Magnetic Dipole Moment - Revision history

Chrisvuong: updated the references so it has substance instead of just a placeholder

2026-04-22T09:08:58Z

updated the references so it has substance instead of just a placeholder

← Older revision		Revision as of 05:08, 22 April 2026
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	==References==		==References==
			* [http://www.phys.ufl.edu/~acosta/phy2061/lectures/MagneticDipoles.pdf Lecture PDF on Magnetic Dipole Moment]
	~~This section contains the the references you used while writing this page~~		* [http://hyperphysics.phy-astr.gsu.edu/hbase/magnetic/magmom.html HyperPhysics: Magnetic Moment]
			* [http://mriquestions.com/magnetic-dipole-moment.html MRI Questions: Magnetic Dipole Moment]

	[[Category:Fields]]		[[Category:Fields]]

Chrisvuong: changed mathematical model + computational model a little bit to improve on clarity

2026-04-22T08:26:28Z

changed mathematical model + computational model a little bit to improve on clarity

← Older revision		Revision as of 04:26, 22 April 2026
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	==Main Idea==		==Main Idea==
	A magnetic dipole moment describes the strength and orientation of a current loop as a magnetic source. For a loop carrying current, the magnetic dipole moment is a vector that points perpendicular to the plane of the loop, with direction ~~given~~ by the right-hand rule.		A magnetic dipole moment describes the strength and orientation of a current loop as a magnetic source. For a loop carrying current, the magnetic dipole moment is a vector that points perpendicular to the plane of the loop, with direction determined by the right-hand rule.

	The magnitude of the magnetic dipole moment is		The magnitude of the magnetic dipole moment is
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	:<math>\mu = NIA</math>		:<math>\mu = NIA</math>

	The magnetic dipole moment is ~~important~~ because it helps predict how a loop behaves in an external magnetic field. In particular, it is used to calculate torque and magnetic potential energy. Current loops, bar magnets, and even atoms can often be modeled as magnetic dipoles.		The magnetic dipole moment is useful because it helps predict how a loop behaves in an external magnetic field. In particular, it is used to calculate torque and magnetic potential energy. Current loops, bar magnets, and even atoms can often be modeled as magnetic dipoles.

	===Mathematical Model===		===Mathematical Model===
	[[File:Magnetic dipole copy.jpg\|right\|400px]]		[[File:Magnetic dipole copy.jpg\|right\|400px]]

	The magnetic dipole moment is represented by a vector <math>\~~mathbf~~{µ}</math>. ~~The~~ magnitude ~~of this~~ is ~~set~~ equal to the current ~~running through~~ the ~~wire~~ multiplied by the area of the circular loop ~~the current runs through. Here~~ the area ~~of the circular loop~~ is ~~defined as~~ <math>\pi R^2</math>. ~~Its~~ direction is ~~determined~~ by the right hand rule. The units ~~for the~~ magnetic dipole moment are ~~amperes times~~ meters squared:		The magnetic dipole moment is represented by the vector <math>\boldsymbol{\mu}</math>. Its magnitude is equal to the current in the loop multiplied by the area enclosed by the loop. For a circular loop, the area is <math>\pi R^2</math>. The direction of <math>\boldsymbol{\mu}</math> is given by the right-hand rule. The SI units of magnetic dipole moment are ampere-meters squared.

	::<math>\|\boldsymbol{ \mu }\| = \mu = ~~I A~~ = I ~~\cdot~~ \pi R^2</math>		::<math>\|\boldsymbol{\mu}\| = \mu = IA = I\pi R^2</math>

	~~A '''~~coil of <math>N</math> ~~current loops''' would thus have a~~ magnetic moment ~~of:~~		For a coil with <math>N</math> turns, the magnetic dipole moment becomes

	:::<math> \|\boldsymbol{\mu}\| = \mu = ~~N I A~~</math>		:::<math>\|\boldsymbol{\mu}\| = \mu = NIA</math>

	*The ~~equation for the~~ '''magnitude of the magnetic field at the center of a current loop''' simplifies as (~~See~~ [[Magnetic Field of a Loop]]):		*The '''magnitude of the magnetic field at the center of a current loop''' simplifies as (see [[Magnetic Field of a Loop]]):

	:::<math>\begin{align}		:::<math>\begin{align}
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	& = \frac{\mu_0}{4 \pi} \frac{2 \pi I}{R} \\		& = \frac{\mu_0}{4 \pi} \frac{2 \pi I}{R} \\
	& = \frac{\mu_0}{4 \pi} \frac{2 \pi \frac{\mu}{\pi R^2}}{R} \text{, where } I = \frac{\mu}{\pi R^2} \\		& = \frac{\mu_0}{4 \pi} \frac{2 \pi \frac{\mu}{\pi R^2}}{R} \text{, where } I = \frac{\mu}{\pi R^2} \\
	B & = \frac{\mu_0}{4 \pi} \frac{2 \mu}{R^3} ~~\ \mathbf{(2)}\\~~		B & = \frac{\mu_0}{4 \pi} \frac{2 \mu}{R^3}
	\end{align}</math>		\end{align}</math>

	*The '''magnitude of the magnetic moment <math>\mu</math> of an electron in circular orbit''' is given by:		*The '''magnitude of the magnetic moment <math>\mu</math> of an electron in circular orbit''' is given by

	:::<math> \|\boldsymbol{\mu}\| = \mu = ~~I A~~ = - \frac{e}{~~2m_{e}~~} L</math>		:::<math>\|\boldsymbol{\mu}\| = \mu = IA = -\frac{e}{2m_e}L</math>

	::::<math>L</math> is the magnitude of the angular momentum of the electron		::::where <math>L</math> is the magnitude of the angular momentum of the electron.

	*The '''torque experienced by a current loop''' ~~due to~~ an external magnetic field is defined as the cross product of the magnetic dipole moment ~~of the loop~~ and the external magnetic field ~~applied to the loop~~:		*The '''torque experienced by a current loop''' in an external magnetic field is defined by the cross product of the magnetic dipole moment and the external magnetic field:

	:::<math>\boldsymbol{\tau} = \boldsymbol{\mu} \times \boldsymbol{B}</math>		:::<math>\boldsymbol{\tau} = \boldsymbol{\mu} \times \boldsymbol{B}</math>

	*The '''magnetic potential energy of the loop''' is ~~also~~ defined as the ~~negated~~ dot product ~~between~~ the magnetic dipole moment ~~of the loop~~ and the external magnetic field ~~applied to the loop~~:		*The '''magnetic potential energy of the loop''' is defined as the negative dot product of the magnetic dipole moment and the external magnetic field:

	[[File:MagneticMomentEnergy.gif\|right\|300px]]		[[File:MagneticMomentEnergy.gif\|right\|300px]]

	:::<math>U(\theta) = - \boldsymbol{\mu} \~~bullet~~ \~~mathbf~~{B} = - [\mu B] \ ~~\text{~~cos}(\theta)</math>		:::<math>U(\theta) = -\boldsymbol{\mu}\cdot\boldsymbol{B} = -\mu B \cos(\theta)</math>

	::::<math>\theta</math> is the angle between the magnetic moment and the external magnetic field		::::Here, <math>\theta</math> is the angle between the magnetic moment and the external magnetic field.

	:*For example, if <math>\theta = 0~~°~~</math>, then ~~we see:~~		:*For example, if <math>\theta = 0^\circ</math>, then

	:::<math>U(0~~°~~) = -[\mu B] \ ~~\text{~~cos}(0~~°~~) = -\mu B</math>		:::<math>U(0^\circ) = -\mu B \cos(0^\circ) = -\mu B</math>

	:*For <math>\theta = 180~~°~~</math>, we get:		:*For <math>\theta = 180^\circ</math>, we get

	:::<math>U(180~~°~~) = -[\mu B] \ ~~\text{~~cos}(180~~°~~) = \mu B</math>		:::<math>U(180^\circ) = -\mu B \cos(180^\circ) = \mu B</math>

	:::~~From this we see~~ that, when ~~there~~ is ~~no separation between~~ the magnetic field~~'s direction and the magnetic moment's direction~~, the loop is at its lowest ~~possible~~ magnetic potential energy ~~state, and when~~ the directions are anti-parallel, the loop is at its highest ~~possible~~ magnetic potential energy ~~state, as shown in the figure~~.		:::This shows that when the magnetic moment is aligned with the magnetic field, the loop is at its lowest magnetic potential energy. When the two directions are anti-parallel, the loop is at its highest magnetic potential energy.

	===Computational Model===		===Computational Model===
	~~Below is~~ a ~~simulating model~~ of a current loop magnetic field ~~using GlowScript~~.		The following GlowScript model gives a simple visualization of the magnetic field produced by a current loop. The arrows represent sample magnetic field vectors along the axis of the loop.

	<glowscript>		<glowscript>
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	arrow(pos=vector(0,0,z0.05), axis=B0.1, color=color.blue)		arrow(pos=vector(0,0,z0.05), axis=B0.1, color=color.blue)
	</glowscript>		</glowscript>

	==Examples==		==Examples==

Chrisvuong: Rewrote Main Idea for clarity

2026-04-22T08:19:39Z

Rewrote Main Idea for clarity

← Older revision		Revision as of 04:19, 22 April 2026
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	==Main Idea==		==Main Idea==
	~~The~~ magnetic dipole moment of a loop ~~of current may be considered to be~~ a ~~measure of the strength of the~~ magnetic ~~field. The magnetic field generated by a magnet points from south to north and is proportional to its magnetic dipole moment~~. In a loop of current, the magnetic dipole moment is a vector that is perpendicular to the loop ~~and can be found using~~ the right-hand-rule~~. The magnetic dipole moment is a measure of the strength of the magnetic dipole~~.		A magnetic dipole moment describes the strength and orientation of a current loop as a magnetic source. For a loop carrying current, the magnetic dipole moment is a vector that points perpendicular to the plane of the loop, with direction given by the right-hand rule.

	The ~~main idea for this topic is to define~~ the magnetic dipole ~~moment and distinguish from the magnetic moment. The magnetic~~ moment is a vector quantity that is used to calculate the torque generated by a magnetic field while the magnetic dipole moment is a value used to define the current of a loop to find the magnetic field on axis.		The magnitude of the magnetic dipole moment is

	The magnetic dipole moment ~~can be thought of as~~ a ~~compass needle. When there is~~ an external magnetic field, ~~a current-carrying loop will rotate~~ to ~~align the~~ magnetic ~~dipole moment along the~~ magnetic ~~field~~.		:<math>\mu = IA</math>

			where <math>I</math> is the current and <math>A</math> is the area enclosed by the loop. For a coil with <math>N</math> turns, the magnitude becomes

			:<math>\mu = NIA</math>

			The magnetic dipole moment is important because it helps predict how a loop behaves in an external magnetic field. In particular, it is used to calculate torque and magnetic potential energy. Current loops, bar magnets, and even atoms can often be modeled as magnetic dipoles.

	===Mathematical Model===		===Mathematical Model===

Chrisvuong at 08:15, 22 April 2026

2026-04-22T08:15:27Z

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	''''''		''''''

	'''Chris Vuong - ~~Fall~~ 2026'''		'''Chris Vuong - Spring 2026'''

	==Main Idea==		==Main Idea==

Chrisvuong at 08:15, 22 April 2026

2026-04-22T08:15:20Z

← Older revision		Revision as of 04:15, 22 April 2026
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	''''''		''''''

	'''~~Aditya Vohara —~~ Fall ~~2025~~'''		'''Chris Vuong - Fall 2026'''

	==Main Idea==		==Main Idea==

Avohara3 at 01:42, 1 December 2025

2025-12-01T01:42:46Z

@@ Line 1: / Line 1: @@
 ''''''
 ==Main Idea==
@@ Line 58: / Line 60: @@
 ===Computational Model===
-::'''Insert Computational Model here'''
+Below is a simulating model of a current loop magnetic field using GlowScript.
 ==Examples==
@@ Line 187: / Line 202: @@
 ==Connectedness==
-::'''Insert Connectedness Section here'''
+Magnetic dipole moment connects to many topics in E&M:
 ==History==
@@ Line 193: / Line 214: @@
 The study of magnetism dates far back in time, but it was not until 1825 that Andre Ampere showed that magnetism is due to perpetually flowing current through loops of wire. He then went on to derive Ampere's Law, which connected magnetic fields to electric currents. This equation was then further adapted to simplify the on axis magnetic field generated by a loop of current to use the magnetic dipole moment.
-At first, people thought magnets, both natural and man-made, are made up of countless magnetic dipoles, each consisting of positive and negative magnetic charges separated by a small distance. This consequently defined the concept of magnetic dipole moment, a vector, pointing from the negative magnetic charge to the positive magnetic charge. When scientists discovered that magnetic charges, or "magnetic monopoles" do not exist, the magnetic properties of matter were believed to be generated by the alignment of molecular currents. Since then, magnetic dipole moment has been redefined using current <math>I</math>, allowing the idea of magnetic dipole to remain.
+At first, people thought magnets, both natural and man-made, are made up of countless magnetic dipoles, each consisting of positive and negative magnetic charges separated by a small distance. This consequently defined the concept of magnetic dipole moment, a vector, pointing from the negative magnetic charge to the positive magnetic charge. When scientists discovered that magnetic charges, or "magnetic monopoles" do not exist, the magnetic properties of matter were believed to be generated by the alignment of molecular currents. Since then, magnetic dipole moment has been redefined using current
 == See also ==

Vbaptist at 02:29, 28 November 2022

2022-11-28T02:29:02Z

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	'''~~Claimed by VBaptist fall 2022~~'''		''''''

	==Main Idea==		==Main Idea==

Vbaptist at 00:51, 20 November 2022

2022-11-20T00:51:26Z

← Older revision		Revision as of 20:51, 19 November 2022
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	'''Claimed by ~~Vaishnan Baptist~~ fall 2022'''		'''Claimed by VBaptist fall 2022'''

	==Main Idea==		==Main Idea==

Vbaptist at 00:51, 20 November 2022

2022-11-20T00:51:12Z

← Older revision		Revision as of 20:51, 19 November 2022
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	'''Claimed by ~~Sonica Sahetiya Fall 2020~~'''		'''Claimed by Vaishnan Baptist fall 2022'''

	==Main Idea==		==Main Idea==

Ssahetiya6: /* Main Idea */

2020-11-17T15:35:41Z

Main Idea

← Older revision		Revision as of 11:35, 17 November 2020
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	The magnetic dipole moment of a loop of current may be considered to be a measure of the strength of the magnetic field. The magnetic field generated by a magnet points from south to north and is proportional to its magnetic dipole moment. In a loop of current, the magnetic dipole moment is a vector that is perpendicular to the loop and can be found using the right-hand-rule. The magnetic dipole moment is a measure of the strength of the magnetic dipole.		The magnetic dipole moment of a loop of current may be considered to be a measure of the strength of the magnetic field. The magnetic field generated by a magnet points from south to north and is proportional to its magnetic dipole moment. In a loop of current, the magnetic dipole moment is a vector that is perpendicular to the loop and can be found using the right-hand-rule. The magnetic dipole moment is a measure of the strength of the magnetic dipole.

	The main idea for this topic is to define the magnetic dipole moment and distinguish from the magnetic moment. The magnetic moment is a vector quantity that is used to calculate the torque generated by a magnetic field while the magnetic dipole moment is a value used to define the current of a loop to find the magnetic field on axis.		The main idea for this topic is to define the magnetic dipole moment and distinguish from the magnetic moment. The magnetic moment is a vector quantity that is used to calculate the torque generated by a magnetic field while the magnetic dipole moment is a value used to define the current of a loop to find the magnetic field on axis.

			The magnetic dipole moment can be thought of as a compass needle. When there is an external magnetic field, a current-carrying loop will rotate to align the magnetic dipole moment along the magnetic field.

	===Mathematical Model===		===Mathematical Model===