Magnetic Torque - Revision history

Aadams335: /* The Main Idea */

2025-04-10T02:53:42Z

The Main Idea

← Older revision		Revision as of 22:53, 9 April 2025
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	Magnetic torque is induced when a magnetic field causes a current carrying coil of wire to twist.		Magnetic torque is induced when a magnetic field causes a current carrying coil of wire to twist.
	[[File:torqueexample.png\|thumb\|Example of Magnetic Torque]]		[[File:torqueexample.png\|thumb\|Example of Magnetic Torque]]
	==The Main Idea==		==The Main Idea: EDITED BY ANNA ADAMS 2025==

	The idea behind this concept is that as current flows through a wire, a magnetic field is produced. This magnetic field causes a force to act upon the wire causing it to twist. An example of this phenomenon is the movement of a compass needle by the Earth's magnetic field. Another example is a hanging coil that twists in the direction of the magnetic field of a bar magnet.		The idea behind this concept is that as current flows through a wire, a magnetic field is produced. This magnetic field causes a force to act upon the wire causing it to twist. An example of this phenomenon is the movement of a compass needle by the Earth's magnetic field. Another example is a hanging coil that twists in the direction of the magnetic field of a bar magnet.

Aadams335: /* The Main Idea */

2025-04-10T02:53:11Z

The Main Idea

← Older revision		Revision as of 22:53, 9 April 2025
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	Here is a video on Asymmetric Magnet Torque		Here is a video on Asymmetric Magnet Torque
	[http://www.youtube.com/watch?v=LD6TX5IH5po Asymmetric Magnet Torque]		[http://www.youtube.com/watch?v=LD6TX5IH5po Asymmetric Magnet Torque]

	==A Mathematical Model==		==A Mathematical Model==
	The overarching equation that encapsulates this physical phenomena is as follows:		The overarching equation that encapsulates this physical phenomena is as follows:

Daniel72: /* Magnetic Dipole Moment */ Clarified the definition of the direction of Magnetic Dipole Moment. It does not in fact point in the direction of the magnetic field (at least not always), but along the magnetic dipole.

2023-11-12T01:12:59Z

Magnetic Dipole Moment: Clarified the definition of the direction of Magnetic Dipole Moment. It does not in fact point in the direction of the magnetic field (at least not always), but along the magnetic dipole.

← Older revision		Revision as of 21:12, 11 November 2023
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	===Magnetic Dipole Moment===		===Magnetic Dipole Moment===

	The magnetic dipole moment of a current carrying loop of wire, '''µ''', is defined as a vector pointing in the direction of the magnetic ~~field that~~ the loop ~~makes along~~ its ~~axis given~~ by the right hand rule.		The magnetic dipole moment of a current carrying loop of wire, '''µ''', is defined as a vector pointing in the direction of the magnetic dipole (South to North) perpendicular to the plane created by the wire loop, and its direction is determined by using the right hand rule (fingers curling along the direction of the current, thumb pointing in dipole direction.)

	<math> µ = IA = Iw*h </math>		<math> µ = IA = Iw*h </math>

Wpoe: /* A Mathematical Model */

2019-09-01T01:01:31Z

A Mathematical Model

← Older revision		Revision as of 21:01, 31 August 2019
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	The torque provided by each of the magnetic forces around the axle is equal to the distance from the axle times the component of the force perpendicular to the lever. Twist applied is due to the w - sides of the loop where torque acts out of the page. This causes a clockwise twist.		The torque provided by each of the magnetic forces around the axle is equal to the distance from the axle times the component of the force perpendicular to the lever. Twist applied is due to the w - sides of the loop where torque acts out of the page. This causes a clockwise twist.

	~~Fperpendicular = IwBsin(x) where the arm is equal to h/2~~
	~~each side exerts a force of 2(IwBsin(x))(h/2)~~

	~~'''τ'''~~ = ~~IwB~~(~~sinx~~) ~~and '''µ'''~~ = ~~Iwh~~		<math> F_{perpendicular} = IwBsin(x) </math> where the arm is equal to h/2, each side exerts a force <math> F = 2(IwBsin(x))(h/2) </math>

	~~'''µ''' x '''B''' = µBsin(x) = '''τ'''~~

	~~The right hand rule for the direction of torque is as follows: the fingers of your right hand curl in the direction the loop will rotate,~~ and ~~your thumb will point the the direction of torque. The direction of the torque vector will be along the axle around which the loop rotates.~~		<math> τ = IwBsin(x) </math> and <math> µ = Iw*h </math>


			<math> τ = µ x B = µBsin(x) </math>


			The right hand rule for the direction of torque is as follows: the fingers of your right hand curl in the direction the loop will rotate, and your thumb will point the the direction of torque. The direction of the torque vector will be along the axle around which the loop rotates. For a more in depth explanation of the right hand rule see [[Right-Hand Rule]]

	===Magnetic Dipole Moment===		===Magnetic Dipole Moment===
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	The magnetic dipole moment of a current carrying loop of wire, '''µ''', is defined as a vector pointing in the direction of the magnetic field that the loop makes along its axis given by the right hand rule.		The magnetic dipole moment of a current carrying loop of wire, '''µ''', is defined as a vector pointing in the direction of the magnetic field that the loop makes along its axis given by the right hand rule.

	µ = IA = ~~Iwh~~		<math> µ = IA = Iw*h </math>

	The coil tends to twist in a direction to make '''µ''' line up with '''B'''.		The coil tends to twist in a direction to make '''µ''' line up with '''B'''.
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	'''τ''' has units of N*m		'''τ''' has units of N*m

	'''µ''' has units of A*m^^2		'''µ''' has units of A*m^2

	'''B''' has units of tesla		'''B''' has units of tesla or T

	From this, it must be that one Nm(which interestingly defines work) is equal to one tesla A*m^^2. From a discussion of units alone, it is important to think about what sorts of questions the professor might ask, meaning questions could include an analyses of the work that must be added to a system to keep it stationary for example.		From this, it must be that one Nm (which interestingly defines work) is equal to one tesla A*m^2. From a discussion of units alone, it is important to think about what sorts of questions the professor might ask, meaning questions could include an analyses of the work that must be added to a system to keep it stationary for example.

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

Wpoe: /* Examples */

2019-09-01T00:48:38Z

Examples

← Older revision		Revision as of 20:48, 31 August 2019
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	==Examples==		==Examples==
	Essentially, there are only a few categories of questions that can be asked relating to magnetic torque. These questions include a simple computation of magnetic torque given the dipole moment of a magnet, and the magnetic field being applied to the observation location. In this situation, you can either utilize a simple cross product, as in the equation listed above, or if the values are given as scalars, and it is known that they are perpendicular to each other in direction, you can utilize the equation: <math> \|τ\| = \|µ\|\|B\|cos(90) = µB </math>. This is the essential question involving the equation listed above for magnetic torque. However, the professor can also ask questions relating to material learned from physics 1 involving angular frequencies and other products of angular momentum.		Essentially, there are only a few categories of questions that can be asked relating to magnetic torque. These questions include a simple computation of magnetic torque given the dipole moment of a magnet, and the magnetic field being applied to the observation location. In this situation, you can either utilize a simple cross product, as in the equation listed above, or if the values are given as scalars, and it is known that they are perpendicular to each other in direction, you can utilize the equation: <math> \|τ\| = \|µ\| * \|B\|cos(90) = \|µ\| * \|B\| </math>. This is the essential question involving the equation listed above for magnetic torque. However, the professor can also ask questions relating to material learned from physics 1 involving angular frequencies and other products of angular momentum.

	[https://www.youtube.com/watch?v=xER1_SYql44 Torque on Current Carrying Loop]		[https://www.youtube.com/watch?v=xER1_SYql44 Torque on Current Carrying Loop]

Wpoe: /* Examples */

2019-09-01T00:48:04Z

Examples

← Older revision		Revision as of 20:48, 31 August 2019
Line 76:		Line 76:

	==Examples==		==Examples==
	Essentially, there are only a few categories of questions that can be asked relating to magnetic torque. These questions include a simple computation of magnetic torque given the dipole moment of a magnet, and the magnetic field being applied to the observation location. In this situation, you can either utilize a simple cross product, as in the equation listed above, or if the values are given as scalars, and it is known that they are perpendicular to each other in direction, you can utilize the equation: <math> \|τ\| = µ~~Bcos~~\|90\|= µB </math>. This is the essential question involving the equation listed above for magnetic torque. However, the professor can also ask questions relating to material learned from physics 1 involving angular frequencies and other products of angular momentum.		Essentially, there are only a few categories of questions that can be asked relating to magnetic torque. These questions include a simple computation of magnetic torque given the dipole moment of a magnet, and the magnetic field being applied to the observation location. In this situation, you can either utilize a simple cross product, as in the equation listed above, or if the values are given as scalars, and it is known that they are perpendicular to each other in direction, you can utilize the equation: <math> \|τ\| = \|µ\|\|B\|cos(90) = µB </math>. This is the essential question involving the equation listed above for magnetic torque. However, the professor can also ask questions relating to material learned from physics 1 involving angular frequencies and other products of angular momentum.

	[https://www.youtube.com/watch?v=xER1_SYql44 Torque on Current Carrying Loop]		[https://www.youtube.com/watch?v=xER1_SYql44 Torque on Current Carrying Loop]

Wpoe: /* Examples */

2019-09-01T00:47:14Z

Examples

← Older revision		Revision as of 20:47, 31 August 2019
Line 76:		Line 76:

	==Examples==		==Examples==
	Essentially, there are only a few categories of questions that can be asked relating to magnetic torque. These questions include a simple computation of magnetic torque given the dipole moment of a magnet, and the magnetic field being applied to the observation location. In this situation, you can either utilize a simple cross product, as in the equation listed above, or if the values are given as scalars, and it is known that they are perpendicular to each other in direction, you can utilize the equation: ~~'''~~\|τ\| = µBcos\|90\|= µB~~'''~~. This is the essential question involving the equation listed above for magnetic torque. However, the professor can also ask questions relating to material learned from physics 1 involving angular frequencies and other products of angular momentum.		Essentially, there are only a few categories of questions that can be asked relating to magnetic torque. These questions include a simple computation of magnetic torque given the dipole moment of a magnet, and the magnetic field being applied to the observation location. In this situation, you can either utilize a simple cross product, as in the equation listed above, or if the values are given as scalars, and it is known that they are perpendicular to each other in direction, you can utilize the equation: <math> \|τ\| = µBcos\|90\|= µB </math>. This is the essential question involving the equation listed above for magnetic torque. However, the professor can also ask questions relating to material learned from physics 1 involving angular frequencies and other products of angular momentum.

	[https://www.youtube.com/watch?v=xER1_SYql44 Torque on Current Carrying Loop]		[https://www.youtube.com/watch?v=xER1_SYql44 Torque on Current Carrying Loop]

Wpoe: /* Examples */

2019-09-01T00:46:14Z

Examples

← Older revision		Revision as of 20:46, 31 August 2019
Line 76:		Line 76:

	==Examples==		==Examples==
	Essentially, there are only a few categories of questions that can be asked relating to magnetic torque. These questions include a simple computation of magnetic torque given the dipole moment of a magnet, and the magnetic field being applied to the observation location. In this situation, you can either utilize a simple cross product, as in the equation listed above, or if the values are given as scalars, and it is known that they are perpendicular to each other in direction, you can utilize the equation: '''\|τ\| = µBcos\|90\|= µB'''. This is the essential question involving the equation listed above for magnetic torque. However, the professor can also ask questions relating to material learned from physics 1 involving angular frequencies and other products of angular momentum. ~~The relationship is defined in the following illustration~~		Essentially, there are only a few categories of questions that can be asked relating to magnetic torque. These questions include a simple computation of magnetic torque given the dipole moment of a magnet, and the magnetic field being applied to the observation location. In this situation, you can either utilize a simple cross product, as in the equation listed above, or if the values are given as scalars, and it is known that they are perpendicular to each other in direction, you can utilize the equation: '''\|τ\| = µBcos\|90\|= µB'''. This is the essential question involving the equation listed above for magnetic torque. However, the professor can also ask questions relating to material learned from physics 1 involving angular frequencies and other products of angular momentum.

	~~[[File:IMG_1362.jpg]]~~

	[https://www.youtube.com/watch?v=xER1_SYql44 Torque on Current Carrying Loop]		[https://www.youtube.com/watch?v=xER1_SYql44 Torque on Current Carrying Loop]

Wpoe: /* The Main Idea */

2019-09-01T00:44:00Z

The Main Idea

← Older revision		Revision as of 20:44, 31 August 2019
Line 25:		Line 25:
	Here is a video on Asymmetric Magnet Torque		Here is a video on Asymmetric Magnet Torque
	[http://www.youtube.com/watch?v=LD6TX5IH5po Asymmetric Magnet Torque]		[http://www.youtube.com/watch?v=LD6TX5IH5po Asymmetric Magnet Torque]
			==A Mathematical Model==

	===A Mathematical Model===
	The overarching equation that encapsulates this physical phenomena is as follows:		The overarching equation that encapsulates this physical phenomena is as follows:
	: <math> \boldsymbol{\tau} = \boldsymbol{\mu} \times\mathbf{B}</math>		: <math> \boldsymbol{\tau} = \boldsymbol{\mu} \times\mathbf{B}</math>
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	From this, it must be that one Nm(which interestingly defines work) is equal to one tesla A*m^^2. From a discussion of units alone, it is important to think about what sorts of questions the professor might ask, meaning questions could include an analyses of the work that must be added to a system to keep it stationary for example.		From this, it must be that one Nm(which interestingly defines work) is equal to one tesla A*m^^2. From a discussion of units alone, it is important to think about what sorts of questions the professor might ask, meaning questions could include an analyses of the work that must be added to a system to keep it stationary for example.

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

	Click here to view the PHET Interactive Model created by the University of Colorado		Click here to view the PHET Interactive Model created by the University of Colorado

Wpoe: /* Magnetic Dipole Moment */

2019-09-01T00:42:21Z

Magnetic Dipole Moment

← Older revision		Revision as of 20:42, 31 August 2019
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	The coil tends to twist in a direction to make '''µ''' line up with '''B'''.		The coil tends to twist in a direction to make '''µ''' line up with '''B'''.

	[[File:~~Magnetic dipole moment~~.~~jpeg~~]]		[[File:Magnetic_Torque_Mathematical_Model.png]]

	===Units Discussion===		===Units Discussion===