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== Patterns of Field in Space ==
Short Description of Topic


The two major components in Physics II are interactions between electric fields and magnetic fields. This broad subject focuses from a simple topic, electric fields to a much complex idea, electromagnetic radiation. Though this course is very broad in terms of materials that it covers, each topic is very important in understanding the phenomena of electric and magnetic interactions between particles (protons, electrons, dipoles, point charge, capacitor, and, etc), as omitting one concept out of hundreds of concept could lead one approaching the problem differently. This Wiki Page will discuss Chapter 21 of the Matters and Interactions Text Book, 4th edition (Patterns of Field in Space), specifically Gauss's Law and Electric Flux. In order to understand these concepts, one first need to understand the definition of electric field and know each component of Gauss's Law.
==The Main Idea==
== Electric Flux ==


"Electric Flux" is a quantitative measure of the amount and direction of electric field over an entire surface of a specified object. There are two components in electric flux: direction of the electric field and magnitude of the electric field. These two sums up and give us the value, electric flux, which has a unit of Vm. In order to determine the direction of the electric field of an object, one need to figure out the x,y,z coordinates of the faces of an object and then calculate the normal vector that comes out of the surface. Secondly, to determine the direction of the electric field of an object, one first need to know the number of dimensions of an object (i.e: 6 faces in a rectangular prism) and areas for each face of the object. Finally, one should be able to calculate the electric flux of an object by multiplying the electric field at a location on each surface of the box by corresponding normal vector and multiplying this value by the area of the surface that was just calculated. One must repeat this process the remaining surfaces (faces) and by adding up all electric flux, that will be the electric flux of the object one wanted to calculate. This value is essential because it will be useful for calculating total charged enclosed inside the object later on. The above written method of calculating electric flux may be confusing at first, but knowing the Gauss's Law, being able to apply this Law to the real problem, and by going through the example below should make sure understanding of this concept.
This page is about an apparatus called the Cyclotron. This device is used to accelerate charged particles (like protons, neutrons, alpha particles, etc.) and ions to high energies. It uses a combination of strong magnetic and electric fields to accelerate the charged particles. The two fields (electric and magnetic) are perpendicular to each other, hence very aptly name "crossed fields". When the charged particle is accelerated by the cyclotron, the frequency of tis revolution in the two semi-secular plates (also called the "Ds") is independent of its energy. This is an important fact in the working of the device, as we will subsequently study in this lesson.


== Gauss's Law ==
The Gauss's Law simplifies definition of "Electric Flux" into a one simple equation.


PRINCIPLE:<br>
The working of the cyclotron is based on the fact that a positively charged particle can be accelerated to a sufficiently high energy with the help of smaller values of oscillating electric field by making it cross the same electric field time and again, with the help of a stringer magnetic field.


[[File:Gauss.JPG]]


CONSTRUCTION:<br>
A cyclotron device consists of two D-shaped hollow evacuated metal chambers (say D1 and D2) called the dees. These dees are placed horizontally with their diametric edges parallel and slightly separated from each other. The dees are connected to a high frequency oscillator which can produce a potential difference of the order of 10^4 volts at a frequency of about 10^7 hertz. The two dees are enclosed in an evacuated steel box and are well insulated from it. The box is placed inn a string magnetic field produced by two pole pieces of an electromagnets N,S. The magnetic field is perpendicular to the plane of the dees. At the centre of the device, P is a place of ionic source or positively charged (Check the diagram).


[http://hyperphysics.phy-astr.gsu.edu/hbase/electric/gaulaw.html Gauss's Law]
WORKING AND THEORY:<br>
The positive ion to be accelerated is produced at P. Suppose, at that instant D1 is at negative potential and D2 is at positive potential. Therefore, the ion will be accelerated towards D1. On reaching inside D1, the ion will be in a field free space (as the two dees are hollow and metallic). Hence it moves with a constant speed in D1, say v. But due to a perpendicular magnetic field of strength B, the ion will describe a circular path of radius r (say) in D1.


[http://www.colorado.edu/physics/phys1120/phys1120_sp08/notes/notes/Knight27_gauss_lect.pdf Gauss's Law Examples]
Now in case the time taken by the positive ion to describe a semicircular path is equal to the time during which half cycle of the electric oscillator is completed, then as the ion arrives in the gap between the two dees, the polarity of the two dees is reversed, i.e. D1 becomes positive and D2 becomes negative. Then, the positive ion is accelerated towards D2 and it enters D2 with a greater speed, which remains constant in D2. The ion will describe a semicircular path of greater radius due to a perpendicular magnetic field and again will arrive in the gap between the two dees exactly at the instant, the polarity of the two dees is reversed. Thus, the positive ion will go on accelerating every time it comes into the gap between the dees and will go on describing a circular path of greater and greater radius with greater and greater speed and finally acquires a sufficiently high energy. The accelerated ops can be removed out of the dees from the window W, by applying at the elected field across the deflecting plates E and F (check the diagram).


====A Computational Model====


How do we visualize or predict using this topic. Consider embedding some vpython code here [https://trinket.io/glowscript/31d0f9ad9e Teach hands-on with GlowScript]


==Examples==
===A Mathematical Model===
 
The charged particle describes a circular path of radius r (say) in D1, due to the perpendicular magnetic field B. Hence, the magnetic force experienced by the particle is balanced by the centripetal force on the particle due to its circular motion (in a circle of radius r). <br>This gives us the following expression:<br>
<math>Bqv = mv^2/r</math>
 
Here: m and q are the mass and the charge of the ion respectively. <br>
 
Therefore:      <math>r = mv/Bq</math>
 
MAXIMUM ENERGY OF POSITIVE ION:<br>
Let <math>v_0, r_o</math> = maximum velocity and maximum radius of the circular path followed by the positive ion in the cyclotron.
 
Then: <math>mv_0^2/r_0 = Bqv_0    or    v_0 = Bqr_0/m</math>


Be sure to show all steps in your solution and include diagrams whenever possible
Therefore: <math>Max K.E. = 1/2 mv_0^2 = 1/2 m(Bqr_0/m)^2 = B^2q^2r_0^2/2m</math>


===Simple===
The electric field has been measured to be vertically upward everywhere on the surface of a box 20 cm long, 4 cm high, and 3 cm deep, shown in the figure. All over the bottom of the box E1 = 1100 V/m, all over the sides E2 = 950 V/m, and all over the top E3 = 750 V/m.


[[File:sss.JPG]]


Since E1, E2, and E3, are all measured to be vertically upward everywhere on the surface of a box, only the bottom surface and the top surface will be focused (multiplying the normal vector of other surfaces than the bottom and top surfaces will result in zero electric flux). The normal vector of the bottom surface is known to be <0,-1,0> and that of the top surface is known to be <0,1,0> assuming vertically upward is in +y direction.
CYCLOTRON FREQUENCY:<br>
If T is the time period of oscillating electric field then:
<math>T = 2t = 2pim/Bq</math>


E1 = <0, 1100, 0> V/m,
The cyclotron frequency is given by
E2 = <0, 950, 0> V/m,
E3 = <0, 750, 0> V/m,


E1 corresponds to the bottom surface according to the diagram. Multiplying vector E1 with its normal vector of the bottom surface equals -1100 (dot product), and multiplying this vector by the area equals -1100 V/m x 0.20 m x 0.03 m = -6.6 Vm.


E3 corresponds to the top surface according to the diagram. Multiplying vector E3 with its normal vector of the top surface equals 750 (dot product) and multiplying this vector by the area equals 750 V/m x 0.20 m x 0.03 m = 4.5 Vm.
What are the mathematical equations that allow us to model this topic.  For example <math>{\frac{d\vec{p}}{dt}}_{system} = \vec{F}_{net}</math> where '''p''' is the momentum of the system and '''F''' is the net force from the surroundings.


Therefore, the sum of the electric flux in this box equals -6.6 Vm + 4.5 Vm = -2.1 Vm
===A Computational Model===


To determine the amount of charge enclosed by the box, we use Gauss's Law. Since we know the sum of the electric flux, in order to find q (inside the box) we just have to multiply summed electric flux and epsilon naught (8.85 e-12 unit)
Go to the following link to have a look at the picture: http://i64.tinypic.com/mil0sz.jpg


Total Charge: -2.1 x 8.85 x 10 ^ (-12) = -1.8585 x 10 ^ (-11) C


===Middling===
==Examples==
===Difficult===
The Large Hadron Collider (LHC) is the world's largest and most powerful particle collider, and its functioning is based on the same principle as a simple cyclotron. It is the largest, most complex experimental facility ever built, and the largest single machine in the world. It was built by the European Organization for Nuclear Research (CERN). The LHC's aim is to allow physicists to test the predictions of different theories of particle physics, high-energy physics and in particular, to further test the properties of the Higgs Boson.


==Connectedness==
==Connectedness==
#How is this topic connected to something that you are interested in?
#How is this topic connected to something that you are interested in?
I have been closely monitoring and following the developments at the Large Hadron Collider at CERN. The device's functioning and the underlying principle it works on got me interested in this field. This led me to study more on cyclotrons and particle accelerators.
#How is it connected to your major?
#How is it connected to your major?
#Is there an interesting industrial application?
#Is there an interesting industrial application?
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==History==
==History==


Thermodynamics was brought up as a science in the 18th and 19th centuries.  However, it was first brought up by Galilei, who introduced the concept of temperature and invented the first thermometer. G. Black first introduced the word 'thermodynamics'.  Later, G. Wilke introduced another unit of measurement known as the calorie that measures heat.  The idea of thermodynamics was brought up by Nicolas Leonard Sadi Carnot.  He is often known as "the father of thermodynamics".  It all began with the development of the steam engine during the Industrial Revolution.  He devised an ideal cycle of operation. During his observations and experimentations, he had the incorrect notion that heat is conserved, however he was able to lay down theorems that led to the development of thermodynamics. In the 20th century, the science of thermodynamics became a conventional term and a basic division of physics. Thermodynamics dealt with the study of general properties of physical systems under equilibrium and the conditions necessary to obtain equilibrium.
The cyclotron was first developed by Lawrence and Livingston at the University of California, Berkeley. Lawrence, having worked extensively on electromagnets before, was behind much of the theoretical work. On the other hand, Livingstone was responsible for translating that to a tangible device. When the device was created, it was the strongest particle accelerator of its kind. This was true till another accelerator was constructed in Leningrad, at the Radium Institute.


== See also ==
== See also ==
Line 70: Line 77:


===External links===
===External links===
[http://www.wsj.com/articles/physicists-restart-souped-up-hadron-collider-1437948498/]
[http://www.theguardian.com/science/cern/]
[http://www.express.co.uk/news/world/565315/Scientists-at-Large-Hadron-Collider-hope-to-make-contact-with-PARALLEL-UNIVERSE-in-days/\


Internet resources on this topic


==References==
==References==


https://www.grc.nasa.gov/www/k-12/airplane/thermo0.html
Baldwin, Paul. "Scientists at Large Hadron Collider Hope to Make Contact with PARALLEL UNIVERSE in Days." N.p., n.d. Web. 05 Dec. 2015.
http://hyperphysics.phy-astr.gsu.edu/hbase/thermo/thereq.html
 
https://www.grc.nasa.gov/www/k-12/airplane/thermo2.html
"Latest Experiment at Large Hadron Collider Reports First Results." MIT News. N.p., n.d. Web. 05 Dec. 2015.
http://www.phys.nthu.edu.tw/~thschang/notes/GP21.pdf
 
http://www.eoearth.org/view/article/153532/
"Large Hadron Collider Starts Doing Science Again." Scientific American. N.p., n.d. Web. 05 Dec. 2015.


[[Category:Which Category did you place this in?]]
[[Category:Which Category did you place this in?]]

Latest revision as of 23:44, 5 December 2015

Work of Adway Dhillon (adhillon6)

Short Description of Topic

The Main Idea

This page is about an apparatus called the Cyclotron. This device is used to accelerate charged particles (like protons, neutrons, alpha particles, etc.) and ions to high energies. It uses a combination of strong magnetic and electric fields to accelerate the charged particles. The two fields (electric and magnetic) are perpendicular to each other, hence very aptly name "crossed fields". When the charged particle is accelerated by the cyclotron, the frequency of tis revolution in the two semi-secular plates (also called the "Ds") is independent of its energy. This is an important fact in the working of the device, as we will subsequently study in this lesson.


PRINCIPLE:
The working of the cyclotron is based on the fact that a positively charged particle can be accelerated to a sufficiently high energy with the help of smaller values of oscillating electric field by making it cross the same electric field time and again, with the help of a stringer magnetic field.


CONSTRUCTION:
A cyclotron device consists of two D-shaped hollow evacuated metal chambers (say D1 and D2) called the dees. These dees are placed horizontally with their diametric edges parallel and slightly separated from each other. The dees are connected to a high frequency oscillator which can produce a potential difference of the order of 10^4 volts at a frequency of about 10^7 hertz. The two dees are enclosed in an evacuated steel box and are well insulated from it. The box is placed inn a string magnetic field produced by two pole pieces of an electromagnets N,S. The magnetic field is perpendicular to the plane of the dees. At the centre of the device, P is a place of ionic source or positively charged (Check the diagram).

WORKING AND THEORY:
The positive ion to be accelerated is produced at P. Suppose, at that instant D1 is at negative potential and D2 is at positive potential. Therefore, the ion will be accelerated towards D1. On reaching inside D1, the ion will be in a field free space (as the two dees are hollow and metallic). Hence it moves with a constant speed in D1, say v. But due to a perpendicular magnetic field of strength B, the ion will describe a circular path of radius r (say) in D1.

Now in case the time taken by the positive ion to describe a semicircular path is equal to the time during which half cycle of the electric oscillator is completed, then as the ion arrives in the gap between the two dees, the polarity of the two dees is reversed, i.e. D1 becomes positive and D2 becomes negative. Then, the positive ion is accelerated towards D2 and it enters D2 with a greater speed, which remains constant in D2. The ion will describe a semicircular path of greater radius due to a perpendicular magnetic field and again will arrive in the gap between the two dees exactly at the instant, the polarity of the two dees is reversed. Thus, the positive ion will go on accelerating every time it comes into the gap between the dees and will go on describing a circular path of greater and greater radius with greater and greater speed and finally acquires a sufficiently high energy. The accelerated ops can be removed out of the dees from the window W, by applying at the elected field across the deflecting plates E and F (check the diagram).


A Mathematical Model

The charged particle describes a circular path of radius r (say) in D1, due to the perpendicular magnetic field B. Hence, the magnetic force experienced by the particle is balanced by the centripetal force on the particle due to its circular motion (in a circle of radius r).
This gives us the following expression:
[math]\displaystyle{ Bqv = mv^2/r }[/math]

Here: m and q are the mass and the charge of the ion respectively.

Therefore: [math]\displaystyle{ r = mv/Bq }[/math]

MAXIMUM ENERGY OF POSITIVE ION:
Let [math]\displaystyle{ v_0, r_o }[/math] = maximum velocity and maximum radius of the circular path followed by the positive ion in the cyclotron.

Then: [math]\displaystyle{ mv_0^2/r_0 = Bqv_0 or v_0 = Bqr_0/m }[/math]

Therefore: [math]\displaystyle{ Max K.E. = 1/2 mv_0^2 = 1/2 m(Bqr_0/m)^2 = B^2q^2r_0^2/2m }[/math]


CYCLOTRON FREQUENCY:
If T is the time period of oscillating electric field then: [math]\displaystyle{ T = 2t = 2pim/Bq }[/math]

The cyclotron frequency is given by


What are the mathematical equations that allow us to model this topic. For example [math]\displaystyle{ {\frac{d\vec{p}}{dt}}_{system} = \vec{F}_{net} }[/math] where p is the momentum of the system and F is the net force from the surroundings.

A Computational Model

Go to the following link to have a look at the picture: http://i64.tinypic.com/mil0sz.jpg


Examples

The Large Hadron Collider (LHC) is the world's largest and most powerful particle collider, and its functioning is based on the same principle as a simple cyclotron. It is the largest, most complex experimental facility ever built, and the largest single machine in the world. It was built by the European Organization for Nuclear Research (CERN). The LHC's aim is to allow physicists to test the predictions of different theories of particle physics, high-energy physics and in particular, to further test the properties of the Higgs Boson.

Connectedness

  1. How is this topic connected to something that you are interested in?

I have been closely monitoring and following the developments at the Large Hadron Collider at CERN. The device's functioning and the underlying principle it works on got me interested in this field. This led me to study more on cyclotrons and particle accelerators.

  1. How is it connected to your major?
  2. Is there an interesting industrial application?

History

The cyclotron was first developed by Lawrence and Livingston at the University of California, Berkeley. Lawrence, having worked extensively on electromagnets before, was behind much of the theoretical work. On the other hand, Livingstone was responsible for translating that to a tangible device. When the device was created, it was the strongest particle accelerator of its kind. This was true till another accelerator was constructed in Leningrad, at the Radium Institute.

See also

Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?

Further reading

Books, Articles or other print media on this topic

External links

[1] [2] [http://www.express.co.uk/news/world/565315/Scientists-at-Large-Hadron-Collider-hope-to-make-contact-with-PARALLEL-UNIVERSE-in-days/\


References

Baldwin, Paul. "Scientists at Large Hadron Collider Hope to Make Contact with PARALLEL UNIVERSE in Days." N.p., n.d. Web. 05 Dec. 2015.

"Latest Experiment at Large Hadron Collider Reports First Results." MIT News. N.p., n.d. Web. 05 Dec. 2015.

"Large Hadron Collider Starts Doing Science Again." Scientific American. N.p., n.d. Web. 05 Dec. 2015.