$ Force Due to Magnetic Field </footer>

### <Success style="font-size:25px"> Force And Torque Due To Magnetic Field L-1 </Success>
### <primary style="font-size:24px"> Charge Per Unit Length </primary>
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- Number of charge present in the unit of length l = n A l

- Total Charge = n A l V

- Total force on the length l

- = n A l q v B

- Current I = charge flowing per unit time = n A v q

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<footer style = "font-size: 18px">Force and Torque due to Magnetic Field $\rightarrow$ Force on a Current Carrying Conductor $\rightarrow$ <span style = "color:blue"> Charge Per Unit Length </span> $\rightarrow$ Force Due to Magnetic Field $\rightarrow$ Force Due to Magnetic Field </footer>

### <Success style="font-size:25px"> Force And Torque Due To Magnetic Field L-1 </Success>
### <primary style="font-size:24px"> Force Due to Magnetic Field </primary>
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- $ \vec{B}=B\hat{k}$   
	
- $\vec{v}=v \sin \phi \hat{\imath}+v\operatorname{cos} \phi \hat{k}$

- Force on one charge =$q \vec{v} \times\vec{B}$

- = $ q(v \sin \phi \hat{\imath}+v\operatorname{cos} \phi \hat{k})\times B\hat{k} $

- = q v$\sin \phi(\hat{\imath}\times\hat{k})$ B

- = -qvB $\sin \phi\hat{\jmath}$

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<footer style = "font-size: 18px">Charge Per Unit Length $\rightarrow$ Force Due to Magnetic Field $\rightarrow$ <span style = "color:blue"> Force Due to Magnetic Field </span> $\rightarrow$ Total Force $\rightarrow$ Force Between Two Current Carrying Conductor </footer>

### <Success style="font-size:25px"> Force And Torque Due To Magnetic Field L-1 </Success>
### <primary style="font-size:24px"> Total Force </primary>
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- Total charge in a length l = nAlq

- Total force on a length l =  -nAlq v B sin $\phi\hat{\jmath}$

- Current I = nAvq

- Total force on a length l = -IBl $sin \phi\hat{j}$

- $\vec{F}=I(\vec{l} \times \vec{B})$

- $\vec{l}=l \sin\phi \hat{i} + l \cos\phi \hat{k}$

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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-01-force-and-torque-due-to-magnetic-field-l-1_7-ustrwp959qu-04.jpg)

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<footer style = "font-size: 18px">Force Due to Magnetic Field $\rightarrow$ Force Due to Magnetic Field $\rightarrow$ <span style = "color:blue"> Total Force </span> $\rightarrow$ Force Between Two Current Carrying Conductor $\rightarrow$ Force On Wire </footer>

### <Success style="font-size:25px"> Force And Torque Due To Magnetic Field L-1 </Success>
### <primary style="font-size:24px"> Force Between Two Current Carrying Conductor </primary>
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- **Force on wire 2 due to wire 1**

- $B_1=\frac{\mu_0 I_1}{2 \pi d}$

- $F_{21}=I_2 l \frac{\mu_0 I_1}{2 \pi d}$ $=\frac{\mu_0 I_1 I_2}{2 \pi d} l$

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<footer style = "font-size: 18px">Force Due to Magnetic Field $\rightarrow$ Total Force $\rightarrow$ <span style = "color:blue"> Force Between Two Current Carrying Conductor </span> $\rightarrow$ Force On Wire $\rightarrow$ Example </footer>

### <Success style="font-size:25px"> Force And Torque Due To Magnetic Field L-1 </Success>
### <primary style="font-size:24px"> Force On Wire </primary>
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- $F_{21}=\frac{\mu_1 I_1 I_2}{2 \pi d}$

- $B_2=\frac{\mu_0 I_2}{2 \pi d}$

- Force on wire 1
 
- $F_{12}=I_1 l \frac{\mu_0 I_2}{2 \pi d} = \frac{\mu_0 I_1 I_2}{2 \pi d} l$

- Force per unit length of wire 1 =$ \frac{\mu_0 I_1 I_2}{2 \pi d}$

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<footer style = "font-size: 18px">Total Force $\rightarrow$ Force Between Two Current Carrying Conductor $\rightarrow$ <span style = "color:blue"> Force On Wire </span> $\rightarrow$ Example $\rightarrow$ Torque on a Current Carrying Loop </footer>

### <Success style="font-size:25px"> Force And Torque Due To Magnetic Field L-1 </Success>
### <primary style="font-size:24px"> Example </primary>
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- Parallel current attract each other

- Anti parallel currents repeal each other

- $I_1=I_2=5A$

- $d=10\mathrm{cm} = 10^{-2}\mathrm{m}$

- $F = \frac{\mu_0 I_1 I_2}{2 \pi d} = \frac{4 \pi \times 10^{-7} \times 5 \times 5}{2 \pi \times 10^{-2}}$ $= 5 \times 10^{-4} N/m$

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<footer style = "font-size: 18px">Force Between Two Current Carrying Conductor $\rightarrow$ Force On Wire $\rightarrow$ <span style = "color:blue"> Example </span> $\rightarrow$ Torque on a Current Carrying Loop $\rightarrow$ Example </footer>

### <Success style="font-size:25px"> Force And Torque Due To Magnetic Field L-1 </Success>
### <primary style="font-size:24px"> Example </primary>
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- **Force on 1**

- $\vec{l} = b \hat{i}$

- $\vec{F}_1 = I(\vec{l} \times \vec{B}) = I b \hat{i} \times(B \sin \phi \hat{j} + B \cos \phi \hat{k})$

- $= I b B \sin \phi \hat{k} - I b B \cos \phi \hat{j}$

- **Force on 2**

- $\vec{l} = a \hat{j} = a \hat{j}$

- $\vec{F}_2 = I(\vec{l} \times \vec{b}) = I a \hat{j} \times (B \sin \phi \hat{j} + B \cos \phi \hat{k})$

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<footer style = "font-size: 18px">Torque on a Current Carrying Loop $\rightarrow$ Example $\rightarrow$ <span style = "color:blue"> Example </span> $\rightarrow$ Example $\rightarrow$ Torque due to Force </footer>

### <Success style="font-size:25px"> Force And Torque Due To Magnetic Field L-1 </Success>
### <primary style="font-size:24px"> Example </primary>
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- **Force on 3**

- $\vec{l} = -b \hat{i}$

- $\vec{F}_3 = I(\vec{l} \times \vec{B}) = -I b \hat{i} \times (B \sin \phi \hat{j} + B \cos \phi \hat{k})$

- $= -I b B \sin \phi \hat{k} + I b B \cos \phi \hat{j}$

- **Force on 4**

- $\vec{l} = -a \hat{j}$

- $\vec{F}_4 = -I a b \cos \phi \hat{i}$

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<footer style = "font-size: 18px">Example $\rightarrow$ Example $\rightarrow$ <span style = "color:blue"> Example </span> $\rightarrow$ Torque due to Force $\rightarrow$ Torque due to Force </footer>

### <Success style="font-size:25px"> Force And Torque Due To Magnetic Field L-1 </Success>
### <primary style="font-size:24px"> Torque due to Force </primary>
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- Total force $=\vec{F_1} + \vec{F}_2 + \vec{F}_3 + \vec{F}_4 = 0 $

- Torque due to $\vec{F}_1$ about 0

- $\vec{\tau}_1 = \vec{r}_1 \times \vec{F}_1$

- $= -\frac{a}{2} \hat{j} \times (I b B \sin \phi \hat{k} - I b B \cos \phi \hat{j})$

- $= \frac {-I b B}{a} \sin \phi \hat{i}$

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<footer style = "font-size: 18px">Example $\rightarrow$ Example $\rightarrow$ <span style = "color:blue"> Torque due to Force </span> $\rightarrow$ Torque due to Force $\rightarrow$ Magnetic Dipole Moment </footer>

### <Success style="font-size:25px"> Force And Torque Due To Magnetic Field L-1 </Success>
### <primary style="font-size:24px"> Torque due to Force </primary>
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- Torque due to $F_{3}$ about 0

- $\tau_{3} =\vec{r}_3 \times \vec{F}_3$

- $= \frac{a}{2} \hat{j} \times (-I b B \sin \phi \hat{k} + I b B \cos \phi \hat{j}) = -\frac{I a b B}{2} \sin \phi \hat{i}$

- Total torque  $\vec{\tau} = \vec{\tau_1}+\vec{\tau}_3$

- $= -I a b B \sin \phi \hat{i}$

- $\vec{\tau} = I a b B \sin \phi (\hat{k} \times \hat{i})$

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<footer style = "font-size: 18px">Example $\rightarrow$ Torque due to Force $\rightarrow$ <span style = "color:blue"> Torque due to Force </span> $\rightarrow$ Magnetic Dipole Moment $\rightarrow$ Torque </footer>

### <Success style="font-size:25px"> Force And Torque Due To Magnetic Field L-1 </Success>
### <primary style="font-size:24px"> Torque </primary>
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- $\vec{\tau}=\vec{m} \times \vec{B}$

- Torque on an electric dipole $\vec{\tau}=\vec{p} \times \vec{E}$

- Loop has N turns (closely arounds)

- $\vec{m}=N I A \hat{k}$

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<footer style = "font-size: 18px">Torque due to Force $\rightarrow$ Magnetic Dipole Moment $\rightarrow$ <span style = "color:blue"> Torque </span> $\rightarrow$ Moving Coil Galvanometer $\rightarrow$ Moving Coil Galvanometer </footer>

### <Success style="font-size:25px"> Force And Torque Due To Magnetic Field L-1 </Success>
### <primary style="font-size:24px"> Moving Coil Galvanometer </primary>
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- Torque due to current I

- $\tau_{current}=N I A B$

- A : Area of loop

- N : Number of loop

- I : Current

- B : Magnetic Fields

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<footer style = "font-size: 18px">Magnetic Dipole Moment $\rightarrow$ Torque $\rightarrow$ <span style = "color:blue"> Moving Coil Galvanometer </span> $\rightarrow$ Moving Coil Galvanometer $\rightarrow$ Thank You </footer>