Physics Book - User contributions [en]

Magnetic Dipole Moment

2015-12-01T21:33:06Z

Gebm03:

by Guillermo Bacardi

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==

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.

===A Mathematical Model===

The magnetic dipole moment is represented by '''µ'''. This is set equal to the current running through the wire multiplied by the area of the circular loop. Here the area of the circular loop is defined as πR^2. The units for the magnetic dipole moment are amperes times meters squared.

<math> \boldsymbol{\mu} = \boldsymbol{I} \times\mathbf{A}</math>

If there is more than one coil in the loop then all of the coils must be accounted for by a value N that represents all of the coils.

<math> \boldsymbol{\mu} = \boldsymbol{NI} \times\mathbf{A}</math>

The overall equation for a magnetic field turns into

<math> \mathbf{B} = \frac{\mu_0}{4\pi}\frac{2\mu}{R^3}</math>

===A Computational Model===

[[File:Magnetic dipole copy.jpg]]

This image shows how the magnetic field around a loop changes at each location but on axis with the center of the loop it points in one direction.

==Examples==

===Simple===
What is the magnetic dipole moment of a 1200 turn circular coil that has a radius of 10 cm and carries a current of 2 amperes?

Solution: µ=NIA N=1200 I = 2 A = π0.1^2

So µ = (1200)(2)(0.0314) = 75.4 Am^2

===Difficult===

What is the magnetic field at a point 3m away from a coil that has 250 turns, a radius of 2m and a current of 4 amperes running through it?

First step is to calculate the dipole moment using µ=NIA. In this situation N=250, A = 4^2π, and I=4. (250)(4π)(4)= 12566.4Am^2

Then plug this into our magnetic field equation <math> \mathbf{B} = \frac{\mu_0}{4\pi}\frac{2\mu}{R^3}</math> and we get

B = 1e-7((2*12566.4)/9) which gives us B=1.4e-4

==History==

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 Amperes force law which connected the 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.

== See also ==

Here are some more resources with extra information on magnetic dipole moments.

===Further reading===

Lecture on magnetic dipole moment [http://www.phys.ufl.edu/~acosta/phy2061/lectures/MagneticDipoles.pdf]

===External links===

Internet resources on magnetic dipole moment [http://hyperphysics.phy-astr.gsu.edu/hbase/magnetic/magmom.html]

==References==

This section contains the the references you used while writing this page

[[Category:Fields]]

Magnetic Dipole Moment

2015-12-01T21:32:27Z

Gebm03: /* References */

Claimed by Guillermo Bacardi

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==

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.

===A Mathematical Model===

The magnetic dipole moment is represented by '''µ'''. This is set equal to the current running through the wire multiplied by the area of the circular loop. Here the area of the circular loop is defined as πR^2. The units for the magnetic dipole moment are amperes times meters squared.

<math> \boldsymbol{\mu} = \boldsymbol{I} \times\mathbf{A}</math>

If there is more than one coil in the loop then all of the coils must be accounted for by a value N that represents all of the coils.

<math> \boldsymbol{\mu} = \boldsymbol{NI} \times\mathbf{A}</math>

The overall equation for a magnetic field turns into

<math> \mathbf{B} = \frac{\mu_0}{4\pi}\frac{2\mu}{R^3}</math>

===A Computational Model===

[[File:Magnetic dipole copy.jpg]]

This image shows how the magnetic field around a loop changes at each location but on axis with the center of the loop it points in one direction.

==Examples==

===Simple===
What is the magnetic dipole moment of a 1200 turn circular coil that has a radius of 10 cm and carries a current of 2 amperes?

Solution: µ=NIA N=1200 I = 2 A = π0.1^2

So µ = (1200)(2)(0.0314) = 75.4 Am^2

===Difficult===

What is the magnetic field at a point 3m away from a coil that has 250 turns, a radius of 2m and a current of 4 amperes running through it?

First step is to calculate the dipole moment using µ=NIA. In this situation N=250, A = 4^2π, and I=4. (250)(4π)(4)= 12566.4Am^2

Then plug this into our magnetic field equation <math> \mathbf{B} = \frac{\mu_0}{4\pi}\frac{2\mu}{R^3}</math> and we get

B = 1e-7((2*12566.4)/9) which gives us B=1.4e-4

==History==

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 Amperes force law which connected the 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.

== See also ==

Here are some more resources with extra information on magnetic dipole moments.

===Further reading===

Lecture on magnetic dipole moment [http://www.phys.ufl.edu/~acosta/phy2061/lectures/MagneticDipoles.pdf]

===External links===

Internet resources on magnetic dipole moment [http://hyperphysics.phy-astr.gsu.edu/hbase/magnetic/magmom.html]

==References==

This section contains the the references you used while writing this page

[[Category:Fields]]

Magnetic Dipole Moment

2015-12-01T21:29:17Z

Gebm03: /* See also */

Magnetic Dipole Moment

2015-12-01T21:27:30Z

Gebm03: /* Further reading */

Claimed by Guillermo Bacardi

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==

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.

===A Mathematical Model===

The magnetic dipole moment is represented by '''µ'''. This is set equal to the current running through the wire multiplied by the area of the circular loop. Here the area of the circular loop is defined as πR^2. The units for the magnetic dipole moment are amperes times meters squared.

<math> \boldsymbol{\mu} = \boldsymbol{I} \times\mathbf{A}</math>

If there is more than one coil in the loop then all of the coils must be accounted for by a value N that represents all of the coils.

<math> \boldsymbol{\mu} = \boldsymbol{NI} \times\mathbf{A}</math>

The overall equation for a magnetic field turns into

<math> \mathbf{B} = \frac{\mu_0}{4\pi}\frac{2\mu}{R^3}</math>

===A Computational Model===

[[File:Magnetic dipole copy.jpg]]

This image shows how the magnetic field around a loop changes at each location but on axis with the center of the loop it points in one direction.

==Examples==

===Simple===
What is the magnetic dipole moment of a 1200 turn circular coil that has a radius of 10 cm and carries a current of 2 amperes?

Solution: µ=NIA N=1200 I = 2 A = π0.1^2

So µ = (1200)(2)(0.0314) = 75.4 Am^2

===Difficult===

What is the magnetic field at a point 3m away from a coil that has 250 turns, a radius of 2m and a current of 4 amperes running through it?

First step is to calculate the dipole moment using µ=NIA. In this situation N=250, A = 4^2π, and I=4. (250)(4π)(4)= 12566.4Am^2

Then plug this into our magnetic field equation <math> \mathbf{B} = \frac{\mu_0}{4\pi}\frac{2\mu}{R^3}</math> and we get

B = 1e-7((2*12566.4)/9) which gives us B=1.4e-4

==History==

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 Amperes force law which connected the 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.

== See also ==

Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?

===Further reading===

Lecture on magnetic dipole moment [http://www.phys.ufl.edu/~acosta/phy2061/lectures/MagneticDipoles.pdf]

===External links===

Internet resources on magnetic dipole moment [http://hyperphysics.phy-astr.gsu.edu/hbase/magnetic/magmom.html]

==References==

This section contains the the references you used while writing this page

[[Category:Which Category did you place this in?]]

Magnetic Dipole Moment

2015-12-01T21:26:36Z

Gebm03: /* Further reading */

Claimed by Guillermo Bacardi

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==

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.

===A Mathematical Model===

The magnetic dipole moment is represented by '''µ'''. This is set equal to the current running through the wire multiplied by the area of the circular loop. Here the area of the circular loop is defined as πR^2. The units for the magnetic dipole moment are amperes times meters squared.

<math> \boldsymbol{\mu} = \boldsymbol{I} \times\mathbf{A}</math>

If there is more than one coil in the loop then all of the coils must be accounted for by a value N that represents all of the coils.

<math> \boldsymbol{\mu} = \boldsymbol{NI} \times\mathbf{A}</math>

The overall equation for a magnetic field turns into

<math> \mathbf{B} = \frac{\mu_0}{4\pi}\frac{2\mu}{R^3}</math>

===A Computational Model===

[[File:Magnetic dipole copy.jpg]]

This image shows how the magnetic field around a loop changes at each location but on axis with the center of the loop it points in one direction.

==Examples==

===Simple===
What is the magnetic dipole moment of a 1200 turn circular coil that has a radius of 10 cm and carries a current of 2 amperes?

Solution: µ=NIA N=1200 I = 2 A = π0.1^2

So µ = (1200)(2)(0.0314) = 75.4 Am^2

===Difficult===

What is the magnetic field at a point 3m away from a coil that has 250 turns, a radius of 2m and a current of 4 amperes running through it?

First step is to calculate the dipole moment using µ=NIA. In this situation N=250, A = 4^2π, and I=4. (250)(4π)(4)= 12566.4Am^2

Then plug this into our magnetic field equation <math> \mathbf{B} = \frac{\mu_0}{4\pi}\frac{2\mu}{R^3}</math> and we get

B = 1e-7((2*12566.4)/9) which gives us B=1.4e-4

==History==

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 Amperes force law which connected the 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.

== See also ==

Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?

===Further reading===

Lecture on magnetic dipole moment http://www.phys.ufl.edu/~acosta/phy2061/lectures/MagneticDipoles.pdf

===External links===

Internet resources on magnetic dipole moment [http://hyperphysics.phy-astr.gsu.edu/hbase/magnetic/magmom.html]

==References==

This section contains the the references you used while writing this page

[[Category:Which Category did you place this in?]]

Magnetic Dipole Moment

2015-12-01T21:25:15Z

Gebm03: /* External links */

Claimed by Guillermo Bacardi

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==

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.

===A Mathematical Model===

The magnetic dipole moment is represented by '''µ'''. This is set equal to the current running through the wire multiplied by the area of the circular loop. Here the area of the circular loop is defined as πR^2. The units for the magnetic dipole moment are amperes times meters squared.

<math> \boldsymbol{\mu} = \boldsymbol{I} \times\mathbf{A}</math>

If there is more than one coil in the loop then all of the coils must be accounted for by a value N that represents all of the coils.

<math> \boldsymbol{\mu} = \boldsymbol{NI} \times\mathbf{A}</math>

The overall equation for a magnetic field turns into

<math> \mathbf{B} = \frac{\mu_0}{4\pi}\frac{2\mu}{R^3}</math>

===A Computational Model===

[[File:Magnetic dipole copy.jpg]]

This image shows how the magnetic field around a loop changes at each location but on axis with the center of the loop it points in one direction.

==Examples==

===Simple===
What is the magnetic dipole moment of a 1200 turn circular coil that has a radius of 10 cm and carries a current of 2 amperes?

Solution: µ=NIA N=1200 I = 2 A = π0.1^2

So µ = (1200)(2)(0.0314) = 75.4 Am^2

===Difficult===

What is the magnetic field at a point 3m away from a coil that has 250 turns, a radius of 2m and a current of 4 amperes running through it?

First step is to calculate the dipole moment using µ=NIA. In this situation N=250, A = 4^2π, and I=4. (250)(4π)(4)= 12566.4Am^2

Then plug this into our magnetic field equation <math> \mathbf{B} = \frac{\mu_0}{4\pi}\frac{2\mu}{R^3}</math> and we get

B = 1e-7((2*12566.4)/9) which gives us B=1.4e-4

==History==

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 Amperes force law which connected the 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.

== See also ==

Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?

===Further reading===

Books, Articles or other print media on this topic

===External links===

Internet resources on magnetic dipole moment [http://hyperphysics.phy-astr.gsu.edu/hbase/magnetic/magmom.html]

==References==

This section contains the the references you used while writing this page

[[Category:Which Category did you place this in?]]

Magnetic Dipole Moment

2015-12-01T21:24:11Z

Gebm03: /* Connectedness */

Claimed by Guillermo Bacardi

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==

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.

===A Mathematical Model===

The magnetic dipole moment is represented by '''µ'''. This is set equal to the current running through the wire multiplied by the area of the circular loop. Here the area of the circular loop is defined as πR^2. The units for the magnetic dipole moment are amperes times meters squared.

<math> \boldsymbol{\mu} = \boldsymbol{I} \times\mathbf{A}</math>

If there is more than one coil in the loop then all of the coils must be accounted for by a value N that represents all of the coils.

<math> \boldsymbol{\mu} = \boldsymbol{NI} \times\mathbf{A}</math>

The overall equation for a magnetic field turns into

<math> \mathbf{B} = \frac{\mu_0}{4\pi}\frac{2\mu}{R^3}</math>

===A Computational Model===

[[File:Magnetic dipole copy.jpg]]

This image shows how the magnetic field around a loop changes at each location but on axis with the center of the loop it points in one direction.

==Examples==

===Simple===
What is the magnetic dipole moment of a 1200 turn circular coil that has a radius of 10 cm and carries a current of 2 amperes?

Solution: µ=NIA N=1200 I = 2 A = π0.1^2

So µ = (1200)(2)(0.0314) = 75.4 Am^2

===Difficult===

What is the magnetic field at a point 3m away from a coil that has 250 turns, a radius of 2m and a current of 4 amperes running through it?

First step is to calculate the dipole moment using µ=NIA. In this situation N=250, A = 4^2π, and I=4. (250)(4π)(4)= 12566.4Am^2

Then plug this into our magnetic field equation <math> \mathbf{B} = \frac{\mu_0}{4\pi}\frac{2\mu}{R^3}</math> and we get

B = 1e-7((2*12566.4)/9) which gives us B=1.4e-4

==History==

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 Amperes force law which connected the 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.

== See also ==

Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?

===Further reading===

Books, Articles or other print media on this topic

===External links===

Internet resources on this topic

==References==

This section contains the the references you used while writing this page

[[Category:Which Category did you place this in?]]

Magnetic Dipole Moment

2015-12-01T21:21:22Z

Gebm03: /* History */

Claimed by Guillermo Bacardi

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==

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.

===A Mathematical Model===

The magnetic dipole moment is represented by '''µ'''. This is set equal to the current running through the wire multiplied by the area of the circular loop. Here the area of the circular loop is defined as πR^2. The units for the magnetic dipole moment are amperes times meters squared.

<math> \boldsymbol{\mu} = \boldsymbol{I} \times\mathbf{A}</math>

If there is more than one coil in the loop then all of the coils must be accounted for by a value N that represents all of the coils.

<math> \boldsymbol{\mu} = \boldsymbol{NI} \times\mathbf{A}</math>

The overall equation for a magnetic field turns into

<math> \mathbf{B} = \frac{\mu_0}{4\pi}\frac{2\mu}{R^3}</math>

===A Computational Model===

[[File:Magnetic dipole copy.jpg]]

This image shows how the magnetic field around a loop changes at each location but on axis with the center of the loop it points in one direction.

==Examples==

===Simple===
What is the magnetic dipole moment of a 1200 turn circular coil that has a radius of 10 cm and carries a current of 2 amperes?

Solution: µ=NIA N=1200 I = 2 A = π0.1^2

So µ = (1200)(2)(0.0314) = 75.4 Am^2

===Difficult===

What is the magnetic field at a point 3m away from a coil that has 250 turns, a radius of 2m and a current of 4 amperes running through it?

First step is to calculate the dipole moment using µ=NIA. In this situation N=250, A = 4^2π, and I=4. (250)(4π)(4)= 12566.4Am^2

Then plug this into our magnetic field equation <math> \mathbf{B} = \frac{\mu_0}{4\pi}\frac{2\mu}{R^3}</math> and we get

B = 1e-7((2*12566.4)/9) which gives us B=1.4e-4

==Connectedness==
#How is this topic connected to something that you are interested in?
#How is it connected to your major?
#Is there an interesting industrial application?

==History==

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 Amperes force law which connected the 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.

== See also ==

Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?

===Further reading===

Books, Articles or other print media on this topic

===External links===

Internet resources on this topic

==References==

This section contains the the references you used while writing this page

[[Category:Which Category did you place this in?]]

Magnetic Dipole Moment

2015-12-01T21:16:05Z

Gebm03: /* History */

Claimed by Guillermo Bacardi

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==

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.

===A Mathematical Model===

The magnetic dipole moment is represented by '''µ'''. This is set equal to the current running through the wire multiplied by the area of the circular loop. Here the area of the circular loop is defined as πR^2. The units for the magnetic dipole moment are amperes times meters squared.

<math> \boldsymbol{\mu} = \boldsymbol{I} \times\mathbf{A}</math>

If there is more than one coil in the loop then all of the coils must be accounted for by a value N that represents all of the coils.

<math> \boldsymbol{\mu} = \boldsymbol{NI} \times\mathbf{A}</math>

The overall equation for a magnetic field turns into

<math> \mathbf{B} = \frac{\mu_0}{4\pi}\frac{2\mu}{R^3}</math>

===A Computational Model===

[[File:Magnetic dipole copy.jpg]]

This image shows how the magnetic field around a loop changes at each location but on axis with the center of the loop it points in one direction.

==Examples==

===Simple===
What is the magnetic dipole moment of a 1200 turn circular coil that has a radius of 10 cm and carries a current of 2 amperes?

Solution: µ=NIA N=1200 I = 2 A = π0.1^2

So µ = (1200)(2)(0.0314) = 75.4 Am^2

===Difficult===

What is the magnetic field at a point 3m away from a coil that has 250 turns, a radius of 2m and a current of 4 amperes running through it?

First step is to calculate the dipole moment using µ=NIA. In this situation N=250, A = 4^2π, and I=4. (250)(4π)(4)= 12566.4Am^2

Then plug this into our magnetic field equation <math> \mathbf{B} = \frac{\mu_0}{4\pi}\frac{2\mu}{R^3}</math> and we get

B = 1e-7((2*12566.4)/9) which gives us B=1.4e-4

==Connectedness==
#How is this topic connected to something that you are interested in?
#How is it connected to your major?
#Is there an interesting industrial application?

==History==

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.

== See also ==

Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?

===Further reading===

Books, Articles or other print media on this topic

===External links===

Internet resources on this topic

==References==

This section contains the the references you used while writing this page

[[Category:Which Category did you place this in?]]

Magnetic Dipole Moment

2015-12-01T21:09:28Z

Gebm03: /* The Main Idea */

Claimed by Guillermo Bacardi

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==

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.

===A Mathematical Model===

The magnetic dipole moment is represented by '''µ'''. This is set equal to the current running through the wire multiplied by the area of the circular loop. Here the area of the circular loop is defined as πR^2. The units for the magnetic dipole moment are amperes times meters squared.

<math> \boldsymbol{\mu} = \boldsymbol{I} \times\mathbf{A}</math>

If there is more than one coil in the loop then all of the coils must be accounted for by a value N that represents all of the coils.

<math> \boldsymbol{\mu} = \boldsymbol{NI} \times\mathbf{A}</math>

The overall equation for a magnetic field turns into

<math> \mathbf{B} = \frac{\mu_0}{4\pi}\frac{2\mu}{R^3}</math>

===A Computational Model===

[[File:Magnetic dipole copy.jpg]]

This image shows how the magnetic field around a loop changes at each location but on axis with the center of the loop it points in one direction.

==Examples==

===Simple===
What is the magnetic dipole moment of a 1200 turn circular coil that has a radius of 10 cm and carries a current of 2 amperes?

Solution: µ=NIA N=1200 I = 2 A = π0.1^2

So µ = (1200)(2)(0.0314) = 75.4 Am^2

===Difficult===

What is the magnetic field at a point 3m away from a coil that has 250 turns, a radius of 2m and a current of 4 amperes running through it?

First step is to calculate the dipole moment using µ=NIA. In this situation N=250, A = 4^2π, and I=4. (250)(4π)(4)= 12566.4Am^2

Then plug this into our magnetic field equation <math> \mathbf{B} = \frac{\mu_0}{4\pi}\frac{2\mu}{R^3}</math> and we get

B = 1e-7((2*12566.4)/9) which gives us B=1.4e-4

==Connectedness==
#How is this topic connected to something that you are interested in?
#How is it connected to your major?
#Is there an interesting industrial application?

==History==

Put this idea in historical context. Give the reader the Who, What, When, Where, and Why.

== See also ==

Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?

===Further reading===

Books, Articles or other print media on this topic

===External links===

Internet resources on this topic

==References==

This section contains the the references you used while writing this page

[[Category:Which Category did you place this in?]]

Magnetic Dipole Moment

2015-12-01T21:02:55Z

Gebm03: /* A Computational Model */

Claimed by Guillermo Bacardi

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==

The main idea for this topic is to define the magnetic dipole moment and distinguish from the magnetic dipole.

===A Mathematical Model===

The magnetic dipole moment is represented by '''µ'''. This is set equal to the current running through the wire multiplied by the area of the circular loop. Here the area of the circular loop is defined as πR^2. The units for the magnetic dipole moment are amperes times meters squared.

<math> \boldsymbol{\mu} = \boldsymbol{I} \times\mathbf{A}</math>

If there is more than one coil in the loop then all of the coils must be accounted for by a value N that represents all of the coils.

<math> \boldsymbol{\mu} = \boldsymbol{NI} \times\mathbf{A}</math>

The overall equation for a magnetic field turns into

<math> \mathbf{B} = \frac{\mu_0}{4\pi}\frac{2\mu}{R^3}</math>

===A Computational Model===

[[File:Magnetic dipole copy.jpg]]

This image shows how the magnetic field around a loop changes at each location but on axis with the center of the loop it points in one direction.

==Examples==

===Simple===
What is the magnetic dipole moment of a 1200 turn circular coil that has a radius of 10 cm and carries a current of 2 amperes?

Solution: µ=NIA N=1200 I = 2 A = π0.1^2

So µ = (1200)(2)(0.0314) = 75.4 Am^2

===Difficult===

What is the magnetic field at a point 3m away from a coil that has 250 turns, a radius of 2m and a current of 4 amperes running through it?

First step is to calculate the dipole moment using µ=NIA. In this situation N=250, A = 4^2π, and I=4. (250)(4π)(4)= 12566.4Am^2

Then plug this into our magnetic field equation <math> \mathbf{B} = \frac{\mu_0}{4\pi}\frac{2\mu}{R^3}</math> and we get

B = 1e-7((2*12566.4)/9) which gives us B=1.4e-4

==Connectedness==
#How is this topic connected to something that you are interested in?
#How is it connected to your major?
#Is there an interesting industrial application?

==History==

Put this idea in historical context. Give the reader the Who, What, When, Where, and Why.

== See also ==

Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?

===Further reading===

Books, Articles or other print media on this topic

===External links===

Internet resources on this topic

==References==

This section contains the the references you used while writing this page

[[Category:Which Category did you place this in?]]

Magnetic Dipole Moment

2015-12-01T21:02:43Z

Gebm03: /* A Computational Model */

Claimed by Guillermo Bacardi

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==

The main idea for this topic is to define the magnetic dipole moment and distinguish from the magnetic dipole.

===A Mathematical Model===

The magnetic dipole moment is represented by '''µ'''. This is set equal to the current running through the wire multiplied by the area of the circular loop. Here the area of the circular loop is defined as πR^2. The units for the magnetic dipole moment are amperes times meters squared.

<math> \boldsymbol{\mu} = \boldsymbol{I} \times\mathbf{A}</math>

If there is more than one coil in the loop then all of the coils must be accounted for by a value N that represents all of the coils.

<math> \boldsymbol{\mu} = \boldsymbol{NI} \times\mathbf{A}</math>

The overall equation for a magnetic field turns into

<math> \mathbf{B} = \frac{\mu_0}{4\pi}\frac{2\mu}{R^3}</math>

===A Computational Model===

[[File:Magnetic dipole copy.jpg]]
This image shows how the magnetic field around a loop changes at each location but on axis with the center of the loop it points in one direction.

==Examples==

===Simple===
What is the magnetic dipole moment of a 1200 turn circular coil that has a radius of 10 cm and carries a current of 2 amperes?

Solution: µ=NIA N=1200 I = 2 A = π0.1^2

So µ = (1200)(2)(0.0314) = 75.4 Am^2

===Difficult===

What is the magnetic field at a point 3m away from a coil that has 250 turns, a radius of 2m and a current of 4 amperes running through it?

First step is to calculate the dipole moment using µ=NIA. In this situation N=250, A = 4^2π, and I=4. (250)(4π)(4)= 12566.4Am^2

Then plug this into our magnetic field equation <math> \mathbf{B} = \frac{\mu_0}{4\pi}\frac{2\mu}{R^3}</math> and we get

B = 1e-7((2*12566.4)/9) which gives us B=1.4e-4

==Connectedness==
#How is this topic connected to something that you are interested in?
#How is it connected to your major?
#Is there an interesting industrial application?

==History==

Put this idea in historical context. Give the reader the Who, What, When, Where, and Why.

== See also ==

Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?

===Further reading===

Books, Articles or other print media on this topic

===External links===

Internet resources on this topic

==References==

This section contains the the references you used while writing this page

[[Category:Which Category did you place this in?]]

Magnetic Dipole Moment

2015-12-01T21:01:37Z

Gebm03: /* A Computational Model */

Claimed by Guillermo Bacardi

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==

The main idea for this topic is to define the magnetic dipole moment and distinguish from the magnetic dipole.

===A Mathematical Model===

The magnetic dipole moment is represented by '''µ'''. This is set equal to the current running through the wire multiplied by the area of the circular loop. Here the area of the circular loop is defined as πR^2. The units for the magnetic dipole moment are amperes times meters squared.

<math> \boldsymbol{\mu} = \boldsymbol{I} \times\mathbf{A}</math>

If there is more than one coil in the loop then all of the coils must be accounted for by a value N that represents all of the coils.

<math> \boldsymbol{\mu} = \boldsymbol{NI} \times\mathbf{A}</math>

The overall equation for a magnetic field turns into

<math> \mathbf{B} = \frac{\mu_0}{4\pi}\frac{2\mu}{R^3}</math>

===A Computational Model===

[[File:Magnetic dipole copy.jpg]]

==Examples==

===Simple===
What is the magnetic dipole moment of a 1200 turn circular coil that has a radius of 10 cm and carries a current of 2 amperes?

Solution: µ=NIA N=1200 I = 2 A = π0.1^2

So µ = (1200)(2)(0.0314) = 75.4 Am^2

===Difficult===

What is the magnetic field at a point 3m away from a coil that has 250 turns, a radius of 2m and a current of 4 amperes running through it?

First step is to calculate the dipole moment using µ=NIA. In this situation N=250, A = 4^2π, and I=4. (250)(4π)(4)= 12566.4Am^2

Then plug this into our magnetic field equation <math> \mathbf{B} = \frac{\mu_0}{4\pi}\frac{2\mu}{R^3}</math> and we get

B = 1e-7((2*12566.4)/9) which gives us B=1.4e-4

==Connectedness==
#How is this topic connected to something that you are interested in?
#How is it connected to your major?
#Is there an interesting industrial application?

==History==

Put this idea in historical context. Give the reader the Who, What, When, Where, and Why.

== See also ==

Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?

===Further reading===

Books, Articles or other print media on this topic

===External links===

Internet resources on this topic

==References==

This section contains the the references you used while writing this page

[[Category:Which Category did you place this in?]]

Magnetic Dipole Moment

2015-12-01T20:52:56Z

Gebm03: /* Difficult */

Claimed by Guillermo Bacardi

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==

The main idea for this topic is to define the magnetic dipole moment and distinguish from the magnetic dipole.

===A Mathematical Model===

The magnetic dipole moment is represented by '''µ'''. This is set equal to the current running through the wire multiplied by the area of the circular loop. Here the area of the circular loop is defined as πR^2. The units for the magnetic dipole moment are amperes times meters squared.

<math> \boldsymbol{\mu} = \boldsymbol{I} \times\mathbf{A}</math>

If there is more than one coil in the loop then all of the coils must be accounted for by a value N that represents all of the coils.

<math> \boldsymbol{\mu} = \boldsymbol{NI} \times\mathbf{A}</math>

The overall equation for a magnetic field turns into

<math> \mathbf{B} = \frac{\mu_0}{4\pi}\frac{2\mu}{R^3}</math>

===A Computational Model===

How do we visualize or predict using this topic. Consider embedding some vpython code here [https://trinket.io/glowscript/31d0f9ad9e Teach hands-on with GlowScript]

==Examples==

===Simple===
What is the magnetic dipole moment of a 1200 turn circular coil that has a radius of 10 cm and carries a current of 2 amperes?

Solution: µ=NIA N=1200 I = 2 A = π0.1^2

So µ = (1200)(2)(0.0314) = 75.4 Am^2

===Difficult===

What is the magnetic field at a point 3m away from a coil that has 250 turns, a radius of 2m and a current of 4 amperes running through it?

First step is to calculate the dipole moment using µ=NIA. In this situation N=250, A = 4^2π, and I=4. (250)(4π)(4)= 12566.4Am^2

Then plug this into our magnetic field equation <math> \mathbf{B} = \frac{\mu_0}{4\pi}\frac{2\mu}{R^3}</math> and we get

B = 1e-7((2*12566.4)/9) which gives us B=1.4e-4

==Connectedness==
#How is this topic connected to something that you are interested in?
#How is it connected to your major?
#Is there an interesting industrial application?

==History==

Put this idea in historical context. Give the reader the Who, What, When, Where, and Why.

== See also ==

Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?

===Further reading===

Books, Articles or other print media on this topic

===External links===

Internet resources on this topic

==References==

This section contains the the references you used while writing this page

[[Category:Which Category did you place this in?]]

Magnetic Dipole Moment

2015-12-01T20:51:20Z

Gebm03: /* Difficult */

Claimed by Guillermo Bacardi

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==

The main idea for this topic is to define the magnetic dipole moment and distinguish from the magnetic dipole.

===A Mathematical Model===

The magnetic dipole moment is represented by '''µ'''. This is set equal to the current running through the wire multiplied by the area of the circular loop. Here the area of the circular loop is defined as πR^2. The units for the magnetic dipole moment are amperes times meters squared.

<math> \boldsymbol{\mu} = \boldsymbol{I} \times\mathbf{A}</math>

If there is more than one coil in the loop then all of the coils must be accounted for by a value N that represents all of the coils.

<math> \boldsymbol{\mu} = \boldsymbol{NI} \times\mathbf{A}</math>

The overall equation for a magnetic field turns into

<math> \mathbf{B} = \frac{\mu_0}{4\pi}\frac{2\mu}{R^3}</math>

===A Computational Model===

How do we visualize or predict using this topic. Consider embedding some vpython code here [https://trinket.io/glowscript/31d0f9ad9e Teach hands-on with GlowScript]

==Examples==

===Simple===
What is the magnetic dipole moment of a 1200 turn circular coil that has a radius of 10 cm and carries a current of 2 amperes?

Solution: µ=NIA N=1200 I = 2 A = π0.1^2

So µ = (1200)(2)(0.0314) = 75.4 Am^2

===Difficult===

What is the magnetic field at a point 3m away from a coil that has 250 turns, a radius of 2m and a current of 4 amperes running through it?

First step is to calculate the dipole moment using µ=NIA. In this situation N=250, A = 4^2π, and I=4. (250)(4π)(4)= 12566.4Am^2

Then plug this into our magnetic field equation

==Connectedness==
#How is this topic connected to something that you are interested in?
#How is it connected to your major?
#Is there an interesting industrial application?

==History==

Put this idea in historical context. Give the reader the Who, What, When, Where, and Why.

== See also ==

Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?

===Further reading===

Books, Articles or other print media on this topic

===External links===

Internet resources on this topic

==References==

This section contains the the references you used while writing this page

[[Category:Which Category did you place this in?]]

Magnetic Dipole Moment

2015-12-01T20:48:29Z

Gebm03: /* Difficult */

Claimed by Guillermo Bacardi

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==

The main idea for this topic is to define the magnetic dipole moment and distinguish from the magnetic dipole.

===A Mathematical Model===

The magnetic dipole moment is represented by '''µ'''. This is set equal to the current running through the wire multiplied by the area of the circular loop. Here the area of the circular loop is defined as πR^2. The units for the magnetic dipole moment are amperes times meters squared.

<math> \boldsymbol{\mu} = \boldsymbol{I} \times\mathbf{A}</math>

If there is more than one coil in the loop then all of the coils must be accounted for by a value N that represents all of the coils.

<math> \boldsymbol{\mu} = \boldsymbol{NI} \times\mathbf{A}</math>

The overall equation for a magnetic field turns into

<math> \mathbf{B} = \frac{\mu_0}{4\pi}\frac{2\mu}{R^3}</math>

===A Computational Model===

How do we visualize or predict using this topic. Consider embedding some vpython code here [https://trinket.io/glowscript/31d0f9ad9e Teach hands-on with GlowScript]

==Examples==

===Simple===
What is the magnetic dipole moment of a 1200 turn circular coil that has a radius of 10 cm and carries a current of 2 amperes?

Solution: µ=NIA N=1200 I = 2 A = π0.1^2

So µ = (1200)(2)(0.0314) = 75.4 Am^2

===Difficult===

What is the magnetic field at a point 3m away from a coil that has 250 turns, a radius of 2m and a current of 4 amperes running through it?

First step is to calculate the dipole moment using µ=NIA. In this situation N=250, A = 4

==Connectedness==
#How is this topic connected to something that you are interested in?
#How is it connected to your major?
#Is there an interesting industrial application?

==History==

Put this idea in historical context. Give the reader the Who, What, When, Where, and Why.

== See also ==

Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?

===Further reading===

Books, Articles or other print media on this topic

===External links===

Internet resources on this topic

==References==

This section contains the the references you used while writing this page

[[Category:Which Category did you place this in?]]

Magnetic Dipole Moment

2015-12-01T20:47:46Z

Gebm03: /* Simple */

Claimed by Guillermo Bacardi

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==

The main idea for this topic is to define the magnetic dipole moment and distinguish from the magnetic dipole.

===A Mathematical Model===

The magnetic dipole moment is represented by '''µ'''. This is set equal to the current running through the wire multiplied by the area of the circular loop. Here the area of the circular loop is defined as πR^2. The units for the magnetic dipole moment are amperes times meters squared.

<math> \boldsymbol{\mu} = \boldsymbol{I} \times\mathbf{A}</math>

If there is more than one coil in the loop then all of the coils must be accounted for by a value N that represents all of the coils.

<math> \boldsymbol{\mu} = \boldsymbol{NI} \times\mathbf{A}</math>

The overall equation for a magnetic field turns into

<math> \mathbf{B} = \frac{\mu_0}{4\pi}\frac{2\mu}{R^3}</math>

===A Computational Model===

How do we visualize or predict using this topic. Consider embedding some vpython code here [https://trinket.io/glowscript/31d0f9ad9e Teach hands-on with GlowScript]

==Examples==

===Simple===
What is the magnetic dipole moment of a 1200 turn circular coil that has a radius of 10 cm and carries a current of 2 amperes?

Solution: µ=NIA N=1200 I = 2 A = π0.1^2

So µ = (1200)(2)(0.0314) = 75.4 Am^2

===Difficult===

What is the magnetic field at a point 3m away from a coil that has 250 turns, a radius of 2m and a current of 4 amperes running through it?

First step is to calculate {\mu}

==Connectedness==
#How is this topic connected to something that you are interested in?
#How is it connected to your major?
#Is there an interesting industrial application?

==History==

Put this idea in historical context. Give the reader the Who, What, When, Where, and Why.

== See also ==

Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?

===Further reading===

Books, Articles or other print media on this topic

===External links===

Internet resources on this topic

==References==

This section contains the the references you used while writing this page

[[Category:Which Category did you place this in?]]

Magnetic Dipole Moment

2015-12-01T20:47:34Z

Gebm03: /* Difficult */

Claimed by Guillermo Bacardi

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==

The main idea for this topic is to define the magnetic dipole moment and distinguish from the magnetic dipole.

===A Mathematical Model===

The magnetic dipole moment is represented by '''µ'''. This is set equal to the current running through the wire multiplied by the area of the circular loop. Here the area of the circular loop is defined as πR^2. The units for the magnetic dipole moment are amperes times meters squared.

<math> \boldsymbol{\mu} = \boldsymbol{I} \times\mathbf{A}</math>

If there is more than one coil in the loop then all of the coils must be accounted for by a value N that represents all of the coils.

<math> \boldsymbol{\mu} = \boldsymbol{NI} \times\mathbf{A}</math>

The overall equation for a magnetic field turns into

<math> \mathbf{B} = \frac{\mu_0}{4\pi}\frac{2\mu}{R^3}</math>

===A Computational Model===

How do we visualize or predict using this topic. Consider embedding some vpython code here [https://trinket.io/glowscript/31d0f9ad9e Teach hands-on with GlowScript]

==Examples==

===Simple===
What is the magnetic dipole moment of a 1200 turn circular coil that has a radius of 10 cm and carries a current of 2 amperes?

Solution: µ=NIA N=1200 I = 2 A = π0.1^2

So µ = (1200)(2)(0.0314) = 75.4 Am^2

===Difficult===

What is the magnetic field at a point 3m away from a coil that has 250 turns, a radius of 2m and a current of 4 amperes running through it?

First step is to calculate {\mu}

==Connectedness==
#How is this topic connected to something that you are interested in?
#How is it connected to your major?
#Is there an interesting industrial application?

==History==

Put this idea in historical context. Give the reader the Who, What, When, Where, and Why.

== See also ==

Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?

===Further reading===

Books, Articles or other print media on this topic

===External links===

Internet resources on this topic

==References==

This section contains the the references you used while writing this page

[[Category:Which Category did you place this in?]]

Magnetic Dipole Moment

2015-12-01T20:47:22Z

Gebm03: /* Difficult */

Claimed by Guillermo Bacardi

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==

The main idea for this topic is to define the magnetic dipole moment and distinguish from the magnetic dipole.

===A Mathematical Model===

The magnetic dipole moment is represented by '''µ'''. This is set equal to the current running through the wire multiplied by the area of the circular loop. Here the area of the circular loop is defined as πR^2. The units for the magnetic dipole moment are amperes times meters squared.

<math> \boldsymbol{\mu} = \boldsymbol{I} \times\mathbf{A}</math>

If there is more than one coil in the loop then all of the coils must be accounted for by a value N that represents all of the coils.

<math> \boldsymbol{\mu} = \boldsymbol{NI} \times\mathbf{A}</math>

The overall equation for a magnetic field turns into

<math> \mathbf{B} = \frac{\mu_0}{4\pi}\frac{2\mu}{R^3}</math>

===A Computational Model===

How do we visualize or predict using this topic. Consider embedding some vpython code here [https://trinket.io/glowscript/31d0f9ad9e Teach hands-on with GlowScript]

==Examples==

===Simple===
What is the magnetic dipole moment of a 1200 turn circular coil that has a radius of 10 cm and carries a current of 2 amperes?

Solution: µ=NIA N=1200 I = 2 A = π0.1^2

So µ = (1200)(2)(0.0314) = 75.4 Am^2

===Difficult===

What is the magnetic field at a point 3m away from a coil that has 250 turns, a radius of 2m and a current of 4 amperes running through it?

First step is to calculate {mu}

==Connectedness==
#How is this topic connected to something that you are interested in?
#How is it connected to your major?
#Is there an interesting industrial application?

==History==

Put this idea in historical context. Give the reader the Who, What, When, Where, and Why.

== See also ==

Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?

===Further reading===

Books, Articles or other print media on this topic

===External links===

Internet resources on this topic

==References==

This section contains the the references you used while writing this page

[[Category:Which Category did you place this in?]]

Magnetic Dipole Moment

2015-12-01T20:45:02Z

Gebm03: /* A Mathematical Model */

Claimed by Guillermo Bacardi

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==

The main idea for this topic is to define the magnetic dipole moment and distinguish from the magnetic dipole.

===A Mathematical Model===

The magnetic dipole moment is represented by '''µ'''. This is set equal to the current running through the wire multiplied by the area of the circular loop. Here the area of the circular loop is defined as πR^2. The units for the magnetic dipole moment are amperes times meters squared.

<math> \boldsymbol{\mu} = \boldsymbol{I} \times\mathbf{A}</math>

If there is more than one coil in the loop then all of the coils must be accounted for by a value N that represents all of the coils.

<math> \boldsymbol{\mu} = \boldsymbol{NI} \times\mathbf{A}</math>

The overall equation for a magnetic field turns into

<math> \mathbf{B} = \frac{\mu_0}{4\pi}\frac{2\mu}{R^3}</math>

===A Computational Model===

How do we visualize or predict using this topic. Consider embedding some vpython code here [https://trinket.io/glowscript/31d0f9ad9e Teach hands-on with GlowScript]

==Examples==

===Simple===
What is the magnetic dipole moment of a 1200 turn circular coil that has a radius of 10 cm and carries a current of 2 amperes?

Solution: µ=NIA N=1200 I = 2 A = π0.1^2

So µ = (1200)(2)(0.0314) = 75.4 Am^2

===Difficult===

==Connectedness==
#How is this topic connected to something that you are interested in?
#How is it connected to your major?
#Is there an interesting industrial application?

==History==

Put this idea in historical context. Give the reader the Who, What, When, Where, and Why.

== See also ==

Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?

===Further reading===

Books, Articles or other print media on this topic

===External links===

Internet resources on this topic

==References==

This section contains the the references you used while writing this page

[[Category:Which Category did you place this in?]]

Magnetic Dipole Moment

2015-12-01T20:44:48Z

Gebm03: /* A Mathematical Model */

Claimed by Guillermo Bacardi

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==

The main idea for this topic is to define the magnetic dipole moment and distinguish from the magnetic dipole.

===A Mathematical Model===

The magnetic dipole moment is represented by '''µ'''. This is set equal to the current running through the wire multiplied by the area of the circular loop. Here the area of the circular loop is defined as πR^2. The units for the magnetic dipole moment are amperes times meters squared.

<math> \boldsymbol{\mu} = \boldsymbol{I} \times\mathbf{A}</math>

If there is more than one coil in the loop then all of the coils must be accounted for by a value N that represents all of the coils.

<math> \boldsymbol{\mu} = \boldsymbol{NI} \times\mathbf{A}</math>

The overall equation for a magnetic field turns into

<math> \mathbf{B} = \frac{\mu_0}{4\pi}\frac{2\mu}{R}^3</math>

===A Computational Model===

How do we visualize or predict using this topic. Consider embedding some vpython code here [https://trinket.io/glowscript/31d0f9ad9e Teach hands-on with GlowScript]

==Examples==

===Simple===
What is the magnetic dipole moment of a 1200 turn circular coil that has a radius of 10 cm and carries a current of 2 amperes?

Solution: µ=NIA N=1200 I = 2 A = π0.1^2

So µ = (1200)(2)(0.0314) = 75.4 Am^2

===Difficult===

==Connectedness==
#How is this topic connected to something that you are interested in?
#How is it connected to your major?
#Is there an interesting industrial application?

==History==

Put this idea in historical context. Give the reader the Who, What, When, Where, and Why.

== See also ==

Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?

===Further reading===

Books, Articles or other print media on this topic

===External links===

Internet resources on this topic

==References==

This section contains the the references you used while writing this page

[[Category:Which Category did you place this in?]]

Magnetic Dipole Moment

2015-12-01T20:44:20Z

Gebm03: /* A Mathematical Model */

Claimed by Guillermo Bacardi

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==

The main idea for this topic is to define the magnetic dipole moment and distinguish from the magnetic dipole.

===A Mathematical Model===

The magnetic dipole moment is represented by '''µ'''. This is set equal to the current running through the wire multiplied by the area of the circular loop. Here the area of the circular loop is defined as πR^2. The units for the magnetic dipole moment are amperes times meters squared.

<math> \boldsymbol{\mu} = \boldsymbol{I} \times\mathbf{A}</math>

If there is more than one coil in the loop then all of the coils must be accounted for by a value N that represents all of the coils.

<math> \boldsymbol{\mu} = \boldsymbol{NI} \times\mathbf{A}</math>

The overall equation for a magnetic field turns into

<math> \mathbf{B} = \frac{\mu_0}{4\pi}\frac{\2mu}{R}^3</math>

===A Computational Model===

How do we visualize or predict using this topic. Consider embedding some vpython code here [https://trinket.io/glowscript/31d0f9ad9e Teach hands-on with GlowScript]

==Examples==

===Simple===
What is the magnetic dipole moment of a 1200 turn circular coil that has a radius of 10 cm and carries a current of 2 amperes?

Solution: µ=NIA N=1200 I = 2 A = π0.1^2

So µ = (1200)(2)(0.0314) = 75.4 Am^2

===Difficult===

==Connectedness==
#How is this topic connected to something that you are interested in?
#How is it connected to your major?
#Is there an interesting industrial application?

==History==

Put this idea in historical context. Give the reader the Who, What, When, Where, and Why.

== See also ==

Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?

===Further reading===

Books, Articles or other print media on this topic

===External links===

Internet resources on this topic

==References==

This section contains the the references you used while writing this page

[[Category:Which Category did you place this in?]]

Magnetic Dipole Moment

2015-12-01T20:43:09Z

Gebm03: /* A Mathematical Model */

Claimed by Guillermo Bacardi

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==

The main idea for this topic is to define the magnetic dipole moment and distinguish from the magnetic dipole.

===A Mathematical Model===

The magnetic dipole moment is represented by '''µ'''. This is set equal to the current running through the wire multiplied by the area of the circular loop. Here the area of the circular loop is defined as πR^2. The units for the magnetic dipole moment are amperes times meters squared.

<math> \boldsymbol{\mu} = \boldsymbol{I} \times\mathbf{A}</math>

If there is more than one coil in the loop then all of the coils must be accounted for by a value N that represents all of the coils.

<math> \boldsymbol{\mu} = \boldsymbol{NI} \times\mathbf{A}</math>

The overall equation for a magnetic field turns into

<math> \mathbf{B} = \frac{\mu_0}{4\pi}</math>

===A Computational Model===

How do we visualize or predict using this topic. Consider embedding some vpython code here [https://trinket.io/glowscript/31d0f9ad9e Teach hands-on with GlowScript]

==Examples==

===Simple===
What is the magnetic dipole moment of a 1200 turn circular coil that has a radius of 10 cm and carries a current of 2 amperes?

Solution: µ=NIA N=1200 I = 2 A = π0.1^2

So µ = (1200)(2)(0.0314) = 75.4 Am^2

===Difficult===

==Connectedness==
#How is this topic connected to something that you are interested in?
#How is it connected to your major?
#Is there an interesting industrial application?

==History==

Put this idea in historical context. Give the reader the Who, What, When, Where, and Why.

== See also ==

Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?

===Further reading===

Books, Articles or other print media on this topic

===External links===

Internet resources on this topic

==References==

This section contains the the references you used while writing this page

[[Category:Which Category did you place this in?]]

Magnetic Dipole Moment

2015-12-01T20:41:44Z

Gebm03: /* A Mathematical Model */

Claimed by Guillermo Bacardi

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==

The main idea for this topic is to define the magnetic dipole moment and distinguish from the magnetic dipole.

===A Mathematical Model===

The magnetic dipole moment is represented by '''µ'''. This is set equal to the current running through the wire multiplied by the area of the circular loop. Here the area of the circular loop is defined as πR^2. The units for the magnetic dipole moment are amperes times meters squared.

<math> \boldsymbol{\mu} = \boldsymbol{I} \times\mathbf{A}</math>

If there is more than one coil in the loop then all of the coils must be accounted for by a value N that represents all of the coils.

<math> \boldsymbol{\mu} = \boldsymbol{NI} \times\mathbf{A}</math>

The overall equation for a magnetic field turns into

<math> \mathbf{B} = \frac{\mu_0I}{4\pi}</math>

===A Computational Model===

How do we visualize or predict using this topic. Consider embedding some vpython code here [https://trinket.io/glowscript/31d0f9ad9e Teach hands-on with GlowScript]

==Examples==

===Simple===
What is the magnetic dipole moment of a 1200 turn circular coil that has a radius of 10 cm and carries a current of 2 amperes?

Solution: µ=NIA N=1200 I = 2 A = π0.1^2

So µ = (1200)(2)(0.0314) = 75.4 Am^2

===Difficult===

==Connectedness==
#How is this topic connected to something that you are interested in?
#How is it connected to your major?
#Is there an interesting industrial application?

==History==

Put this idea in historical context. Give the reader the Who, What, When, Where, and Why.

== See also ==

Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?

===Further reading===

Books, Articles or other print media on this topic

===External links===

Internet resources on this topic

==References==

This section contains the the references you used while writing this page

[[Category:Which Category did you place this in?]]

Magnetic Dipole Moment

2015-12-01T20:39:26Z

Gebm03: /* A Mathematical Model */

Claimed by Guillermo Bacardi

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==

The main idea for this topic is to define the magnetic dipole moment and distinguish from the magnetic dipole.

===A Mathematical Model===

The magnetic dipole moment is represented by '''µ'''. This is set equal to the current running through the wire multiplied by the area of the circular loop. Here the area of the circular loop is defined as πR^2. The units for the magnetic dipole moment are amperes times meters squared.

<math> \boldsymbol{\mu} = \boldsymbol{I} \times\mathbf{A}</math>

If there is more than one coil in the loop then all of the coils must be accounted for by a value N that represents all of the coils.

<math> \boldsymbol{\mu} = \boldsymbol{NI} \times\mathbf{A}</math>

The overall equation for a magnetic field turns into

<math> \mathbf{B} = \frac{\mu_0I}{4\pi}\</math>

===A Computational Model===

How do we visualize or predict using this topic. Consider embedding some vpython code here [https://trinket.io/glowscript/31d0f9ad9e Teach hands-on with GlowScript]

==Examples==

===Simple===
What is the magnetic dipole moment of a 1200 turn circular coil that has a radius of 10 cm and carries a current of 2 amperes?

Solution: µ=NIA N=1200 I = 2 A = π0.1^2

So µ = (1200)(2)(0.0314) = 75.4 Am^2

===Difficult===

==Connectedness==
#How is this topic connected to something that you are interested in?
#How is it connected to your major?
#Is there an interesting industrial application?

==History==

Put this idea in historical context. Give the reader the Who, What, When, Where, and Why.

== See also ==

Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?

===Further reading===

Books, Articles or other print media on this topic

===External links===

Internet resources on this topic

==References==

This section contains the the references you used while writing this page

[[Category:Which Category did you place this in?]]

Magnetic Dipole Moment

2015-12-01T20:38:51Z

Gebm03: /* A Mathematical Model */

Claimed by Guillermo Bacardi

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==

The main idea for this topic is to define the magnetic dipole moment and distinguish from the magnetic dipole.

===A Mathematical Model===

The magnetic dipole moment is represented by '''µ'''. This is set equal to the current running through the wire multiplied by the area of the circular loop. Here the area of the circular loop is defined as πR^2. The units for the magnetic dipole moment are amperes times meters squared.

<math> \boldsymbol{\mu} = \boldsymbol{I} \times\mathbf{A}</math>

If there is more than one coil in the loop then all of the coils must be accounted for by a value N that represents all of the coils.

<math> \boldsymbol{\mu} = \boldsymbol{NI} \times\mathbf{A}</math>

The overall equation for a magnetic field turns into

<math> \mathbf{B} = \frac{\mu_0I}{4\pi}\int_{\mathrm{wire}}\frac{\mathrm{d}\boldsymbol{\ell} \times \mathbf{\hat r}}{r^2},</math>

===A Computational Model===

How do we visualize or predict using this topic. Consider embedding some vpython code here [https://trinket.io/glowscript/31d0f9ad9e Teach hands-on with GlowScript]

==Examples==

===Simple===
What is the magnetic dipole moment of a 1200 turn circular coil that has a radius of 10 cm and carries a current of 2 amperes?

Solution: µ=NIA N=1200 I = 2 A = π0.1^2

So µ = (1200)(2)(0.0314) = 75.4 Am^2

===Difficult===

==Connectedness==
#How is this topic connected to something that you are interested in?
#How is it connected to your major?
#Is there an interesting industrial application?

==History==

Put this idea in historical context. Give the reader the Who, What, When, Where, and Why.

== See also ==

Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?

===Further reading===

Books, Articles or other print media on this topic

===External links===

Internet resources on this topic

==References==

This section contains the the references you used while writing this page

[[Category:Which Category did you place this in?]]

Magnetic Dipole Moment

2015-12-01T20:30:20Z

Gebm03: /* Examples */

Magnetic Dipole Moment

2015-12-01T20:30:06Z

Gebm03: /* A Mathematical Model */

Claimed by Guillermo Bacardi

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==

The main idea for this topic is to define the magnetic dipole moment and distinguish from the magnetic dipole.

===A Mathematical Model===

The magnetic dipole moment is represented by '''µ'''. This is set equal to the current running through the wire multiplied by the area of the circular loop. Here the area of the circular loop is defined as πR^2. The units for the magnetic dipole moment are amperes times meters squared.

<math> \boldsymbol{\mu} = \boldsymbol{I} \times\mathbf{A}</math>

If there is more than one coil in the loop then all of the coils must be accounted for by a value N that represents all of the coils.

<math> \boldsymbol{\mu} = \boldsymbol{NI} \times\mathbf{A}</math>

===A Computational Model===

How do we visualize or predict using this topic. Consider embedding some vpython code here [https://trinket.io/glowscript/31d0f9ad9e Teach hands-on with GlowScript]

==Examples==

Be sure to show all steps in your solution and include diagrams whenever possible

===Simple===
What is the magnetic dipole moment of a 1200 turn circular coil that has a radius of 10 cm and carries a current of 2 amperes?

Solution: µ=NIA N=1200 I = 2 A = π0.1^2

So µ = (1200)(2)(0.0314) = 75.4 Am^2

===Middling===
===Difficult===

==Connectedness==
#How is this topic connected to something that you are interested in?
#How is it connected to your major?
#Is there an interesting industrial application?

==History==

Put this idea in historical context. Give the reader the Who, What, When, Where, and Why.

== See also ==

Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?

===Further reading===

Books, Articles or other print media on this topic

===External links===

Internet resources on this topic

==References==

This section contains the the references you used while writing this page

[[Category:Which Category did you place this in?]]

Magnetic Dipole Moment

2015-12-01T20:29:24Z

Gebm03: /* Simple */

Magnetic Dipole Moment

2015-12-01T20:29:03Z

Gebm03: /* Examples */

Magnetic Dipole Moment

2015-12-01T20:28:30Z

Gebm03: /* Simple */

Magnetic Dipole Moment

2015-12-01T20:26:45Z

Gebm03: /* Simple */

Magnetic Dipole Moment

2015-12-01T20:25:32Z

Gebm03: /* Simple */

Magnetic Dipole Moment

2015-12-01T20:24:13Z

Gebm03: /* Simple */

Magnetic Dipole Moment

2015-12-01T20:23:25Z

Gebm03:

Magnetic Dipole Moment

2015-12-01T20:22:57Z

Gebm03: /* A Computational Model */

Magnetic Dipole Moment

2015-12-01T20:21:48Z

Gebm03: /* Simple */

Magnetic Dipole Moment

2015-12-01T20:17:19Z

Gebm03:

Magnetic Dipole Moment

2015-12-01T20:16:44Z

Gebm03:

File:Magnetic dipole copy.jpg

2015-12-01T20:15:26Z

Gebm03:

Magnetic Dipole Moment

2015-12-01T20:15:07Z

Gebm03:

Magnetic Dipole Moment

2015-12-01T20:04:48Z

Gebm03:

Magnetic Dipole Moment

2015-12-01T20:03:13Z

Gebm03:

Magnetic Dipole Moment

2015-12-01T19:59:55Z

Gebm03:

Magnetic Dipole Moment

2015-12-01T19:59:44Z

Gebm03:

Magnetic Dipole Moment

2015-12-01T19:59:21Z

Gebm03:

Magnetic Dipole Moment

2015-12-01T19:59:07Z

Gebm03:

Magnetic Dipole Moment

2015-12-01T19:58:47Z

Gebm03:

Magnetic Dipole Moment

2015-12-01T19:58:36Z

Gebm03:

Magnetic Dipole Moment

2015-12-01T19:57:57Z

Gebm03: