Biot-Savart Law for Currents - Revision history

Aochal: /* Claimed by Abigail Ochal Fall 2020 */

2020-11-15T19:13:37Z

Claimed by Abigail Ochal Fall 2020

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	== '''Claimed by Abigail Ochal Fall 2020''' ==		'''Claimed by Abigail Ochal Fall 2020'''


	==Biot-Savart Law==		==Biot-Savart Law==

Aochal at 19:13, 15 November 2020

2020-11-15T19:13:18Z

← Older revision		Revision as of 15:13, 15 November 2020
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	'''Claimed by Abigail Ochal Fall 2020'''
			== '''Claimed by Abigail Ochal Fall 2020''' ==


	==Biot-Savart Law==		==Biot-Savart Law==

Aochal: /* Connectedness */

2020-11-15T19:12:18Z

Connectedness

← Older revision		Revision as of 15:12, 15 November 2020
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	http://www.glowscript.org/#/user/matterandinteractions/folder/matterandinteractions/program/17-B-loop-with-r-dB.		http://www.glowscript.org/#/user/matterandinteractions/folder/matterandinteractions/program/17-B-loop-with-r-dB.
	==Connectedness==		==Connectedness==
	In biochemistry, there are lots of instruments that rely on magnets and magnetic fields to gather information about different molecules. One example is proton nuclear magnetic resonance (H+ NMR), which creates peaks corresponding to hydrogen atoms (protons) on adjacent carbon atoms in organic molecules. Another example, which is commonly used in medicine, is magnetic resonance imaging (MRI), which takes images using magnets to interact with protons in the body. For more information, go to the "External Links" Section.		In biochemistry, there are lots of instruments that rely on magnets and magnetic fields to gather information about different molecules.

			One example is proton nuclear magnetic resonance (H+ NMR), which creates peaks corresponding to hydrogen atoms (protons) on adjacent carbon atoms in organic molecules.

			Another example, which is commonly used in medicine, is magnetic resonance imaging (MRI), which takes images using magnets to interact with protons in the body. For more information, go to the "External Links" Section.

	==History==		==History==
	Jean-Baptiste Biot and Félix Savart worked together to understand current and magnetic fields during the 1820's. Find more information about the history in "External Links"		Jean-Baptiste Biot and Félix Savart worked together to understand current and magnetic fields during the 1820's. Find more information about the history in "External Links"

Aochal at 19:11, 15 November 2020

2020-11-15T19:11:32Z

← Older revision		Revision as of 15:11, 15 November 2020
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	http://www.glowscript.org/#/user/matterandinteractions/folder/matterandinteractions/program/17-B-loop-with-r-dB.		http://www.glowscript.org/#/user/matterandinteractions/folder/matterandinteractions/program/17-B-loop-with-r-dB.
			==Connectedness==
			In biochemistry, there are lots of instruments that rely on magnets and magnetic fields to gather information about different molecules. One example is proton nuclear magnetic resonance (H+ NMR), which creates peaks corresponding to hydrogen atoms (protons) on adjacent carbon atoms in organic molecules. Another example, which is commonly used in medicine, is magnetic resonance imaging (MRI), which takes images using magnets to interact with protons in the body. For more information, go to the "External Links" Section.
			==History==
			Jean-Baptiste Biot and Félix Savart worked together to understand current and magnetic fields during the 1820's. Find more information about the history in "External Links"
	== See also ==		== See also ==
	[Right Hand Rule[http://www.physicsbook.gatech.edu/Right-Hand_Rule]]		[Right Hand Rule[http://www.physicsbook.gatech.edu/Right-Hand_Rule]]
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	==External Links==		==External Links==
	[[Category:Which Category did you place this in?]]		[[Category:Which Category did you place this in?]]

			[https://www.nibib.nih.gov/science-education/science-topics/magnetic-resonance-imaging-mri More information on MRI's]

			[https://www.britannica.com/biography/Jean-Baptiste-Biot History of Biot-Savart]

Aochal: /* A Mathematical Model */

2020-11-15T18:57:06Z

A Mathematical Model

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	<math>B = \frac{\mu_0I}{4\pi}\frac{\mathrm{d}\boldsymbol{\ell} \times \mathbf{\hat r}}{r^2},</math>		<math>B = \frac{\mu_0I}{4\pi}\frac{\mathrm{d}\boldsymbol{\ell} \times \mathbf{\hat r}}{r^2},</math>
	[[File:biotsavartlawforcurrentsaochal.png\|~~350~~ px\|thumb\|alt text]]		[[File:biotsavartlawforcurrentsaochal.png\|400 px\|thumb\|alt text]]

	Because the shape of the current carrying wire can vary from a straight wire to a loop, we must integrate over the region of the wire.		Because the shape of the current carrying wire can vary from a straight wire to a loop, we must integrate over the region of the wire.

Aochal: /* Long Wire Integration Example */

2020-11-15T18:56:18Z

Long Wire Integration Example

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	==Long Wire Integration Example==		==Long Wire Integration Example==
	[[File:IMG_2469.jpg\|~~200px~~\|thumb\|alt text]]		[[File:IMG_2469.jpg\|300px\|thumb\|alt text]]
	====For a long wire of length L positioned along the x axis with current flowing in the positive x direction (as shown by image on right)====		====For a long wire of length L positioned along the x axis with current flowing in the positive x direction (as shown by image on right)====
	First, we start off with our adjusted Biot-Savart Formula for a slice of wire.		First, we start off with our adjusted Biot-Savart Formula for a slice of wire.

Aochal: /* Current Loop Without Integration */

2020-11-15T18:54:58Z

Current Loop Without Integration

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 ==Current Loop Integration Example==
 '''Saved for Elizabeth Clayton 10/7/2020'''
 ==A Computational Model==
 The following link shows the magnetic field produced by small segments of wire in a loop individually.

Aochal: /* Current Loop Without Integration */

2020-11-15T18:53:36Z

Current Loop Without Integration

← Older revision		Revision as of 14:53, 15 November 2020
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	==Current Loop Without Integration==		==Current Loop Without Integration==
	Sometimes it is necessary to set up integrals to solve magnetic field problems in physics. However, there are other ways to go about certain problems if integration is intimidating. One shortcut for this would be to find the magnitude of the magnetic field and then using the right hand rule to find the direction. This way, there are a few more steps, but there is no integration, and everything is more intuitive.		Sometimes it is necessary to set up integrals to solve magnetic field problems in physics. However, there are other ways to go about certain problems if integration is intimidating. One shortcut for this would be to find the magnitude of the magnetic field and then using the right hand rule to find the direction. This way, there are a few more steps, but there is no integration, and everything is more intuitive.


	For completing this, we follow the same steps as stated previously:		For completing this, we follow the same steps as stated previously:

	1. Breaking up the current carrying loop into smaller pieces,		Step 1. Breaking up the current carrying loop into smaller pieces,

	2. Find the magnitude of the magnetic field for each piece,		Step 2. Find the magnitude of the magnetic field for each piece,

	3. Use Right Hand Rule to determine the direction for each piece,		Step 3. Use Right Hand Rule to determine the direction for each piece,

	4. Use the superposition principle to find the net magnetic field of the loop		Step 4. Use the superposition principle to find the net magnetic field of the loop

	==A Computational Model==		==A Computational Model==

Aochal: /* Current Loop Without Integration */

2020-11-15T18:52:58Z

Current Loop Without Integration

← Older revision		Revision as of 14:52, 15 November 2020
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	For completing this, we follow the same steps as stated previously:		For completing this, we follow the same steps as stated previously:

	1. Breaking up the current carrying loop into smaller pieces,		1. Breaking up the current carrying loop into smaller pieces,
	2. Find the magnitude of the magnetic field for each piece.
			2. Find the magnitude of the magnetic field for each piece,

	3. Use Right Hand Rule to determine the direction for each piece,		3. Use Right Hand Rule to determine the direction for each piece,

	4. Use the superposition principle to find the net magnetic field of the loop		4. Use the superposition principle to find the net magnetic field of the loop

Aochal: /* A Mathematical Model */

2020-11-15T18:52:34Z

A Mathematical Model

← Older revision		Revision as of 14:52, 15 November 2020
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	<math> B = \frac{\mu_0}{4\pi}\frac{LI}{r(r^2 + (L/2)^2)^{1/2}} </math> for length <math> L </math>, conventional current <math> I </math>, a perpendicular distance <math> r </math> from the center of the wire, or,		<math> B = \frac{\mu_0}{4\pi}\frac{LI}{r(r^2 + (L/2)^2)^{1/2}} </math> for length <math> L </math>, conventional current <math> I </math>, a perpendicular distance <math> r </math> from the center of the wire, or,
	<math> B = \frac{\mu_0}{4\pi}\frac{2I}{r} </math> if <math> L\>>\>> r. </math>		<math> B = \frac{\mu_0}{4\pi}\frac{2I}{r} </math> if <math> L\>>\>> r. </math>


	==Right Hand Rule==		==Right Hand Rule==