The Differential Form of Ampere's Law - Revision history

Yahiaali at 04:56, 28 November 2016

2016-11-28T04:56:35Z

← Older revision		Revision as of 00:56, 28 November 2016
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	~~'''Claimed by Yahia Ali (Fall 2016)'''~~

	Many physical laws taught in Physics I and II are only correct at non-relativistic speeds (where the speed is much less than the speed of light). This is caused by a phenomenon known as "relativistic retardation" that refers to the fact that changes in magnetic and electric fields propagate at the speed of light and, therefore, cannot be measured instantaneously. Typically, this is not an issue if the particles are moving much slower than the speed of light because the error between non-relativistic forms of physical laws is often so small that it is irrelevant. As particles approach speeds close to the speed of light these differences can become significant and methods for finding electric or magnetic fields (such as the Biot-Savart law) are no longer accurate. This is not true for Ampere's Law which makes it useful for problems involving particles moving at near light speeds.		Many physical laws taught in Physics I and II are only correct at non-relativistic speeds (where the speed is much less than the speed of light). This is caused by a phenomenon known as "relativistic retardation" that refers to the fact that changes in magnetic and electric fields propagate at the speed of light and, therefore, cannot be measured instantaneously. Typically, this is not an issue if the particles are moving much slower than the speed of light because the error between non-relativistic forms of physical laws is often so small that it is irrelevant. As particles approach speeds close to the speed of light these differences can become significant and methods for finding electric or magnetic fields (such as the Biot-Savart law) are no longer accurate. This is not true for Ampere's Law which makes it useful for problems involving particles moving at near light speeds.

Yahiaali: /* A Computational Model */

2016-11-28T04:54:00Z

A Computational Model

← Older revision		Revision as of 00:54, 28 November 2016
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	'''Model of Curl Around a Wire with Conventional Current Moving Out of the Screen'''		'''Model of Curl Around a Wire with Conventional Current Moving Out of the Screen'''

	Glowscript link: https://trinket.io/glowscript/7c5c057c59		Glowscript link: https://trinket.io/glowscript/7c5c057c59?toggleCode=true

	The direction of curl is given by the right hand rule by putting your thumb in the direction of the current. The way your hand curls is the way the magnetic field curls.		The direction of curl is given by the right hand rule by putting your thumb in the direction of the current. The way your hand curls is the way the magnetic field curls.

Yahiaali: /* A Computational Model */

2016-11-28T04:53:25Z

A Computational Model

← Older revision		Revision as of 00:53, 28 November 2016
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	===A Computational Model===		===A Computational Model===

	'''Model of Curl Around a Wire with Conventional Current Moving Out of the Screen''': https://trinket.io/glowscript/7c5c057c59		'''Model of Curl Around a Wire with Conventional Current Moving Out of the Screen'''

			Glowscript link: https://trinket.io/glowscript/7c5c057c59

	The direction of curl is given by the right hand rule by putting your thumb in the direction of the current. The way your hand curls is the way the magnetic field curls.		The direction of curl is given by the right hand rule by putting your thumb in the direction of the current. The way your hand curls is the way the magnetic field curls.

Yahiaali: /* A Computational Model */

2016-11-28T04:48:57Z

A Computational Model

← Older revision		Revision as of 00:48, 28 November 2016
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	===A Computational Model===		===A Computational Model===

	Model of Curl Around a Wire with Conventional Current Moving Out of the Screen		'''Model of Curl Around a Wire with Conventional Current Moving Out of the Screen''': https://trinket.io/glowscript/7c5c057c59

	https://trinket.io~~/embed~~/glowscript/~~7c5c057c5~~

	The direction of curl is given by the right hand rule by putting your thumb in the direction of the current. The way your hand curls is the way the magnetic field curls.		The direction of curl is given by the right hand rule by putting your thumb in the direction of the current. The way your hand curls is the way the magnetic field curls.

Yahiaali: /* A Computational Model */

2016-11-28T04:39:09Z

A Computational Model

← Older revision		Revision as of 00:39, 28 November 2016
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	===A Computational Model===		===A Computational Model===

	~~[[File~~:~~curltext~~.~~png]]~~		Model of Curl Around a Wire with Conventional Current Moving Out of the Screen

			https://trinket.io/embed/glowscript/7c5c057c5

	The direction of curl is given by the right hand rule by putting your thumb in the direction of the current. The way your hand curls is the way the magnetic field curls.		The direction of curl is given by the right hand rule by putting your thumb in the direction of the current. The way your hand curls is the way the magnetic field curls.

	~~Model of Curl Around a Wire with Conventional Current Moving Out of the Screen~~
	~~https://trinket.io/embed/glowscript/7c5c057c5~~

	==Examples==		==Examples==

Yahiaali: /* Curl */

2016-11-28T04:38:16Z

Curl

← Older revision		Revision as of 00:38, 28 November 2016
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	The direction of curl is given by the right hand rule by putting your thumb in the direction of the current. The way your hand curls is the way the magnetic field curls.		The direction of curl is given by the right hand rule by putting your thumb in the direction of the current. The way your hand curls is the way the magnetic field curls.

	~~<iframe src="~~https://trinket.io/embed/glowscript/~~7c5c057c59" width="100%" height="600" frameborder="0" marginwidth="0" marginheight="0" allowfullscreen></iframe>~~		Model of Curl Around a Wire with Conventional Current Moving Out of the Screen
			https://trinket.io/embed/glowscript/7c5c057c5

	==Examples==		==Examples==

Yahiaali: /* A Computational Model */

2016-11-28T04:34:09Z

A Computational Model

← Older revision		Revision as of 00:34, 28 November 2016
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	The direction of curl is given by the right hand rule by putting your thumb in the direction of the current. The way your hand curls is the way the magnetic field curls.		The direction of curl is given by the right hand rule by putting your thumb in the direction of the current. The way your hand curls is the way the magnetic field curls.

			<iframe src="https://trinket.io/embed/glowscript/7c5c057c59" width="100%" height="600" frameborder="0" marginwidth="0" marginheight="0" allowfullscreen></iframe>

	==Examples==		==Examples==

Yahiaali: /* Curl */

2016-11-28T04:03:57Z

Curl

← Older revision		Revision as of 00:03, 28 November 2016
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	[[File:curltext.png]]		[[File:curltext.png]]

	The direction of curl is given by the right hand rule by putting your thumb in the direction of the current. The way your hand curls is the way the magnetic field curls.		The direction of curl is given by the right hand rule by putting your thumb in the direction of the current. The way your hand curls is the way the magnetic field curls.

	==Examples==		==Examples==

Yahiaali at 03:58, 28 November 2016

2016-11-28T03:58:52Z

← Older revision		Revision as of 23:58, 27 November 2016
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	[[File:Tiefe Hirnstimulation - Sonden RoeSchaedel ap.jpg]]		[[File:Tiefe Hirnstimulation - Sonden RoeSchaedel ap.jpg]]
	X-Ray of a patient with Deep Brain Stimulation
	Attribution: https://en.wikipedia.org/wiki/Deep_brain_stimulation		X-Ray of a patient with Deep Brain Stimulation. Attribution: https://en.wikipedia.org/wiki/Deep_brain_stimulation

	The differential form of Ampere's is simply another way of representing Ampere's Law and therefore does not differ from the integral form of Ampere's Law in its applications. In the field of biomedical engineering, the application of Ampere's Law in advanced computational models of the human brain may one day lead to a better understanding of the electromagnetic effects that the activation of one neuron may have on an adjacent neuron. On a slightly larger scale, deep brain stimulation procedures involve the use of implantable electrodes to electrically stimulate targeted areas of the brain for the treatment of neurological illnesses such as Parkinsons' disease. Knowledge of Ampere's Law would imply that the use of one of these electrodes in the brain creates a curling magnetic field around the electrode that could affect neurons outside of those being intentionally targeted.		The differential form of Ampere's is simply another way of representing Ampere's Law and therefore does not differ from the integral form of Ampere's Law in its applications. In the field of biomedical engineering, the application of Ampere's Law in advanced computational models of the human brain may one day lead to a better understanding of the electromagnetic effects that the activation of one neuron may have on an adjacent neuron. On a slightly larger scale, deep brain stimulation procedures involve the use of implantable electrodes to electrically stimulate targeted areas of the brain for the treatment of neurological illnesses such as Parkinsons' disease. Knowledge of Ampere's Law would imply that the use of one of these electrodes in the brain creates a curling magnetic field around the electrode that could affect neurons outside of those being intentionally targeted.
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	===Further reading===		===Further reading===
	http://www.physnet.org/modules/pdf_modules/m138.pdf		#http://www.physnet.org/modules/pdf_modules/m138.pdf
			#http://ww3.haverford.edu/physics-astro/songs/ampere.PDF
	http://ww3.haverford.edu/physics-astro/songs/ampere.PDF


	==References==		==References==

	http://www.physics.byu.edu/faculty/rees/220/book/Lesson8.pdf		#http://www.physics.byu.edu/faculty/rees/220/book/Lesson8.pdf
	Matter and Interactions, 4th Edition		#Matter and Interactions, 4th Edition
	Deep Brain Stimulation (WebMD): http://www.webmd.com/parkinsons-disease/guide/dbs-parkinsons#1		#Deep Brain Stimulation (WebMD): http://www.webmd.com/parkinsons-disease/guide/dbs-parkinsons#1

	[[Category: Maxwell's Equations]]		[[Category: Maxwell's Equations]]

Yahiaali: /* Connectedness */

2016-11-28T03:57:31Z

Connectedness

← Older revision		Revision as of 23:57, 27 November 2016
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	[[File:Tiefe Hirnstimulation - Sonden RoeSchaedel ap.jpg]]		[[File:Tiefe Hirnstimulation - Sonden RoeSchaedel ap.jpg]]
			X-Ray of a patient with Deep Brain Stimulation
			Attribution: https://en.wikipedia.org/wiki/Deep_brain_stimulation

	The differential form of Ampere's is simply another way of representing Ampere's Law and therefore does not differ from the integral form of Ampere's Law in its applications. In the field of biomedical engineering, the application of Ampere's Law in advanced computational models of the human brain may one day lead to a better understanding of the electromagnetic effects that the activation of one neuron may have on an adjacent neuron. On a slightly larger scale, deep brain stimulation procedures involve the use of implantable electrodes to electrically stimulate targeted areas of the brain for the treatment of neurological illnesses such as Parkinsons' disease. Knowledge of Ampere's Law would imply that the use of one of these electrodes in the brain creates a curling magnetic field around the electrode that could affect neurons outside of those being intentionally targeted.		The differential form of Ampere's is simply another way of representing Ampere's Law and therefore does not differ from the integral form of Ampere's Law in its applications. In the field of biomedical engineering, the application of Ampere's Law in advanced computational models of the human brain may one day lead to a better understanding of the electromagnetic effects that the activation of one neuron may have on an adjacent neuron. On a slightly larger scale, deep brain stimulation procedures involve the use of implantable electrodes to electrically stimulate targeted areas of the brain for the treatment of neurological illnesses such as Parkinsons' disease. Knowledge of Ampere's Law would imply that the use of one of these electrodes in the brain creates a curling magnetic field around the electrode that could affect neurons outside of those being intentionally targeted.