physics-class-12-unit-04-chapter-06-motion-chargesin-presence-of-electric-and-magnetic-fields-l-6-7-kdjidznfbpe

### <Success style="font-size:25px"> Motion Chargesin Presence Of Electric And Magnetic Fields L-6 </Success>
### <primary style="font-size:24px"> Cyclotron Frequency </primary>
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- $\vec{F}=q \vec{E}+q(\vec{V} \times \vec{B})$

- $ \frac{m v^2}{R}=q v B $

- $R=\frac{m v}{q B} $

- $ \omega=\frac{v}{R}=\frac{q B}{m}$

- $ f=\frac{\omega}{2 \pi}=\frac{q B}{2 \pi m}$

- Cyclotron Frequency

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<footer style = "font-size: 18px"> $\rightarrow$ Magnetostatics $\rightarrow$ <span style = "color:blue"> Cyclotron Frequency </span> $\rightarrow$ Velocity of Electromagnetic Wave $\rightarrow$ Thomson Experiment </footer>

### <Success style="font-size:25px"> Motion Chargesin Presence Of Electric And Magnetic Fields L-6 </Success>
### <primary style="font-size:24px"> Velocity of Electromagnetic Wave </primary>
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- $ q e  =q V B $

- $ v =\frac{E}{B}$

- Velocity 
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<footer style = "font-size: 18px">Magnetostatics $\rightarrow$ Cyclotron Frequency $\rightarrow$ <span style = "color:blue"> Velocity of Electromagnetic Wave </span> $\rightarrow$ Thomson Experiment $\rightarrow$ Particle in Electromagnetic Field </footer>

### <Success style="font-size:25px"> Motion Chargesin Presence Of Electric And Magnetic Fields L-6 </Success>
### <primary style="font-size:24px"> Particle in Electromagnetic Field </primary>
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- F = | e | E in the upward direction Net accelaration in upward direction

- = $\frac{|e|E}{m}$

- Time taken to propogate a length L

- = $\frac{L}{v}$

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<footer style = "font-size: 18px">Velocity of Electromagnetic Wave $\rightarrow$ Thomson Experiment $\rightarrow$ <span style = "color:blue"> Particle in Electromagnetic Field </span> $\rightarrow$ Particle in Electromagnetic Field $\rightarrow$ Particle in Electromagnetic Field </footer>

- $ d =\frac{1}{2} a \cdot t^2  =\frac{1}{2} \cdot \frac{|e| E}{m} \cdot \frac{L^2}{v^2}$

- $ \frac{|E|}{m} =\frac{2 d v^2}{E L^2} $

- $ v =\frac{E}{B} $

- $ \frac{|e|}{m} =\frac{2 d}{E L^2} \cdot \frac{E^2}{B^2}=\frac{2 d E}{L^2 B^2}$

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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-06-motion-charges-presence-of-electric-magnetic-fields-l-6_7-kdjidznfbpe-173-1071.6.jpg)

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<footer style = "font-size: 18px">Thomson Experiment $\rightarrow$ Particle in Electromagnetic Field $\rightarrow$ <span style = "color:blue"> Particle in Electromagnetic Field </span> $\rightarrow$ Particle in Electromagnetic Field $\rightarrow$ Spectrometer </footer>

### <Success style="font-size:25px"> Motion Chargesin Presence Of Electric And Magnetic Fields L-6 </Success>
### <primary style="font-size:24px"> Spectrometer </primary>
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- $v=\frac{E}{B}$

- $x=2R$

- $R=\frac{mv}{q B^{\prime}}$

- $x=\frac{2mv}{q B^{\prime}}$

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<footer style = "font-size: 18px">Particle in Electromagnetic Field $\rightarrow$ Particle in Electromagnetic Field $\rightarrow$ <span style = "color:blue"> Spectrometer </span> $\rightarrow$ Helical Path $\rightarrow$ Helical Path </footer>

### <Success style="font-size:25px"> Motion Chargesin Presence Of Electric And Magnetic Fields L-6 </Success>
### <primary style="font-size:24px"> Helical Path </primary>
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- $ R =\frac{m v}{q B} $

- $\vec{B} =B \hat{k}$

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

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

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

- $ = -q v B \cos \hat{j}$

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<footer style = "font-size: 18px">Particle in Electromagnetic Field $\rightarrow$ Spectrometer $\rightarrow$ <span style = "color:blue"> Helical Path </span> $\rightarrow$ Helical Path $\rightarrow$ Example </footer>

### <Success style="font-size:25px"> Motion Chargesin Presence Of Electric And Magnetic Fields L-6 </Success>
### <primary style="font-size:24px"> Helical Path </primary>
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- $ v \cos \phi=v_{\perp}$

- $v \sin \phi=v_{11} $

- Radius R$=\frac{m v_{\perp}}{q B}$

- Particle complete one revolution

- $T=\frac{2 \pi}{\omega} = \frac{2 \pi R}{v_{\perp}} = \frac{2 \pi m}{q B}$

- Distance moves along z-direction in time

- $T=v_{11}T=\frac{2 \pi m v_{11}}{qB}$ Pitch

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<footer style = "font-size: 18px">Spectrometer $\rightarrow$ Helical Path $\rightarrow$ <span style = "color:blue"> Helical Path </span> $\rightarrow$ Example $\rightarrow$ Partial Acceleration </footer>

### <Success style="font-size:25px"> Motion Chargesin Presence Of Electric And Magnetic Fields L-6 </Success>
### <primary style="font-size:24px"> Example </primary>
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- $v=10^6m/s$

- $q=1.6 \times 10^{-19}c$

- $Q = 45^o$

- $B=5 \times 10^{-4}T$

- $m=9.1 \times 10^{-31}kg$

- pitch $=\frac{2 \pi m v_{11}}{qB}=\frac{2 \pi \times 9.1 \times 10^{-31} \times 10{6}}{1.6 \times 10^{-19} \times 5 \times 10^{-7}}\frac{1}{\sqrt{2}}$

- $\simeq 5.1cm$

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<footer style = "font-size: 18px">Helical Path $\rightarrow$ Helical Path $\rightarrow$ <span style = "color:blue"> Example </span> $\rightarrow$ Partial Acceleration $\rightarrow$ Institute </footer>

### <Success style="font-size:25px"> Motion Chargesin Presence Of Electric And Magnetic Fields L-6 </Success>
### <primary style="font-size:24px"> Institute </primary>
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- **IUAC:** Inter University Acceleration Centre Delhi.

- **VECC:** Variable Energy Cyclotron Kolkata.

- **RRCAT:** Raja Remanna centre for Advanced Technology, Indore.

- **TIFR-BARE:** Tata Institute of Fundamental Research - Bharta Atomic Research Centre, Mumbai.

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<footer style = "font-size: 18px">Example $\rightarrow$ Partial Acceleration $\rightarrow$ <span style = "color:blue"> Institute </span> $\rightarrow$ Cyclotron $\rightarrow$ Cyclotron </footer>