# 0.9 Cyclotron

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High speed charged particles are required for nuclear and atomic investigations. Cyclotron is one of the devices popularly known as “particle accelerator” to accelerate charged particle to a very high speed. It uses “crossed” magnetic and electric fields at right angles to achieve the objective. The chief role of magnetic field is to make the process of acceleration confined to a small and manageable region. As far as the change in speed is concerned, it is affected only by the electric field. Recall that magnetic field can not change magnitude of velocity i.e. speed.

But we should be careful in extrapolating above facts to obvious conclusions. As a matter of fact, we shall find that magnetic field actually affects the speed attained by the charged particle indirectly by controlling number of revolutions in the cyclotron. On the other hand, the speed acquired by the charged particle is independent of applied voltage. We shall explore all these aspects in detail in this module.

## Acceleration due to electric field

Electric force accelerates particle only to change its speed if motion of the charged particle is in the direction of electric field. A potential difference V accelerates particle to achieve a speed as given by :

$\frac{1}{2}m{v}^{2}=eV$

$⇒v=\sqrt{\left(\frac{2eV}{m}\right)}$

There is, however, difficulty in generating potential difference greater than ${10}^{6}$ V. For this limiting value, the speed attained by a proton would be :

$⇒v=\sqrt{\left(2X1.6X{10}^{-19}X{10}^{6}/1.66X{10}^{-27}\right)}$ $⇒v=\sqrt{\left(1.928X{10}^{14}\right)}=1.39X{10}^{7}\phantom{\rule{1em}{0ex}}m/s$

This is just 4.63 % of the speed of light and is not good enough. This speed of the particle is thus required to be subjected to repeated application of electric force. This is done linearly by electric force in what is known as “linear accelerator”. Else, we use magnetic field to bend the path of motion and present the charged particle repeatedly to electric field for acceleration as in cyclotron. We should know that there is relative size and cost comparison and advantages between linear accelerator and cyclotron. Sometimes though, the two types of accelerators are used in conjunction where cyclotron functions as the initial accelerator for the system of particle accelerators.

## The particles accelerated by cyclotron

The accelerators are used for accelerating charged elementary particles or charged ions. It can not accelerate a neutral particle. Besides, the cyclotron as described generally, is not used for accelerating light mass particles like electron or positron. The reason is that electron having negligible mass accelerates rather too quickly for repeated acceleration within the given size of cyclotron. Instead, the light mass charged particles are accelerated by a device known as “betatron” which uses torus shaped vacuum tube as secondary coil. The tube is a hollow cylinder shaped in a circle. The varying magnetic field, produced by secondary coil, sets up electric field which, in turn, accelerates electron through the tube. On the other hand, the magnetic field due to primary coil, spins the electron and keeps it in the center of the path.

#### Questions & Answers

how do they get the third part x = (32)5/4
kinnecy Reply
can someone help me with some logarithmic and exponential equations.
Jeffrey Reply
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ninjadapaul
20/(×-6^2)
Salomon
okay, so you have 6 raised to the power of 2. what is that part of your answer
ninjadapaul
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ninjadapaul
it think it's written 20/(X-6)^2 so it's 20 divided by X-6 squared
Salomon
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Salomon
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Salomon
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ninjadapaul
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ninjadapaul
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ninjadapaul
Commplementary angles
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a perfect square v²+2v+_
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algebra 2 Inequalities:If equation 2 = 0 it is an open set?
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The answer is neither. The function, 2 = 0 cannot exist. Hence, the function is undefined.
Al
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Differences Between Laspeyres and Paasche Indices
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. After 3 months on a diet, Lisa had lost 12% of her original weight. She lost 21 pounds. What was Lisa's original weight?
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AMJAD
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Yes, Nanotechnology has a very fast field of applications and their is always something new to do with it...
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AMJAD
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AMJAD
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Stotaw
In this morden time nanotechnology used in many field . 1-Electronics-manufacturad IC ,RAM,MRAM,solar panel etc 2-Helth and Medical-Nanomedicine,Drug Dilivery for cancer treatment etc 3- Atomobile -MEMS, Coating on car etc. and may other field for details you can check at Google
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Prasenjit Reply
At high concentrations (>0.01 M), the relation between absorptivity coefficient and absorbance is no longer linear. This is due to the electrostatic interactions between the quantum dots in close proximity. If the concentration of the solution is high, another effect that is seen is the scattering of light from the large number of quantum dots. This assumption only works at low concentrations of the analyte. Presence of stray light.
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the Beer law works very well for dilute solutions but fails for very high concentrations. why?
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Source:  OpenStax, Electricity and magnetism. OpenStax CNX. Oct 20, 2009 Download for free at http://cnx.org/content/col10909/1.13
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