Magnetic Field of a Solenoid

2015-12-06T02:55:45Z

Ramin8:

Created by ramin8 !!

A Solenoid is a type of electromagnet, which consists of a coil tightly wound into a helix. Usually it produces a uniform magnetic field when an electric current is run through it. The purpose of a solenoid is to create a controlled magnetic field.

==The Main Idea==

The purpose of this application is to explore another way to apply the Biot-Sarvart law. The magnetic field is uniform along the axis of the solenoid, when electric current is run through it. The solenoid has has to have coils much larger than the radius.

===A Mathematical Model===

This is the formula for the magnetic field inside a long solenoid:
<math> B = {\mu _{0}} \frac{NI}{L}</math>
This formula is used inside a long solenoid, when the radius of the solenoid is much smaller than the length.
B is the magnetic field.
<math>{\mu _{0}}</math> is a constant.
N is the number of loops in the solenoid.
L is the length of the solenoid.

To determine the direction of the magnetic field: use your right hand and curl your fingers towards the direction of the current and the direction that your thumb is pointing to is the direction of the magnetic field.

===A Computational Model===
A solenoid has a length of .5 meters and a radius of .03 meters and wound around 50 times a wire that has a current of 1 ampere. Find the magnetic field vectors.
from visual import ∗

scene . width=1024 scene.x = scene.y = 0

scene . background = color . white

L = 0.5

R = 0.03

kmag = 1e-7

I = 1

Nturns=50. ## number of turns in solenoid

Nelts=20. ## number of line segments per turn

bscale = 600. ## scale factor for B arrows

.## make a solenoid

dxx = L/(Nturns∗Nelts)

xx = arange(L/2., L/2+dxx, dxx)

omega = 2∗pi∗Nturns/L

solenoid = curve(x=xx, y=R∗sin(xx∗omega), z=R∗cos(xx∗omega), color=(.9,.7,0),radius =0.001)

.## make a list of zero lth arrows at observation locations

Barrows =[] ## empty list

dx = L/4.

zz=0.

for x in arange(

==Examples==

===Difficult===
To solve for the magnetic field of a solenoid, we need to do a three step process.

Imagine a solenoid with a length L that is made up of N loops wound, each with a radius R and a current I. Each loop is one piece.
[[File:Screen Shot 2015-12-05 at 6.12.26 PM.jpg]]

Step 2: Write an Equation for the Magnetic Field Due to One Piece

The origin of the solenoid is at its center. To find the location of one piece we have to find the integration variable, which is x, and then the distance from the loop to the observation location is d-z. There are also N/L loops in the solenoid so the number of loops in the length <math>\Delta x</math> is N/L*<math>\Delta E</math>.

So this the equation we have so far using the magnetic field formula, shown as the top image on the right.
[[File:FullSizeRenderRadz.jpg|200px|thumb|right|Equation]]

Step 2: Add Up all the Pieces

The net magnetic field lies along the axis and the sum is <math>\Delta B</math>.

This can be turned into a integral from -L/2 to L/2, shown as the bottom image on the right.
[[File:FullSizeRenderRads1.jpg|200px|thumb|right|The Integral]]

The integral can be solved out using a standard table of integrals or an integration calculator.

==Connectedness==
There are many applications to solenoids that we use as a part of our everyday lives. They can be found in medical equipment, air conditioning devices, electric locking mechanisms, cars, and many others. To find out more about each of these applications in detail please go to [[Solenoid Applications]].
One example is the car starter solenoid. The starter solenoid receives a large electric current from the car battery and a small electric current from the ignition switch. When the switch is turned on, the small current forces the starter solenoid to close contacts and relays the large electric current to the starter motor.

==History==

Andre-Marie Ampere originally coined the word "Solenoid" in the 1820's, which he used to describe a helical coil. He probably used solenoid while he was developing the theory for Ampere's Law, which can be used to find the magnetic field of a solenoid.
[[File:Andre-marie-ampere-3.jpg|200px|thumb|right|alt text]]

== See also ==

[[Ampere's Law]]

[[Right-Hand Rule]]

[[Solenoid Applications]]

[[Magnetic Field of A Loop]]

===Further reading===

http://hyperphysics.phy-astr.gsu.edu/hbase/magnetic/solenoid.html

===External links===
[http://www.gouldvalve.com/wp-content/uploads/2009/05/typical-uses-pages-1-3.pdf]

==References==

http://hyperphysics.phy-astr.gsu.edu/hbase/magnetic/solenoid.html
http://www.bachofen.ch/fr/schalttechnik/ProdukteF_Composants/Befehlsgeraete_Schalter_Mikroschalter/Johnson_Electric_LEDEX_Solenoids_EN_2014.pdf

Matters and Interactions, 3rd Edition
[[Category: Fields]]

Magnetic Field of a Solenoid

2015-12-06T02:54:40Z

Ramin8:

Created by ramin8 !!

A Solenoid is a type of electromagnet, which consists of a coil tightly wound into a helix. Usually it produces a uniform magnetic field when an electric current is run through it. The purpose of a solenoid is to create a controlled magnetic field.

==The Main Idea==

The purpose of this application is to explore another way to apply the Biot-Sarvart law. The magnetic field is uniform along the axis of the solenoid, when electric current is run through it. The solenoid has has to have coils much larger than the radius.

===A Mathematical Model===

This is the formula for the magnetic field inside a long solenoid:
<math> B = {\mu _{0}} \frac{NI}{L}</math>
This formula is used inside a long solenoid, when the radius of the solenoid is much smaller than the length.
B is the magnetic field.
<math>{\mu _{0}}</math> is a constant.
N is the number of loops in the solenoid.
L is the length of the solenoid.

To determine the direction of the magnetic field: use your right hand and curl your fingers towards the direction of the current and the direction that your thumb is pointing to is the direction of the magnetic field.

===A Computational Model===
A solenoid has a length of .5 meters and a radius of .03 meters and wound around 50 times a wire that has a current of 1 ampere. Find the magnetic field vectors.
from visual import ∗

scene . width=1024 scene.x = scene.y = 0

scene . background = color . white

L = 0.5

R = 0.03

kmag = 1e-7

I = 1

Nturns=50. ## number of turns in solenoid

Nelts=20. ## number of line segments per turn

bscale = 600. ## scale factor for B arrows

.## make a solenoid

dxx = L/(Nturns∗Nelts)

xx = arange(L/2., L/2+dxx, dxx)

omega = 2∗pi∗Nturns/L

solenoid = curve(x=xx, y=R∗sin(xx∗omega), z=R∗cos(xx∗omega), color=(.9,.7,0),radius =0.001)

.## make a list of zero lth arrows at observation locations

Barrows =[] ## empty list

dx = L/4.

zz=0.

for x in arange(

==Examples==

===Difficult===
To solve for the magnetic field of a solenoid, we need to do a three step process.

Imagine a solenoid with a length L that is made up of N loops wound, each with a radius R and a current I. Each loop is one piece.
[[File:Screen Shot 2015-12-05 at 6.12.26 PM.jpg]]

Step 2: Write an Equation for the Magnetic Field Due to One Piece

The origin of the solenoid is at its center. To find the location of one piece we have to find the integration variable, which is x, and then the distance from the loop to the observation location is d-z. There are also N/L loops in the solenoid so the number of loops in the length <math>\Delta x</math> is N/L*<math>\Delta E</math>.

So this the equation we have so far using the magnetic field formula:
[[File:FullSizeRenderRadz.jpg|200px|thumb|right|alt text]]

Step 2: Add Up all the Pieces

The net magnetic field lies along the axis and the sum is <math>\Delta B</math>.

This can be turned into a integral from -L/2 to L/2:
[[File:FullSizeRenderRads1.jpg|200px|thumb|right|alt text]]

The integral can be solved out using a standard table of integrals or an integration calculator.

==Connectedness==
There are many applications to solenoids that we use as a part of our everyday lives. They can be found in medical equipment, air conditioning devices, electric locking mechanisms, cars, and many others. To find out more about each of these applications in detail please go to [[Solenoid Applications]].
One example is the car starter solenoid. The starter solenoid receives a large electric current from the car battery and a small electric current from the ignition switch. When the switch is turned on, the small current forces the starter solenoid to close contacts and relays the large electric current to the starter motor.

==History==

Andre-Marie Ampere originally coined the word "Solenoid" in the 1820's, which he used to describe a helical coil. He probably used solenoid while he was developing the theory for Ampere's Law, which can be used to find the magnetic field of a solenoid.
[[File:Andre-marie-ampere-3.jpg|200px|thumb|right|alt text]]

== See also ==

[[Ampere's Law]]

[[Right-Hand Rule]]

[[Solenoid Applications]]

[[Magnetic Field of A Loop]]

===Further reading===

http://hyperphysics.phy-astr.gsu.edu/hbase/magnetic/solenoid.html

===External links===
[http://www.gouldvalve.com/wp-content/uploads/2009/05/typical-uses-pages-1-3.pdf]

==References==

http://hyperphysics.phy-astr.gsu.edu/hbase/magnetic/solenoid.html
http://www.bachofen.ch/fr/schalttechnik/ProdukteF_Composants/Befehlsgeraete_Schalter_Mikroschalter/Johnson_Electric_LEDEX_Solenoids_EN_2014.pdf

Matters and Interactions, 3rd Edition
[[Category: Fields]]

Magnetic Field of a Solenoid

2015-12-06T02:52:50Z

Ramin8:

Created by ramin8 !!

A Solenoid is a type of electromagnet, which consists of a coil tightly wound into a helix. Usually it produces a uniform magnetic field when an electric current is run through it. The purpose of a solenoid is to create a controlled magnetic field.

==The Main Idea==

The purpose of this application is to explore another way to apply the Biot-Sarvart law. The magnetic field is uniform along the axis of the solenoid, when electric current is run through it. The solenoid has has to have coils much larger than the radius.

===A Mathematical Model===

This is the formula for the magnetic field inside a long solenoid:
<math> B = {\mu _{0}} \frac{NI}{L}</math>
This formula is used inside a long solenoid, when the radius of the solenoid is much smaller than the length.
B is the magnetic field.
<math>{\mu _{0}}</math> is a constant.
N is the number of loops in the solenoid.
L is the length of the solenoid.

To determine the direction of the magnetic field: use your right hand and curl your fingers towards the direction of the current and the direction that your thumb is pointing to is the direction of the magnetic field.

===A Computational Model===
A solenoid has a length of .5 meters and a radius of .03 meters and wound around 50 times a wire that has a current of 1 ampere. Find the magnetic field vectors.
from visual import ∗

scene . width=1024 scene.x = scene.y = 0

scene . background = color . white

L = 0.5

R = 0.03

kmag = 1e-7

I = 1

Nturns=50. ## number of turns in solenoid

Nelts=20. ## number of line segments per turn

bscale = 600. ## scale factor for B arrows

.## make a solenoid

dxx = L/(Nturns∗Nelts)

xx = arange(L/2., L/2+dxx, dxx)

omega = 2∗pi∗Nturns/L

solenoid = curve(x=xx, y=R∗sin(xx∗omega), z=R∗cos(xx∗omega), color=(.9,.7,0),radius =0.001)

.## make a list of zero lth arrows at observation locations

Barrows =[] ## empty list

dx = L/4.

zz=0.

for x in arange(

==Examples==

===Difficult===
To solve for the magnetic field of a solenoid, we need to do a three step process.

Imagine a solenoid with a length L that is made up of N loops wound, each with a radius R and a current I. Each loop is one piece.
[[File:Screen Shot 2015-12-05 at 6.12.26 PM.jpg]]

Step 2: Write an Equation for the Magnetic Field Due to One Piece

The origin of the solenoid is at its center. To find the location of one piece we have to find the integration variable, which is x, and then the distance from the loop to the observation location is d-z. There are also N/L loops in the solenoid so the number of loops in the length <math>\Delta x</math> is N/L*<math>\Delta E</math>.

So this the equation we have so far using the magnetic field formula:
[[File:FullSizeRenderRadz.jpg]]

Step 2: Add Up all the Pieces

The net magnetic field lies along the axis and the sum is <math>\Delta B</math>.

This can be turned into a integral from -L/2 to L/2:
[[File:FullSizeRenderRads1.jpg]]

The integral can be solved out using a standard table of integrals or an integration calculator.

==Connectedness==
There are many applications to solenoids that we use as a part of our everyday lives. They can be found in medical equipment, air conditioning devices, electric locking mechanisms, cars, and many others. To find out more about each of these applications in detail please go to [[Solenoid Applications]].
One example is the car starter solenoid. The starter solenoid receives a large electric current from the car battery and a small electric current from the ignition switch. When the switch is turned on, the small current forces the starter solenoid to close contacts and relays the large electric current to the starter motor.

==History==

Andre-Marie Ampere originally coined the word "Solenoid" in the 1820's, which he used to describe a helical coil. He probably used solenoid while he was developing the theory for Ampere's Law, which can be used to find the magnetic field of a solenoid.
[[File:Andre-marie-ampere-3.jpg]]

== See also ==

[[Ampere's Law]]

[[Right-Hand Rule]]

[[Solenoid Applications]]

[[Magnetic Field of A Loop]]

===Further reading===

http://hyperphysics.phy-astr.gsu.edu/hbase/magnetic/solenoid.html

===External links===
[http://www.gouldvalve.com/wp-content/uploads/2009/05/typical-uses-pages-1-3.pdf]

==References==

http://hyperphysics.phy-astr.gsu.edu/hbase/magnetic/solenoid.html
http://www.bachofen.ch/fr/schalttechnik/ProdukteF_Composants/Befehlsgeraete_Schalter_Mikroschalter/Johnson_Electric_LEDEX_Solenoids_EN_2014.pdf

Matters and Interactions, 3rd Edition
[[Category: Fields]]

File:FullSizeRenderRadz.jpg

2015-12-06T02:52:15Z

Ramin8:

File:FullSizeRenderRads1.jpg

2015-12-06T02:51:32Z

Ramin8:

Magnetic Field of a Solenoid

Magnetic Field of a Solenoid

2015-12-05T16:26:08Z

Ramin8:

Claimed by ramin8 !!

A Solenoid is a type of electromagnet, which consists of a coil tightly wound into a helix. Usually it produces a uniform magnetic field when an electric current is run through it. The purpose of a solenoid is to create a controlled magnetic field.

==The Main Idea==

The purpose of this application is to explore another way to apply the Biot-Sarvart law. The magnetic field is uniform along the axis of the solenoid, when electric current is run through it. The solenoid has has to have coils much larger than the radius.

===A Mathematical Model===

This is the formula for the magnetic field inside a long solenoid:
<math> B = {\mu _{0}} \frac{NI}{L}</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==

To solve for the magnetic field of a solenoid, you can use a four step process.

Step 1: Cut up the distribution into pieces and Draw the |Delta|B
Consider this: a solenoid the length of L that's made up for N circular loops tightly wound, each with a radius of R and a conventional current in the loops is I.

We want to find the magnetic field contributed by each of the loops at any location along the axis of the solenoid.

Step 2: Write an Expression for the Magnetic Field Due to One Piece.
The origin is located at the center of the solenoid.
[[File:solenoid.jpg]]
===Simple===
===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===
[http://www.scientificamerican.com/article/bring-science-home-reaction-time/]

==References==

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

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

Magnetic Field of a Solenoid

2015-12-04T17:08:31Z

Ramin8:

Claimed by ramin8 !!

A Solenoid is a type of electromagnet, which consists of a coil tightly wound into a helix. Usually it produces a uniform magnetic field when an electric current is run through it. The purpose of a solenoid is to create a controlled magnetic field.

==The Main Idea==

The purpose of this application is to explore another way to apply the Biot-Sarvart law. The magnetic field is uniform along the axis of the solenoid, when electric current is run through it. The solenoid has has to have coils much larger than the radius.

===A Mathematical Model===

This is the formula for the magnetic field inside a long solenoid:
<math> B = {\mu _{0}} \frac{NI}{L}</math>

To solve for the magnetic field of a solenoid, you can use a four step process.
Step: Cut up the distribution into pieces and Draw the |Delta|B
Consider this: a solenoid the length of L that's made up for N circular loops tightly wound, each with a radius of R and a conventional current in the loops is I.

===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===
===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===
[http://www.scientificamerican.com/article/bring-science-home-reaction-time/]

==References==

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

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

Magnetic Field of a Solenoid

2015-12-04T16:41:13Z

Ramin8:

Magnetic Field of a Solenoid

2015-12-04T16:37:39Z

Ramin8:

2015-11-30T22:08:38Z

Ramin8:

Claimed by ramin8 !!