On Denoting - Revision history

23.243.116.88: /* Reference to something that does not exist */

2014-11-01T09:04:03Z

Reference to something that does not exist

← Older revision		Revision as of 11:04, 1 November 2014
Line 1:		Line 1:
	~~Hello. Let me~~ introduce ~~the writer~~. ~~Her title is Emilia Shroyer but it~~'s ~~not the most feminine name out there~~. ~~North Dakota~~ is ~~our beginning place~~. ~~One of the very very best issues in the world for me~~ is to ~~do aerobics and now I~~'~~m trying to earn money with it. Hiring is his profession~~.<br><br>~~Feel free to surf to my~~ weblog :: [http://~~nuvem~~.tk/~~altergalactica~~/~~NumbersdbEstepvu nuvem.tk~~]		I would like to introduce myself to you, I am Jayson Simcox but I don't like when people use my complete title. For years she's been residing in Kentucky but her spouse wants them to transfer. He is an information officer. It's not a typical factor but what she likes doing is to perform domino but she doesn't have the time recently.<br><br>My weblog :: [http://bigpolis.com/blogs/post/6503 live psychic reading]

en>Hmainsbot1: AWB general fixes and delink dates per :WP:DATELINK, :WP:YEARLINK and :MOS:UNLINKYEARS using AWB

2014-02-17T04:58:43Z

AWB general fixes and delink dates per WP:DATELINK, WP:YEARLINK and MOS:UNLINKYEARS using AWB

← Older revision		Revision as of 06:58, 17 February 2014
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	~~The '''gyroradius''' (also known as '''radius of gyration''', '''Larmor radius''' or '''cyclotron radius''') is the [[radius]] of the circular motion of a [[charged particle]] in~~ the ~~presence of a uniform [[magnetic field]]~~.		Hello. Let me introduce the writer. Her title is Emilia Shroyer but it's not the most feminine name out there. North Dakota is our beginning place. One of the very very best issues in the world for me is to do aerobics and now I'm trying to earn money with it. Hiring is his profession.<br><br>Feel free to surf to my weblog :: [http://nuvem.tk/altergalactica/NumbersdbEstepvu nuvem.tk]

	~~:<math>r_g = \frac{m v_{\perp}}{\|q\| B}</math>~~
	~~where~~
	~~:*<math>r_g \ </math>~~ is the ~~gyroradius,~~
	~~:*<math>m \ </math> is the mass of the charged particle,~~
	~~:*<math>v_{\perp}</math> is the velocity component perpendicular to the direction of the magnetic field,~~
	~~:*<math>q \ </math> is the charge of the particle, and~~
	~~:*<math>B \ </math>~~ is ~~the constant magnetic field~~.

	~~(All units are in [[SI]])~~

	~~Similarly, the [[frequency]]~~ of ~~this circular motion is known as~~ the ~~'''gyrofrequency''' or '''[[cyclotron frequency]]''', and is given in radian/second by:~~
	~~:<math>\omega_g = \frac{\|q\| B}{m}</math>~~
	~~and~~ in ~~Hz by:~~
	~~:<math>\ f_g = \frac{q B}{2 \pi m}</math>~~
	~~For electrons, this works out to be~~
	~~:<math>\nu_e = (2.8\times10^{10}\,\mathrm{Hz}/\mathrm{T})\times B</math>~~

	~~==Relativistic case==~~
	~~The formula for~~ the ~~gyroradius also holds~~ for ~~[[Special_relativity\|relativistic motion]]. In that case, the velocity and mass of the moving object has~~ to ~~be replaced by the relativistic momentum <math>m v_{\perp} \rightarrow p_{\perp}</math>:~~

	~~<math>r_g = \frac{p_{\perp}}{\|q\| B}</math>~~

	~~For rule-of-thumb calculations in [[Particle_accelerator\|accelerator]]~~ and ~~[[Astroparticle_physics\|astroparticle]] physics, the physical quantities can be expressed in proper units, which results in the simple numerical formula~~

	~~:<math>r_g/\mathrm{~~m~~} = 3~~.~~3 \times \frac{p_{\perp}/(\mathrm{GeV/c})}{\|Z\| (B/\mathrm{T})}</math>~~
	~~where~~
	~~:*<math>Z \ </math>~~ is ~~the charge of the moving object in elementary units~~.

	~~==Derivation==~~
	~~If the charged particle is moving, then it will experience a [[Lorentz force]] given by:~~

	~~:<math>\vec{F} = q(\vec{v} \times \vec{B})</math>~~
	~~where <math>\vec{v}</math> is the velocity vector, <math>\vec{B}</math> is the magnetic field vector, and~~ <~~math~~>q<~~/math~~> ~~is the particle's [[electric charge]].~~

	~~Notice that the direction of the force is given by the [[cross product]] of the velocity and magnetic field. Thus, the Lorentz force will always act perpendicular~~ to ~~the direction of motion, causing the particle to move in a circle ([[gyration\|gyrate]]). The radius of this circle <math>r_g</math> can be determined by equating the magnitude of the Lorentz force~~ to ~~the [[centripetal force]]:~~

	:~~<math>\frac{m v_{\perp}^2}{r_g} = qv_{\perp}B</math>~~
	~~where~~
	:~~<math>m</math> is the particle~~ [~~[mass]] (for high velocities the [[relativistic mass]]),~~
	:~~<math>{v_{\perp}}<~~/~~math> is the velocity component perpendicular to the direction of the magnetic field, and~~
	~~:<math>B<~~/~~math> is the strength of the field~~.

	~~Solving for <math>r_g<~~/~~math>, the gyroradius is determined to be:~~
	~~:<math>r_g = \frac{m v_{\perp}}{q B}<~~/~~math>~~

	~~Thus, the gyroradius is directly proportional to the particle mass and velocity, and inversely proportional to the particle electric charge, and the magnetic field strength~~.

	~~==See also==~~
	* [[Cyclotron]]
	* [[Magnetosphere particle motion]]

	~~==References & further reading==~~
	~~<div class="references-small">~~
	# {{cite book \| first=Francis F. \| last=Chen \| title=Introduction to Plasma Physics and Controlled Fusion, Vol. 1: Plasma Physics, 2nd ed. \| publisher=Plenum Press \| location=New York, NY USA \| year=1984 \| isbn=0-306-41332-9}}
	~~</div>~~

	~~[[Category:Plasma physics]]~~
	~~[[Category:Accelerator physics]~~]

78.30.132.61 at 12:42, 1 January 2014

2014-01-01T12:42:57Z

← Older revision		Revision as of 14:42, 1 January 2014
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	~~I would like~~ to ~~introduce myself to you~~, ~~I am Andrew~~ and ~~my spouse doesn't like it at all~~. ~~Office supervising~~ is ~~exactly where her main income arrives from. I~~'~~ve usually cherished residing~~ in ~~Alaska~~. ~~To climb is some thing she would never give up~~.<br><br>~~Also visit my webpage~~ - ~~free psychic;~~ [~~http~~://~~www~~.~~weddingwall~~.~~com~~.au/~~groups~~/~~easy-advice-~~for-~~successful~~-~~personal~~-~~development~~-~~today~~/ ~~view publisher site~~],		The '''gyroradius''' (also known as '''radius of gyration''', '''Larmor radius''' or '''cyclotron radius''') is the [[radius]] of the circular motion of a [[charged particle]] in the presence of a uniform [[magnetic field]].

			:<math>r_g = \frac{m v_{\perp}}{\|q\| B}</math>
			where
			:*<math>r_g \ </math> is the gyroradius,
			:*<math>m \ </math> is the mass of the charged particle,
			:*<math>v_{\perp}</math> is the velocity component perpendicular to the direction of the magnetic field,
			:*<math>q \ </math> is the charge of the particle, and
			:*<math>B \ </math> is the constant magnetic field.

			(All units are in [[SI]])

			Similarly, the [[frequency]] of this circular motion is known as the '''gyrofrequency''' or '''[[cyclotron frequency]]''', and is given in radian/second by:
			:<math>\omega_g = \frac{\|q\| B}{m}</math>
			and in Hz by:
			:<math>\ f_g = \frac{q B}{2 \pi m}</math>
			For electrons, this works out to be
			:<math>\nu_e = (2.8\times10^{10}\,\mathrm{Hz}/\mathrm{T})\times B</math>

			==Relativistic case==
			The formula for the gyroradius also holds for [[Special_relativity\|relativistic motion]]. In that case, the velocity and mass of the moving object has to be replaced by the relativistic momentum <math>m v_{\perp} \rightarrow p_{\perp}</math>:

			<math>r_g = \frac{p_{\perp}}{\|q\| B}</math>

			For rule-of-thumb calculations in [[Particle_accelerator\|accelerator]] and [[Astroparticle_physics\|astroparticle]] physics, the physical quantities can be expressed in proper units, which results in the simple numerical formula

			:<math>r_g/\mathrm{m} = 3.3 \times \frac{p_{\perp}/(\mathrm{GeV/c})}{\|Z\| (B/\mathrm{T})}</math>
			where
			:*<math>Z \ </math> is the charge of the moving object in elementary units.

			==Derivation==
			If the charged particle is moving, then it will experience a [[Lorentz force]] given by:

			:<math>\vec{F} = q(\vec{v} \times \vec{B})</math>
			where <math>\vec{v}</math> is the velocity vector, <math>\vec{B}</math> is the magnetic field vector, and <math>q</math> is the particle's [[electric charge]].

			Notice that the direction of the force is given by the [[cross product]] of the velocity and magnetic field. Thus, the Lorentz force will always act perpendicular to the direction of motion, causing the particle to move in a circle ([[gyration\|gyrate]]). The radius of this circle <math>r_g</math> can be determined by equating the magnitude of the Lorentz force to the [[centripetal force]]:

			:<math>\frac{m v_{\perp}^2}{r_g} = qv_{\perp}B</math>
			where
			:<math>m</math> is the particle [[mass]] (for high velocities the [[relativistic mass]]),
			:<math>{v_{\perp}}</math> is the velocity component perpendicular to the direction of the magnetic field, and
			:<math>B</math> is the strength of the field.

			Solving for <math>r_g</math>, the gyroradius is determined to be:
			:<math>r_g = \frac{m v_{\perp}}{q B}</math>

			Thus, the gyroradius is directly proportional to the particle mass and velocity, and inversely proportional to the particle electric charge, and the magnetic field strength.

			==See also==
			* [[Cyclotron]]
			* [[Magnetosphere particle motion]]

			==References & further reading==
			<div class="references-small">
			# {{cite book \| first=Francis F. \| last=Chen \| title=Introduction to Plasma Physics and Controlled Fusion, Vol. 1: Plasma Physics, 2nd ed. \| publisher=Plenum Press \| location=New York, NY USA \| year=1984 \| isbn=0-306-41332-9}}
			</div>

			[[Category:Plasma physics]]
			[[Category:Accelerator physics]]

en>Patriciathornton: /* Russell's concept of a denoting phrase */

2012-08-07T22:24:00Z

Russell's concept of a denoting phrase

New page

I would like to introduce myself to you, I am Andrew and my spouse doesn't like it at all. Office supervising is exactly where her main income arrives from. I've usually cherished residing in Alaska. To climb is some thing she would never give up.<br><br>Also visit my webpage - free psychic; [http://www.weddingwall.com.au/groups/easy-advice-for-successful-personal-development-today/ view publisher site],