Physics Book - User contributions [en]

Magnetic Field of a Solenoid Using Ampere's Law

2016-11-28T04:39:57Z

Mchandler30: /* Connectedness */

Claimed by Mary Jane Chandler Fall 2016

This page explains how to use Ampere's Law to solve for the magnetic field of a solenoid.

==The Main Idea==

A solenoid is a cylindrical coil of wire that produces a uniform magnetic field when it is carrying an electric current. A solenoid is a form of an electromagnet that can create strong controlled magnetic fields throughout the coil except at the ends. Ampere's Law states that the magnetic field in space around an electric current is proportional to the source of the electric current. This can be applied to solve the magnetic field of a Solenoid.

[[File:solenoidfrombook.png]]

As you can see in this model, in the middle of the solenoid the field is constant throughout the entirety of the interior and is parallel to the axis. At the ends of a solenoid the magnetic field starts to point outward at varying angles.

===Equation===

If there are <math>N</math> loops of wire that compose a solenoid of length <math>L</math>, and we know that Ampere's Law gives us the form:

<math>{\oint\,\vec{B}•d\vec{l} = μ_{0}∑I_{inside path}}</math>

We can then solve for <math>B</math>:

<math>{B = \frac{μ_{0}NI}{L}}</math>

The Right Hand Rule can be used to find the direction of the magnetic field by using your right hand and curling your fingers in the direction of the current with your thumb pointing in the direction of the magnetic field. This is always along the axis for a solenoid.

[[File:Righthand.png]]

==Examples==

===Solving for the Magnetic Field===
Find the magnetic field produced by a 20 cm long solenoid if the number of loops is 200 and current passing through it is 8 A.

For this example all of the variables are given so it is just a simple math calculation using Ampere's Law, as given above, but for reiteration.

<math>{\oint\,\vec{B}•d\vec{l} = μ_{0}∑I_{inside path}}</math>

<math>{B = \frac{200*8}{.2}}</math>
<math>{B = 8,000} </math>

Once you have solved for <math>B</math> all you have to do is find the direction of the magnetic field using the Right Hand Rule.

*Must convert 20 cm to .2 m

===Solving for the Current===
A solenoid has a magnetic field of 6x10-4 T, 2000 turns, and is 10 cm long. What is the current through the solenoid?
For this example you are solving for I. Very similar to the above question, just rearranging the calculation of Ampere's Law.

<math>{I = \frac{LB}{μ_{0}N}}</math>

<math>{I = \frac{.1*6E-4}{2000}}</math>
<math>{I = 3E-8 A} </math>

*Must change 10 cm to .1 for the cm to m conversion

==Connection==
#Solenoids are important because they can create controlled magnetic fields making them useful for a variety of applications
#As a Biology major this relates to my major because solenoids are very important in the medical field. An example of solenoids is that they are very beneficial when it comes to controlling the flow of medicine that enters the bloodstream of individuals.

==See Also==
[[Ampere's Law]]

[[Magnetic Field of a Long Thick Wire Using Ampere's Law]]

[[Magnetic Field of Coaxial Cable Using Ampere's Law]]

[[Magnetic Field of a Toroid Using Ampere's Law]]

===Further Reading===

Chabay, Sherwood. (2015). Matter and Interactions (4th ed., Vol. 2). Raleigh, North Carolina: Wiley.

===External Links===

*http://www.physicstutorials.org/home/magnetism/magnetic-field-around-a-solenoid

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

==References==
Chabay, Sherwood. (2015). Matter and Interactions (4th ed., Vol. 2). Raleigh, North Carolina: Wiley. Pg 887-888.

[[Category:Maxwell's Equations]]

Magnetic Field of a Solenoid Using Ampere's Law

2016-11-28T04:39:25Z

Mchandler30: /* External Links */

Claimed by Mary Jane Chandler Fall 2016

This page explains how to use Ampere's Law to solve for the magnetic field of a solenoid.

==The Main Idea==

A solenoid is a cylindrical coil of wire that produces a uniform magnetic field when it is carrying an electric current. A solenoid is a form of an electromagnet that can create strong controlled magnetic fields throughout the coil except at the ends. Ampere's Law states that the magnetic field in space around an electric current is proportional to the source of the electric current. This can be applied to solve the magnetic field of a Solenoid.

[[File:solenoidfrombook.png]]

As you can see in this model, in the middle of the solenoid the field is constant throughout the entirety of the interior and is parallel to the axis. At the ends of a solenoid the magnetic field starts to point outward at varying angles.

===Equation===

If there are <math>N</math> loops of wire that compose a solenoid of length <math>L</math>, and we know that Ampere's Law gives us the form:

<math>{\oint\,\vec{B}•d\vec{l} = μ_{0}∑I_{inside path}}</math>

We can then solve for <math>B</math>:

<math>{B = \frac{μ_{0}NI}{L}}</math>

The Right Hand Rule can be used to find the direction of the magnetic field by using your right hand and curling your fingers in the direction of the current with your thumb pointing in the direction of the magnetic field. This is always along the axis for a solenoid.

[[File:Righthand.png]]

==Examples==

===Solving for the Magnetic Field===
Find the magnetic field produced by a 20 cm long solenoid if the number of loops is 200 and current passing through it is 8 A.

For this example all of the variables are given so it is just a simple math calculation using Ampere's Law, as given above, but for reiteration.

<math>{\oint\,\vec{B}•d\vec{l} = μ_{0}∑I_{inside path}}</math>

<math>{B = \frac{200*8}{.2}}</math>
<math>{B = 8,000} </math>

Once you have solved for <math>B</math> all you have to do is find the direction of the magnetic field using the Right Hand Rule.

*Must convert 20 cm to .2 m

===Solving for the Current===
A solenoid has a magnetic field of 6x10-4 T, 2000 turns, and is 10 cm long. What is the current through the solenoid?
For this example you are solving for I. Very similar to the above question, just rearranging the calculation of Ampere's Law.

<math>{I = \frac{LB}{μ_{0}N}}</math>

<math>{I = \frac{.1*6E-4}{2000}}</math>
<math>{I = 3E-8 A} </math>

*Must change 10 cm to .1 for the cm to m conversion

==Connectedness==
#Solenoids are important because they can create controlled magnetic fields making them useful for a variety of applications
#As a Biology major this relates to my major because solenoids are very important in the medical field. An example of solenoids is that they are very beneficial when it comes to controlling the flow of medicine that enters the bloodstream of individuals.

==See Also==
[[Ampere's Law]]

[[Magnetic Field of a Long Thick Wire Using Ampere's Law]]

[[Magnetic Field of Coaxial Cable Using Ampere's Law]]

[[Magnetic Field of a Toroid Using Ampere's Law]]

===Further Reading===

Chabay, Sherwood. (2015). Matter and Interactions (4th ed., Vol. 2). Raleigh, North Carolina: Wiley.

===External Links===

*http://www.physicstutorials.org/home/magnetism/magnetic-field-around-a-solenoid

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

==References==
Chabay, Sherwood. (2015). Matter and Interactions (4th ed., Vol. 2). Raleigh, North Carolina: Wiley. Pg 887-888.

[[Category:Maxwell's Equations]]

Magnetic Field of a Solenoid Using Ampere's Law

2016-11-28T04:38:33Z

Mchandler30: /* References */

Claimed by Mary Jane Chandler Fall 2016

This page explains how to use Ampere's Law to solve for the magnetic field of a solenoid.

==The Main Idea==

A solenoid is a cylindrical coil of wire that produces a uniform magnetic field when it is carrying an electric current. A solenoid is a form of an electromagnet that can create strong controlled magnetic fields throughout the coil except at the ends. Ampere's Law states that the magnetic field in space around an electric current is proportional to the source of the electric current. This can be applied to solve the magnetic field of a Solenoid.

[[File:solenoidfrombook.png]]

As you can see in this model, in the middle of the solenoid the field is constant throughout the entirety of the interior and is parallel to the axis. At the ends of a solenoid the magnetic field starts to point outward at varying angles.

===Equation===

If there are <math>N</math> loops of wire that compose a solenoid of length <math>L</math>, and we know that Ampere's Law gives us the form:

<math>{\oint\,\vec{B}•d\vec{l} = μ_{0}∑I_{inside path}}</math>

We can then solve for <math>B</math>:

<math>{B = \frac{μ_{0}NI}{L}}</math>

The Right Hand Rule can be used to find the direction of the magnetic field by using your right hand and curling your fingers in the direction of the current with your thumb pointing in the direction of the magnetic field. This is always along the axis for a solenoid.

[[File:Righthand.png]]

==Examples==

===Solving for the Magnetic Field===
Find the magnetic field produced by a 20 cm long solenoid if the number of loops is 200 and current passing through it is 8 A.

For this example all of the variables are given so it is just a simple math calculation using Ampere's Law, as given above, but for reiteration.

<math>{\oint\,\vec{B}•d\vec{l} = μ_{0}∑I_{inside path}}</math>

<math>{B = \frac{200*8}{.2}}</math>
<math>{B = 8,000} </math>

Once you have solved for <math>B</math> all you have to do is find the direction of the magnetic field using the Right Hand Rule.

*Must convert 20 cm to .2 m

===Solving for the Current===
A solenoid has a magnetic field of 6x10-4 T, 2000 turns, and is 10 cm long. What is the current through the solenoid?
For this example you are solving for I. Very similar to the above question, just rearranging the calculation of Ampere's Law.

<math>{I = \frac{LB}{μ_{0}N}}</math>

<math>{I = \frac{.1*6E-4}{2000}}</math>
<math>{I = 3E-8 A} </math>

*Must change 10 cm to .1 for the cm to m conversion

==Connectedness==
#Solenoids are important because they can create controlled magnetic fields making them useful for a variety of applications
#As a Biology major this relates to my major because solenoids are very important in the medical field. An example of solenoids is that they are very beneficial when it comes to controlling the flow of medicine that enters the bloodstream of individuals.

==See Also==
[[Ampere's Law]]

[[Magnetic Field of a Long Thick Wire Using Ampere's Law]]

[[Magnetic Field of Coaxial Cable Using Ampere's Law]]

[[Magnetic Field of a Toroid Using Ampere's Law]]

===Further Reading===

Chabay, Sherwood. (2015). Matter and Interactions (4th ed., Vol. 2). Raleigh, North Carolina: Wiley.

===External Links===
*http://www.one-school.net/Malaysia/UniversityandCollege/SPM/revisioncard/physics/electromagnetism/electromagnet.html

*http://www.physicstutorials.org/home/magnetism/magnetic-field-around-a-solenoid

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

==References==
Chabay, Sherwood. (2015). Matter and Interactions (4th ed., Vol. 2). Raleigh, North Carolina: Wiley. Pg 887-888.

[[Category:Maxwell's Equations]]

Magnetic Field of a Solenoid Using Ampere's Law

2016-11-28T04:37:38Z

Mchandler30: /* Difficult */

Claimed by Mary Jane Chandler Fall 2016

This page explains how to use Ampere's Law to solve for the magnetic field of a solenoid.

==The Main Idea==

A solenoid is a cylindrical coil of wire that produces a uniform magnetic field when it is carrying an electric current. A solenoid is a form of an electromagnet that can create strong controlled magnetic fields throughout the coil except at the ends. Ampere's Law states that the magnetic field in space around an electric current is proportional to the source of the electric current. This can be applied to solve the magnetic field of a Solenoid.

[[File:solenoidfrombook.png]]

As you can see in this model, in the middle of the solenoid the field is constant throughout the entirety of the interior and is parallel to the axis. At the ends of a solenoid the magnetic field starts to point outward at varying angles.

===Equation===

If there are <math>N</math> loops of wire that compose a solenoid of length <math>L</math>, and we know that Ampere's Law gives us the form:

<math>{\oint\,\vec{B}•d\vec{l} = μ_{0}∑I_{inside path}}</math>

We can then solve for <math>B</math>:

<math>{B = \frac{μ_{0}NI}{L}}</math>

The Right Hand Rule can be used to find the direction of the magnetic field by using your right hand and curling your fingers in the direction of the current with your thumb pointing in the direction of the magnetic field. This is always along the axis for a solenoid.

[[File:Righthand.png]]

==Examples==

===Solving for the Magnetic Field===
Find the magnetic field produced by a 20 cm long solenoid if the number of loops is 200 and current passing through it is 8 A.

For this example all of the variables are given so it is just a simple math calculation using Ampere's Law, as given above, but for reiteration.

<math>{\oint\,\vec{B}•d\vec{l} = μ_{0}∑I_{inside path}}</math>

<math>{B = \frac{200*8}{.2}}</math>
<math>{B = 8,000} </math>

Once you have solved for <math>B</math> all you have to do is find the direction of the magnetic field using the Right Hand Rule.

*Must convert 20 cm to .2 m

===Solving for the Current===
A solenoid has a magnetic field of 6x10-4 T, 2000 turns, and is 10 cm long. What is the current through the solenoid?
For this example you are solving for I. Very similar to the above question, just rearranging the calculation of Ampere's Law.

<math>{I = \frac{LB}{μ_{0}N}}</math>

<math>{I = \frac{.1*6E-4}{2000}}</math>
<math>{I = 3E-8 A} </math>

*Must change 10 cm to .1 for the cm to m conversion

==Connectedness==
#Solenoids are important because they can create controlled magnetic fields making them useful for a variety of applications
#As a Biology major this relates to my major because solenoids are very important in the medical field. An example of solenoids is that they are very beneficial when it comes to controlling the flow of medicine that enters the bloodstream of individuals.

==See Also==
[[Ampere's Law]]

[[Magnetic Field of a Long Thick Wire Using Ampere's Law]]

[[Magnetic Field of Coaxial Cable Using Ampere's Law]]

[[Magnetic Field of a Toroid Using Ampere's Law]]

===Further Reading===

Chabay, Sherwood. (2015). Matter and Interactions (4th ed., Vol. 2). Raleigh, North Carolina: Wiley.

===External Links===
*http://www.one-school.net/Malaysia/UniversityandCollege/SPM/revisioncard/physics/electromagnetism/electromagnet.html

*http://www.physicstutorials.org/home/magnetism/magnetic-field-around-a-solenoid

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

==References==
Chabay, Sherwood. (2015). Matter and Interactions (4th ed., Vol. 2). Raleigh, North Carolina: Wiley. Pg 887-888.
Physics 2212 Spring 2016 Lab Quiz 8

[[Category:Maxwell's Equations]]

Magnetic Field of a Solenoid Using Ampere's Law

2016-11-28T04:37:23Z

Mchandler30: /* Solving for the Magnetic Field */

Claimed by Mary Jane Chandler Fall 2016

This page explains how to use Ampere's Law to solve for the magnetic field of a solenoid.

==The Main Idea==

A solenoid is a cylindrical coil of wire that produces a uniform magnetic field when it is carrying an electric current. A solenoid is a form of an electromagnet that can create strong controlled magnetic fields throughout the coil except at the ends. Ampere's Law states that the magnetic field in space around an electric current is proportional to the source of the electric current. This can be applied to solve the magnetic field of a Solenoid.

[[File:solenoidfrombook.png]]

As you can see in this model, in the middle of the solenoid the field is constant throughout the entirety of the interior and is parallel to the axis. At the ends of a solenoid the magnetic field starts to point outward at varying angles.

===Equation===

If there are <math>N</math> loops of wire that compose a solenoid of length <math>L</math>, and we know that Ampere's Law gives us the form:

<math>{\oint\,\vec{B}•d\vec{l} = μ_{0}∑I_{inside path}}</math>

We can then solve for <math>B</math>:

<math>{B = \frac{μ_{0}NI}{L}}</math>

The Right Hand Rule can be used to find the direction of the magnetic field by using your right hand and curling your fingers in the direction of the current with your thumb pointing in the direction of the magnetic field. This is always along the axis for a solenoid.

[[File:Righthand.png]]

==Examples==

===Solving for the Magnetic Field===
Find the magnetic field produced by a 20 cm long solenoid if the number of loops is 200 and current passing through it is 8 A.

For this example all of the variables are given so it is just a simple math calculation using Ampere's Law, as given above, but for reiteration.

<math>{\oint\,\vec{B}•d\vec{l} = μ_{0}∑I_{inside path}}</math>

<math>{B = \frac{200*8}{.2}}</math>
<math>{B = 8,000} </math>

Once you have solved for <math>B</math> all you have to do is find the direction of the magnetic field using the Right Hand Rule.

*Must convert 20 cm to .2 m

===Solving for the Current===
A solenoid has a magnetic field of 6x10-4 T, 2000 turns, and is 10 cm long. What is the current through the solenoid?
For this example you are solving for I. Very similar to the above question, just rearranging the calculation of Ampere's Law.

<math>{I = \frac{LB}{μ_{0}N}}</math>

<math>{I = \frac{.1*6E-4}{2000}}</math>
<math>{I = 3E-8 A} </math>

*Must change 10 cm to .1 for the cm to m conversion

===Difficult===
A long, tightly wound solenoid has a circular cross section of radius 0.02 m. The solenoid is connected to a power supply (not shown), and this current changes with time, so the magnetic field inside the solenoid also changes with time. At time t = 0 s, the magnitude of the magnetic field inside the solenoid is 1.8 T. At time t = 0.3 s, the magnitude of the magnetic field inside the solenoid is 0.5 T. The direction of the magnetic field inside the solenoid is shown in the diagram. The solenoid passes through a coil of wire, which has 45 turns of radius 0.15 m. The coil is connected to a voltmeter (not shown).

[[File:hardexdigram.png]]

a.) At the same instant (t = 0.3 seconds), what will the absolute value of the reading on the
voltmeter be?
[[File:harda.jpg|700x900px]]

b.) The resistance of the coil is 2 ohms. At time t = 0.3 seconds, what is the conventional current
in the coil?
[[File:hardb.jpg|700x900px]]

c.) At time t = 0.3 seconds, what is the magnitude of the non-coulomb electric field ENC in
the coil?
[[File:hardc.jpg|700x900px]]

==Connectedness==
#Solenoids are important because they can create controlled magnetic fields making them useful for a variety of applications
#As a Biology major this relates to my major because solenoids are very important in the medical field. An example of solenoids is that they are very beneficial when it comes to controlling the flow of medicine that enters the bloodstream of individuals.

==See Also==
[[Ampere's Law]]

[[Magnetic Field of a Long Thick Wire Using Ampere's Law]]

[[Magnetic Field of Coaxial Cable Using Ampere's Law]]

[[Magnetic Field of a Toroid Using Ampere's Law]]

===Further Reading===

Chabay, Sherwood. (2015). Matter and Interactions (4th ed., Vol. 2). Raleigh, North Carolina: Wiley.

===External Links===
*http://www.one-school.net/Malaysia/UniversityandCollege/SPM/revisioncard/physics/electromagnetism/electromagnet.html

*http://www.physicstutorials.org/home/magnetism/magnetic-field-around-a-solenoid

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

==References==
Chabay, Sherwood. (2015). Matter and Interactions (4th ed., Vol. 2). Raleigh, North Carolina: Wiley. Pg 887-888.
Physics 2212 Spring 2016 Lab Quiz 8

[[Category:Maxwell's Equations]]

Magnetic Field of a Solenoid Using Ampere's Law

2016-11-28T04:36:56Z

Mchandler30: /* Solving for the Current */

Claimed by Mary Jane Chandler Fall 2016

This page explains how to use Ampere's Law to solve for the magnetic field of a solenoid.

==The Main Idea==

A solenoid is a cylindrical coil of wire that produces a uniform magnetic field when it is carrying an electric current. A solenoid is a form of an electromagnet that can create strong controlled magnetic fields throughout the coil except at the ends. Ampere's Law states that the magnetic field in space around an electric current is proportional to the source of the electric current. This can be applied to solve the magnetic field of a Solenoid.

[[File:solenoidfrombook.png]]

As you can see in this model, in the middle of the solenoid the field is constant throughout the entirety of the interior and is parallel to the axis. At the ends of a solenoid the magnetic field starts to point outward at varying angles.

===Equation===

If there are <math>N</math> loops of wire that compose a solenoid of length <math>L</math>, and we know that Ampere's Law gives us the form:

<math>{\oint\,\vec{B}•d\vec{l} = μ_{0}∑I_{inside path}}</math>

We can then solve for <math>B</math>:

<math>{B = \frac{μ_{0}NI}{L}}</math>

The Right Hand Rule can be used to find the direction of the magnetic field by using your right hand and curling your fingers in the direction of the current with your thumb pointing in the direction of the magnetic field. This is always along the axis for a solenoid.

[[File:Righthand.png]]

==Examples==

===Solving for the Magnetic Field===
Find the magnetic field produced by a 20 cm long solenoid if the number of loops is 200 and current passing through it is 8 A.

For this example all of the variables are given so it is just a simple math calculation using Ampere's Law, as given above, but for reiteration.

<math>{\oint\,\vec{B}•d\vec{l} = μ_{0}∑I_{inside path}}</math>

<math>{B = \frac{200*8}{.2}}</math>
<math>{B = 8,000} </math>

Once you have solved for <math>B</math> all you have to do is find the direction of the magnetic field using the Right Hand Rule.

===Solving for the Current===
A solenoid has a magnetic field of 6x10-4 T, 2000 turns, and is 10 cm long. What is the current through the solenoid?
For this example you are solving for I. Very similar to the above question, just rearranging the calculation of Ampere's Law.

<math>{I = \frac{LB}{μ_{0}N}}</math>

<math>{I = \frac{.1*6E-4}{2000}}</math>
<math>{I = 3E-8 A} </math>

*Must change 10 cm to .1 for the cm to m conversion

===Difficult===
A long, tightly wound solenoid has a circular cross section of radius 0.02 m. The solenoid is connected to a power supply (not shown), and this current changes with time, so the magnetic field inside the solenoid also changes with time. At time t = 0 s, the magnitude of the magnetic field inside the solenoid is 1.8 T. At time t = 0.3 s, the magnitude of the magnetic field inside the solenoid is 0.5 T. The direction of the magnetic field inside the solenoid is shown in the diagram. The solenoid passes through a coil of wire, which has 45 turns of radius 0.15 m. The coil is connected to a voltmeter (not shown).

[[File:hardexdigram.png]]

a.) At the same instant (t = 0.3 seconds), what will the absolute value of the reading on the
voltmeter be?
[[File:harda.jpg|700x900px]]

b.) The resistance of the coil is 2 ohms. At time t = 0.3 seconds, what is the conventional current
in the coil?
[[File:hardb.jpg|700x900px]]

c.) At time t = 0.3 seconds, what is the magnitude of the non-coulomb electric field ENC in
the coil?
[[File:hardc.jpg|700x900px]]

==Connectedness==
#Solenoids are important because they can create controlled magnetic fields making them useful for a variety of applications
#As a Biology major this relates to my major because solenoids are very important in the medical field. An example of solenoids is that they are very beneficial when it comes to controlling the flow of medicine that enters the bloodstream of individuals.

==See Also==
[[Ampere's Law]]

[[Magnetic Field of a Long Thick Wire Using Ampere's Law]]

[[Magnetic Field of Coaxial Cable Using Ampere's Law]]

[[Magnetic Field of a Toroid Using Ampere's Law]]

===Further Reading===

Chabay, Sherwood. (2015). Matter and Interactions (4th ed., Vol. 2). Raleigh, North Carolina: Wiley.

===External Links===
*http://www.one-school.net/Malaysia/UniversityandCollege/SPM/revisioncard/physics/electromagnetism/electromagnet.html

*http://www.physicstutorials.org/home/magnetism/magnetic-field-around-a-solenoid

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

==References==
Chabay, Sherwood. (2015). Matter and Interactions (4th ed., Vol. 2). Raleigh, North Carolina: Wiley. Pg 887-888.
Physics 2212 Spring 2016 Lab Quiz 8

[[Category:Maxwell's Equations]]

Magnetic Field of a Solenoid Using Ampere's Law

2016-11-28T04:36:45Z

Mchandler30: /* Middling */

Claimed by Mary Jane Chandler Fall 2016

This page explains how to use Ampere's Law to solve for the magnetic field of a solenoid.

==The Main Idea==

A solenoid is a cylindrical coil of wire that produces a uniform magnetic field when it is carrying an electric current. A solenoid is a form of an electromagnet that can create strong controlled magnetic fields throughout the coil except at the ends. Ampere's Law states that the magnetic field in space around an electric current is proportional to the source of the electric current. This can be applied to solve the magnetic field of a Solenoid.

[[File:solenoidfrombook.png]]

As you can see in this model, in the middle of the solenoid the field is constant throughout the entirety of the interior and is parallel to the axis. At the ends of a solenoid the magnetic field starts to point outward at varying angles.

===Equation===

If there are <math>N</math> loops of wire that compose a solenoid of length <math>L</math>, and we know that Ampere's Law gives us the form:

<math>{\oint\,\vec{B}•d\vec{l} = μ_{0}∑I_{inside path}}</math>

We can then solve for <math>B</math>:

<math>{B = \frac{μ_{0}NI}{L}}</math>

The Right Hand Rule can be used to find the direction of the magnetic field by using your right hand and curling your fingers in the direction of the current with your thumb pointing in the direction of the magnetic field. This is always along the axis for a solenoid.

[[File:Righthand.png]]

==Examples==

===Solving for the Magnetic Field===
Find the magnetic field produced by a 20 cm long solenoid if the number of loops is 200 and current passing through it is 8 A.

For this example all of the variables are given so it is just a simple math calculation using Ampere's Law, as given above, but for reiteration.

<math>{\oint\,\vec{B}•d\vec{l} = μ_{0}∑I_{inside path}}</math>

<math>{B = \frac{200*8}{.2}}</math>
<math>{B = 8,000} </math>

Once you have solved for <math>B</math> all you have to do is find the direction of the magnetic field using the Right Hand Rule.

===Solving for the Current===
A solenoid has a magnetic field of 6x10-4 T, 2000 turns, and is 10 cm long. What is the current through the solenoid?
For this example you are solving for I. Very similar to the above question, just rearranging the calculation of Ampere's Law.

<math>{I = \frac{LB}{μ_{0}N}}</math>

<math>{I = \frac{.1*6E-4}{2000}}</math>
<math>{I = 3E-8 A} </math>

*Must change 10 cm to .1 for the cm to m conversion*

===Difficult===
A long, tightly wound solenoid has a circular cross section of radius 0.02 m. The solenoid is connected to a power supply (not shown), and this current changes with time, so the magnetic field inside the solenoid also changes with time. At time t = 0 s, the magnitude of the magnetic field inside the solenoid is 1.8 T. At time t = 0.3 s, the magnitude of the magnetic field inside the solenoid is 0.5 T. The direction of the magnetic field inside the solenoid is shown in the diagram. The solenoid passes through a coil of wire, which has 45 turns of radius 0.15 m. The coil is connected to a voltmeter (not shown).

[[File:hardexdigram.png]]

a.) At the same instant (t = 0.3 seconds), what will the absolute value of the reading on the
voltmeter be?
[[File:harda.jpg|700x900px]]

b.) The resistance of the coil is 2 ohms. At time t = 0.3 seconds, what is the conventional current
in the coil?
[[File:hardb.jpg|700x900px]]

c.) At time t = 0.3 seconds, what is the magnitude of the non-coulomb electric field ENC in
the coil?
[[File:hardc.jpg|700x900px]]

==Connectedness==
#Solenoids are important because they can create controlled magnetic fields making them useful for a variety of applications
#As a Biology major this relates to my major because solenoids are very important in the medical field. An example of solenoids is that they are very beneficial when it comes to controlling the flow of medicine that enters the bloodstream of individuals.

==See Also==
[[Ampere's Law]]

[[Magnetic Field of a Long Thick Wire Using Ampere's Law]]

[[Magnetic Field of Coaxial Cable Using Ampere's Law]]

[[Magnetic Field of a Toroid Using Ampere's Law]]

===Further Reading===

Chabay, Sherwood. (2015). Matter and Interactions (4th ed., Vol. 2). Raleigh, North Carolina: Wiley.

===External Links===
*http://www.one-school.net/Malaysia/UniversityandCollege/SPM/revisioncard/physics/electromagnetism/electromagnet.html

*http://www.physicstutorials.org/home/magnetism/magnetic-field-around-a-solenoid

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

==References==
Chabay, Sherwood. (2015). Matter and Interactions (4th ed., Vol. 2). Raleigh, North Carolina: Wiley. Pg 887-888.
Physics 2212 Spring 2016 Lab Quiz 8

[[Category:Maxwell's Equations]]

Magnetic Field of a Solenoid Using Ampere's Law

2016-11-28T04:35:52Z

Mchandler30: /* Easy */

Claimed by Mary Jane Chandler Fall 2016

This page explains how to use Ampere's Law to solve for the magnetic field of a solenoid.

==The Main Idea==

A solenoid is a cylindrical coil of wire that produces a uniform magnetic field when it is carrying an electric current. A solenoid is a form of an electromagnet that can create strong controlled magnetic fields throughout the coil except at the ends. Ampere's Law states that the magnetic field in space around an electric current is proportional to the source of the electric current. This can be applied to solve the magnetic field of a Solenoid.

[[File:solenoidfrombook.png]]

As you can see in this model, in the middle of the solenoid the field is constant throughout the entirety of the interior and is parallel to the axis. At the ends of a solenoid the magnetic field starts to point outward at varying angles.

===Equation===

If there are <math>N</math> loops of wire that compose a solenoid of length <math>L</math>, and we know that Ampere's Law gives us the form:

<math>{\oint\,\vec{B}•d\vec{l} = μ_{0}∑I_{inside path}}</math>

We can then solve for <math>B</math>:

<math>{B = \frac{μ_{0}NI}{L}}</math>

The Right Hand Rule can be used to find the direction of the magnetic field by using your right hand and curling your fingers in the direction of the current with your thumb pointing in the direction of the magnetic field. This is always along the axis for a solenoid.

[[File:Righthand.png]]

==Examples==

===Solving for the Magnetic Field===
Find the magnetic field produced by a 20 cm long solenoid if the number of loops is 200 and current passing through it is 8 A.

For this example all of the variables are given so it is just a simple math calculation using Ampere's Law, as given above, but for reiteration.

<math>{\oint\,\vec{B}•d\vec{l} = μ_{0}∑I_{inside path}}</math>

<math>{B = \frac{200*8}{.2}}</math>
<math>{B = 8,000} </math>

Once you have solved for <math>B</math> all you have to do is find the direction of the magnetic field using the Right Hand Rule.

===Middling===
A solenoid has a magnetic field of 6x10-4 T, 2000 turns, and is 10 cm long. What is the current through the solenoid?
For this example you are solving for I. Very similar to the above question, just rearranging the calculation of Ampere's Law.

<math>{I = \frac{LB}{μ_{0}N}}</math>

<math>{I = \frac{.1*6E-4}{2000}}</math>
<math>{I = 3E-8} </math>

===Difficult===
A long, tightly wound solenoid has a circular cross section of radius 0.02 m. The solenoid is connected to a power supply (not shown), and this current changes with time, so the magnetic field inside the solenoid also changes with time. At time t = 0 s, the magnitude of the magnetic field inside the solenoid is 1.8 T. At time t = 0.3 s, the magnitude of the magnetic field inside the solenoid is 0.5 T. The direction of the magnetic field inside the solenoid is shown in the diagram. The solenoid passes through a coil of wire, which has 45 turns of radius 0.15 m. The coil is connected to a voltmeter (not shown).

[[File:hardexdigram.png]]

a.) At the same instant (t = 0.3 seconds), what will the absolute value of the reading on the
voltmeter be?
[[File:harda.jpg|700x900px]]

b.) The resistance of the coil is 2 ohms. At time t = 0.3 seconds, what is the conventional current
in the coil?
[[File:hardb.jpg|700x900px]]

c.) At time t = 0.3 seconds, what is the magnitude of the non-coulomb electric field ENC in
the coil?
[[File:hardc.jpg|700x900px]]

==Connectedness==
#Solenoids are important because they can create controlled magnetic fields making them useful for a variety of applications
#As a Biology major this relates to my major because solenoids are very important in the medical field. An example of solenoids is that they are very beneficial when it comes to controlling the flow of medicine that enters the bloodstream of individuals.

==See Also==
[[Ampere's Law]]

[[Magnetic Field of a Long Thick Wire Using Ampere's Law]]

[[Magnetic Field of Coaxial Cable Using Ampere's Law]]

[[Magnetic Field of a Toroid Using Ampere's Law]]

===Further Reading===

Chabay, Sherwood. (2015). Matter and Interactions (4th ed., Vol. 2). Raleigh, North Carolina: Wiley.

===External Links===
*http://www.one-school.net/Malaysia/UniversityandCollege/SPM/revisioncard/physics/electromagnetism/electromagnet.html

*http://www.physicstutorials.org/home/magnetism/magnetic-field-around-a-solenoid

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

==References==
Chabay, Sherwood. (2015). Matter and Interactions (4th ed., Vol. 2). Raleigh, North Carolina: Wiley. Pg 887-888.
Physics 2212 Spring 2016 Lab Quiz 8

[[Category:Maxwell's Equations]]

Magnetic Field of a Solenoid Using Ampere's Law

2016-11-28T04:35:02Z

Mchandler30: /* Examples */

Claimed by Mary Jane Chandler Fall 2016

This page explains how to use Ampere's Law to solve for the magnetic field of a solenoid.

==The Main Idea==

A solenoid is a cylindrical coil of wire that produces a uniform magnetic field when it is carrying an electric current. A solenoid is a form of an electromagnet that can create strong controlled magnetic fields throughout the coil except at the ends. Ampere's Law states that the magnetic field in space around an electric current is proportional to the source of the electric current. This can be applied to solve the magnetic field of a Solenoid.

[[File:solenoidfrombook.png]]

As you can see in this model, in the middle of the solenoid the field is constant throughout the entirety of the interior and is parallel to the axis. At the ends of a solenoid the magnetic field starts to point outward at varying angles.

===Equation===

If there are <math>N</math> loops of wire that compose a solenoid of length <math>L</math>, and we know that Ampere's Law gives us the form:

<math>{\oint\,\vec{B}•d\vec{l} = μ_{0}∑I_{inside path}}</math>

We can then solve for <math>B</math>:

<math>{B = \frac{μ_{0}NI}{L}}</math>

The Right Hand Rule can be used to find the direction of the magnetic field by using your right hand and curling your fingers in the direction of the current with your thumb pointing in the direction of the magnetic field. This is always along the axis for a solenoid.

[[File:Righthand.png]]

==Examples==

===Easy===
Find the magnetic field produced by a 20 cm long solenoid if the number of loops is 200 and current passing through it is 8 A.

For this example all of the variables are given so it is just a simple math calculation using Ampere's Law, as given above, but for reiteration.

<math>{\oint\,\vec{B}•d\vec{l} = μ_{0}∑I_{inside path}}</math>

<math>{B = \frac{200*8}{.2}}</math>
<math>{B = 8,000} </math>

Once you have solved for <math>B</math> all you have to do is find the direction of the magnetic field using the Right Hand Rule.

===Middling===
A solenoid has a magnetic field of 6x10-4 T, 2000 turns, and is 10 cm long. What is the current through the solenoid?
For this example you are solving for I. Very similar to the above question, just rearranging the calculation of Ampere's Law.

<math>{I = \frac{LB}{μ_{0}N}}</math>

<math>{I = \frac{.1*6E-4}{2000}}</math>
<math>{I = 3E-8} </math>

===Difficult===
A long, tightly wound solenoid has a circular cross section of radius 0.02 m. The solenoid is connected to a power supply (not shown), and this current changes with time, so the magnetic field inside the solenoid also changes with time. At time t = 0 s, the magnitude of the magnetic field inside the solenoid is 1.8 T. At time t = 0.3 s, the magnitude of the magnetic field inside the solenoid is 0.5 T. The direction of the magnetic field inside the solenoid is shown in the diagram. The solenoid passes through a coil of wire, which has 45 turns of radius 0.15 m. The coil is connected to a voltmeter (not shown).

[[File:hardexdigram.png]]

a.) At the same instant (t = 0.3 seconds), what will the absolute value of the reading on the
voltmeter be?
[[File:harda.jpg|700x900px]]

b.) The resistance of the coil is 2 ohms. At time t = 0.3 seconds, what is the conventional current
in the coil?
[[File:hardb.jpg|700x900px]]

c.) At time t = 0.3 seconds, what is the magnitude of the non-coulomb electric field ENC in
the coil?
[[File:hardc.jpg|700x900px]]

==Connectedness==
#Solenoids are important because they can create controlled magnetic fields making them useful for a variety of applications
#As a Biology major this relates to my major because solenoids are very important in the medical field. An example of solenoids is that they are very beneficial when it comes to controlling the flow of medicine that enters the bloodstream of individuals.

==See Also==
[[Ampere's Law]]

[[Magnetic Field of a Long Thick Wire Using Ampere's Law]]

[[Magnetic Field of Coaxial Cable Using Ampere's Law]]

[[Magnetic Field of a Toroid Using Ampere's Law]]

===Further Reading===

Chabay, Sherwood. (2015). Matter and Interactions (4th ed., Vol. 2). Raleigh, North Carolina: Wiley.

===External Links===
*http://www.one-school.net/Malaysia/UniversityandCollege/SPM/revisioncard/physics/electromagnetism/electromagnet.html

*http://www.physicstutorials.org/home/magnetism/magnetic-field-around-a-solenoid

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

==References==
Chabay, Sherwood. (2015). Matter and Interactions (4th ed., Vol. 2). Raleigh, North Carolina: Wiley. Pg 887-888.
Physics 2212 Spring 2016 Lab Quiz 8

[[Category:Maxwell's Equations]]

Magnetic Field of a Solenoid Using Ampere's Law

2016-11-28T04:28:52Z

Mchandler30: /* Examples */

Claimed by Mary Jane Chandler Fall 2016

This page explains how to use Ampere's Law to solve for the magnetic field of a solenoid.

==The Main Idea==

A solenoid is a cylindrical coil of wire that produces a uniform magnetic field when it is carrying an electric current. A solenoid is a form of an electromagnet that can create strong controlled magnetic fields throughout the coil except at the ends. Ampere's Law states that the magnetic field in space around an electric current is proportional to the source of the electric current. This can be applied to solve the magnetic field of a Solenoid.

[[File:solenoidfrombook.png]]

As you can see in this model, in the middle of the solenoid the field is constant throughout the entirety of the interior and is parallel to the axis. At the ends of a solenoid the magnetic field starts to point outward at varying angles.

===Equation===

If there are <math>N</math> loops of wire that compose a solenoid of length <math>L</math>, and we know that Ampere's Law gives us the form:

<math>{\oint\,\vec{B}•d\vec{l} = μ_{0}∑I_{inside path}}</math>

We can then solve for <math>B</math>:

<math>{B = \frac{μ_{0}NI}{L}}</math>

The Right Hand Rule can be used to find the direction of the magnetic field by using your right hand and curling your fingers in the direction of the current with your thumb pointing in the direction of the magnetic field. This is always along the axis for a solenoid.

[[File:Righthand.png]]

==Examples==

===Easy===
Find the magnetic field produced by a 40 cm long solenoid if the number of loops is 400 and current passing through it is 5 A.

For this example all of the variables are given so it is just a simple math calculation using Ampere's Law, as given above, but for reiteration.

<math>{\oint\,\vec{B}•d\vec{l} = μ_{0}∑I_{inside path}}</math>

<math>{B = \frac{400*5}{.4}}</math>
<math>{B = 5,000} </math>

Once you have solved for <math>B</math> all you have to do is find the direction of the magnetic field using the Right Hand Rule.

===Middling===
A solenoid has a magnetic field of 5x10-4 T, 3000 turns, and is 30 cm long. What is the current through the solenoid?
For this example you are solving for I. Very similar to the above question, just rearranging the calculation of Ampere's Law.

<math>{I = \frac{LB}{μ_{0}N}}</math>

<math>{I = \frac{.3*5x10^-4}{3000}}</math>
<math>{I = 5E-8} </math>

===Difficult===
A long, tightly wound solenoid has a circular cross section of radius 0.02 m. The solenoid is connected to a power supply (not shown), and this current changes with time, so the magnetic field inside the solenoid also changes with time. At time t = 0 s, the magnitude of the magnetic field inside the solenoid is 1.8 T. At time t = 0.3 s, the magnitude of the magnetic field inside the solenoid is 0.5 T. The direction of the magnetic field inside the solenoid is shown in the diagram. The solenoid passes through a coil of wire, which has 45 turns of radius 0.15 m. The coil is connected to a voltmeter (not shown).

[[File:hardexdigram.png]]

a.) At the same instant (t = 0.3 seconds), what will the absolute value of the reading on the
voltmeter be?
[[File:harda.jpg|700x900px]]

b.) The resistance of the coil is 2 ohms. At time t = 0.3 seconds, what is the conventional current
in the coil?
[[File:hardb.jpg|700x900px]]

c.) At time t = 0.3 seconds, what is the magnitude of the non-coulomb electric field ENC in
the coil?
[[File:hardc.jpg|700x900px]]

==Connectedness==
#Solenoids are important because they can create controlled magnetic fields making them useful for a variety of applications
#As a Biology major this relates to my major because solenoids are very important in the medical field. An example of solenoids is that they are very beneficial when it comes to controlling the flow of medicine that enters the bloodstream of individuals.

==See Also==
[[Ampere's Law]]

[[Magnetic Field of a Long Thick Wire Using Ampere's Law]]

[[Magnetic Field of Coaxial Cable Using Ampere's Law]]

[[Magnetic Field of a Toroid Using Ampere's Law]]

===Further Reading===

Chabay, Sherwood. (2015). Matter and Interactions (4th ed., Vol. 2). Raleigh, North Carolina: Wiley.

===External Links===
*http://www.one-school.net/Malaysia/UniversityandCollege/SPM/revisioncard/physics/electromagnetism/electromagnet.html

*http://www.physicstutorials.org/home/magnetism/magnetic-field-around-a-solenoid

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

==References==
Chabay, Sherwood. (2015). Matter and Interactions (4th ed., Vol. 2). Raleigh, North Carolina: Wiley. Pg 887-888.
Physics 2212 Spring 2016 Lab Quiz 8

[[Category:Maxwell's Equations]]

Magnetic Field of a Solenoid Using Ampere's Law

2016-11-28T04:27:59Z

Mchandler30: /* Examples */

Claimed by Mary Jane Chandler Fall 2016

This page explains how to use Ampere's Law to solve for the magnetic field of a solenoid.

==The Main Idea==

A solenoid is a cylindrical coil of wire that produces a uniform magnetic field when it is carrying an electric current. A solenoid is a form of an electromagnet that can create strong controlled magnetic fields throughout the coil except at the ends. Ampere's Law states that the magnetic field in space around an electric current is proportional to the source of the electric current. This can be applied to solve the magnetic field of a Solenoid.

[[File:solenoidfrombook.png]]

As you can see in this model, in the middle of the solenoid the field is constant throughout the entirety of the interior and is parallel to the axis. At the ends of a solenoid the magnetic field starts to point outward at varying angles.

===Equation===

If there are <math>N</math> loops of wire that compose a solenoid of length <math>L</math>, and we know that Ampere's Law gives us the form:

<math>{\oint\,\vec{B}•d\vec{l} = μ_{0}∑I_{inside path}}</math>

We can then solve for <math>B</math>:

<math>{B = \frac{μ_{0}NI}{L}}</math>

The Right Hand Rule can be used to find the direction of the magnetic field by using your right hand and curling your fingers in the direction of the current with your thumb pointing in the direction of the magnetic field. This is always along the axis for a solenoid.

[[File:Righthand.png]]

==Examples==

===Easy===
Find the magnetic field produced by a 40 cm long solenoid if the number of loops is 400 and current passing through it is 5 A.

For this example all of the variables are given so it is just a simple math calculation using Ampere's Law, as given above, but for reiteration.

<math>{\oint\,\vec{B}•d\vec{l} = μ_{0}∑I_{inside path}}</math>

<math>{B = \frac{{400}{5}{.4}}}</math>
<math>{B = 5,000} </math>

Once you have solved for <math>B</math> all you have to do is find the direction of the magnetic field using the Right Hand Rule.

===Middling===
A solenoid has a magnetic field of 5x10-4 T, 3000 turns, and is 30 cm long. What is the current through the solenoid?
For this example you are solving for I. Very similar to the above question, just rearranging the calculation of Ampere's Law.

<math>{I = \frac{LB}{μ_{0}N}}</math>

<math>{I = \frac{.3*5x10^-4}{3000}}</math>
<math>{I = 5E-8} </math>

===Difficult===
A long, tightly wound solenoid has a circular cross section of radius 0.02 m. The solenoid is connected to a power supply (not shown), and this current changes with time, so the magnetic field inside the solenoid also changes with time. At time t = 0 s, the magnitude of the magnetic field inside the solenoid is 1.8 T. At time t = 0.3 s, the magnitude of the magnetic field inside the solenoid is 0.5 T. The direction of the magnetic field inside the solenoid is shown in the diagram. The solenoid passes through a coil of wire, which has 45 turns of radius 0.15 m. The coil is connected to a voltmeter (not shown).

[[File:hardexdigram.png]]

a.) At the same instant (t = 0.3 seconds), what will the absolute value of the reading on the
voltmeter be?
[[File:harda.jpg|700x900px]]

b.) The resistance of the coil is 2 ohms. At time t = 0.3 seconds, what is the conventional current
in the coil?
[[File:hardb.jpg|700x900px]]

c.) At time t = 0.3 seconds, what is the magnitude of the non-coulomb electric field ENC in
the coil?
[[File:hardc.jpg|700x900px]]

==Connectedness==
#Solenoids are important because they can create controlled magnetic fields making them useful for a variety of applications
#As a Biology major this relates to my major because solenoids are very important in the medical field. An example of solenoids is that they are very beneficial when it comes to controlling the flow of medicine that enters the bloodstream of individuals.

==See Also==
[[Ampere's Law]]

[[Magnetic Field of a Long Thick Wire Using Ampere's Law]]

[[Magnetic Field of Coaxial Cable Using Ampere's Law]]

[[Magnetic Field of a Toroid Using Ampere's Law]]

===Further Reading===

Chabay, Sherwood. (2015). Matter and Interactions (4th ed., Vol. 2). Raleigh, North Carolina: Wiley.

===External Links===
*http://www.one-school.net/Malaysia/UniversityandCollege/SPM/revisioncard/physics/electromagnetism/electromagnet.html

*http://www.physicstutorials.org/home/magnetism/magnetic-field-around-a-solenoid

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

==References==
Chabay, Sherwood. (2015). Matter and Interactions (4th ed., Vol. 2). Raleigh, North Carolina: Wiley. Pg 887-888.
Physics 2212 Spring 2016 Lab Quiz 8

[[Category:Maxwell's Equations]]

Magnetic Field of a Solenoid Using Ampere's Law

2016-11-28T04:27:25Z

Mchandler30: /* Examples */

Claimed by Mary Jane Chandler Fall 2016

This page explains how to use Ampere's Law to solve for the magnetic field of a solenoid.

==The Main Idea==

A solenoid is a cylindrical coil of wire that produces a uniform magnetic field when it is carrying an electric current. A solenoid is a form of an electromagnet that can create strong controlled magnetic fields throughout the coil except at the ends. Ampere's Law states that the magnetic field in space around an electric current is proportional to the source of the electric current. This can be applied to solve the magnetic field of a Solenoid.

[[File:solenoidfrombook.png]]

As you can see in this model, in the middle of the solenoid the field is constant throughout the entirety of the interior and is parallel to the axis. At the ends of a solenoid the magnetic field starts to point outward at varying angles.

===Equation===

If there are <math>N</math> loops of wire that compose a solenoid of length <math>L</math>, and we know that Ampere's Law gives us the form:

<math>{\oint\,\vec{B}•d\vec{l} = μ_{0}∑I_{inside path}}</math>

We can then solve for <math>B</math>:

<math>{B = \frac{μ_{0}NI}{L}}</math>

The Right Hand Rule can be used to find the direction of the magnetic field by using your right hand and curling your fingers in the direction of the current with your thumb pointing in the direction of the magnetic field. This is always along the axis for a solenoid.

[[File:Righthand.png]]

==Examples==

===Easy===
Find the magnetic field produced by a 40 cm long solenoid if the number of loops is 400 and current passing through it is 5 A.

For this example all of the variables are given so it is just a simple math calculation using Ampere's Law, as given above, but for reiteration.

<math>{\oint\,\vec{B}•d\vec{l} = μ_{0}∑I_{inside path}}</math>

<math>{B = \frac{{400*5}{.4}}}</math>
<math>{B = 5,000} </math>

Once you have solved for <math>B</math> all you have to do is find the direction of the magnetic field using the Right Hand Rule.

===Middling===
A solenoid has a magnetic field of 5x10-4 T, 3000 turns, and is 30 cm long. What is the current through the solenoid?
For this example you are solving for I. Very similar to the above question, just rearranging the calculation of Ampere's Law.

<math>{I = \frac{LB}{μ_{0}N}}</math>

<math>{I = \frac{.3*5x10^-4}{3000}}</math>
<math>{I = 5E-8} </math>

===Difficult===
A long, tightly wound solenoid has a circular cross section of radius 0.02 m. The solenoid is connected to a power supply (not shown), and this current changes with time, so the magnetic field inside the solenoid also changes with time. At time t = 0 s, the magnitude of the magnetic field inside the solenoid is 1.8 T. At time t = 0.3 s, the magnitude of the magnetic field inside the solenoid is 0.5 T. The direction of the magnetic field inside the solenoid is shown in the diagram. The solenoid passes through a coil of wire, which has 45 turns of radius 0.15 m. The coil is connected to a voltmeter (not shown).

[[File:hardexdigram.png]]

a.) At the same instant (t = 0.3 seconds), what will the absolute value of the reading on the
voltmeter be?
[[File:harda.jpg|700x900px]]

b.) The resistance of the coil is 2 ohms. At time t = 0.3 seconds, what is the conventional current
in the coil?
[[File:hardb.jpg|700x900px]]

c.) At time t = 0.3 seconds, what is the magnitude of the non-coulomb electric field ENC in
the coil?
[[File:hardc.jpg|700x900px]]

==Connectedness==
#Solenoids are important because they can create controlled magnetic fields making them useful for a variety of applications
#As a Biology major this relates to my major because solenoids are very important in the medical field. An example of solenoids is that they are very beneficial when it comes to controlling the flow of medicine that enters the bloodstream of individuals.

==See Also==
[[Ampere's Law]]

[[Magnetic Field of a Long Thick Wire Using Ampere's Law]]

[[Magnetic Field of Coaxial Cable Using Ampere's Law]]

[[Magnetic Field of a Toroid Using Ampere's Law]]

===Further Reading===

Chabay, Sherwood. (2015). Matter and Interactions (4th ed., Vol. 2). Raleigh, North Carolina: Wiley.

===External Links===
*http://www.one-school.net/Malaysia/UniversityandCollege/SPM/revisioncard/physics/electromagnetism/electromagnet.html

*http://www.physicstutorials.org/home/magnetism/magnetic-field-around-a-solenoid

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

==References==
Chabay, Sherwood. (2015). Matter and Interactions (4th ed., Vol. 2). Raleigh, North Carolina: Wiley. Pg 887-888.
Physics 2212 Spring 2016 Lab Quiz 8

[[Category:Maxwell's Equations]]

Magnetic Field of a Solenoid Using Ampere's Law

2016-11-28T04:24:26Z

Mchandler30: /* Middling */

Claimed by Mary Jane Chandler Fall 2016

This page explains how to use Ampere's Law to solve for the magnetic field of a solenoid.

==The Main Idea==

A solenoid is a cylindrical coil of wire that produces a uniform magnetic field when it is carrying an electric current. A solenoid is a form of an electromagnet that can create strong controlled magnetic fields throughout the coil except at the ends. Ampere's Law states that the magnetic field in space around an electric current is proportional to the source of the electric current. This can be applied to solve the magnetic field of a Solenoid.

[[File:solenoidfrombook.png]]

As you can see in this model, in the middle of the solenoid the field is constant throughout the entirety of the interior and is parallel to the axis. At the ends of a solenoid the magnetic field starts to point outward at varying angles.

===Equation===

If there are <math>N</math> loops of wire that compose a solenoid of length <math>L</math>, and we know that Ampere's Law gives us the form:

<math>{\oint\,\vec{B}•d\vec{l} = μ_{0}∑I_{inside path}}</math>

We can then solve for <math>B</math>:

<math>{B = \frac{μ_{0}NI}{L}}</math>

The Right Hand Rule can be used to find the direction of the magnetic field by using your right hand and curling your fingers in the direction of the current with your thumb pointing in the direction of the magnetic field. This is always along the axis for a solenoid.

[[File:Righthand.png]]

==Examples==

===Easy===
Find the magnetic field produced by a 40 cm long solenoid if the number of loops is 400 and current passing through it is 5 A.

For this example all of the variables are given so it is just a simple math calculation using Ampere's Law, as given above, but for reiteration.

<math>{\oint\,\vec{B}•d\vec{l} = μ_{0}∑I_{inside path}}</math>

<math>B = ((400*5)/.4)</math>
<math>B = 5,000 </math>

Once you have solved for <math>B</math> all you have to do is find the direction of the magnetic field using the Right Hand Rule.

===Middling===
A solenoid has a magnetic field of 5x10-4 T, 3000 turns, and is 30 cm long. What is the current through the solenoid?
For this example you are solving for I. Very similar to the above question, just rearranging the calculation of Ampere's Law.

<math>{I = \frac{LB}{μ_{0}N}}</math>

<math>{I = \frac{.3*5x10-4}{3000}}</math>

===Difficult===
A long, tightly wound solenoid has a circular cross section of radius 0.02 m. The solenoid is connected to a power supply (not shown), and this current changes with time, so the magnetic field inside the solenoid also changes with time. At time t = 0 s, the magnitude of the magnetic field inside the solenoid is 1.8 T. At time t = 0.3 s, the magnitude of the magnetic field inside the solenoid is 0.5 T. The direction of the magnetic field inside the solenoid is shown in the diagram. The solenoid passes through a coil of wire, which has 45 turns of radius 0.15 m. The coil is connected to a voltmeter (not shown).

[[File:hardexdigram.png]]

a.) At the same instant (t = 0.3 seconds), what will the absolute value of the reading on the
voltmeter be?
[[File:harda.jpg|700x900px]]

b.) The resistance of the coil is 2 ohms. At time t = 0.3 seconds, what is the conventional current
in the coil?
[[File:hardb.jpg|700x900px]]

c.) At time t = 0.3 seconds, what is the magnitude of the non-coulomb electric field ENC in
the coil?
[[File:hardc.jpg|700x900px]]

==Connectedness==
#Solenoids are important because they can create controlled magnetic fields making them useful for a variety of applications
#As a Biology major this relates to my major because solenoids are very important in the medical field. An example of solenoids is that they are very beneficial when it comes to controlling the flow of medicine that enters the bloodstream of individuals.

==See Also==
[[Ampere's Law]]

[[Magnetic Field of a Long Thick Wire Using Ampere's Law]]

[[Magnetic Field of Coaxial Cable Using Ampere's Law]]

[[Magnetic Field of a Toroid Using Ampere's Law]]

===Further Reading===

Chabay, Sherwood. (2015). Matter and Interactions (4th ed., Vol. 2). Raleigh, North Carolina: Wiley.

===External Links===
*http://www.one-school.net/Malaysia/UniversityandCollege/SPM/revisioncard/physics/electromagnetism/electromagnet.html

*http://www.physicstutorials.org/home/magnetism/magnetic-field-around-a-solenoid

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

==References==
Chabay, Sherwood. (2015). Matter and Interactions (4th ed., Vol. 2). Raleigh, North Carolina: Wiley. Pg 887-888.
Physics 2212 Spring 2016 Lab Quiz 8

[[Category:Maxwell's Equations]]

Magnetic Field of a Solenoid Using Ampere's Law

2016-11-28T04:22:24Z

Mchandler30: /* Easy */

Claimed by Mary Jane Chandler Fall 2016

This page explains how to use Ampere's Law to solve for the magnetic field of a solenoid.

==The Main Idea==

A solenoid is a cylindrical coil of wire that produces a uniform magnetic field when it is carrying an electric current. A solenoid is a form of an electromagnet that can create strong controlled magnetic fields throughout the coil except at the ends. Ampere's Law states that the magnetic field in space around an electric current is proportional to the source of the electric current. This can be applied to solve the magnetic field of a Solenoid.

[[File:solenoidfrombook.png]]

As you can see in this model, in the middle of the solenoid the field is constant throughout the entirety of the interior and is parallel to the axis. At the ends of a solenoid the magnetic field starts to point outward at varying angles.

===Equation===

If there are <math>N</math> loops of wire that compose a solenoid of length <math>L</math>, and we know that Ampere's Law gives us the form:

<math>{\oint\,\vec{B}•d\vec{l} = μ_{0}∑I_{inside path}}</math>

We can then solve for <math>B</math>:

<math>{B = \frac{μ_{0}NI}{L}}</math>

The Right Hand Rule can be used to find the direction of the magnetic field by using your right hand and curling your fingers in the direction of the current with your thumb pointing in the direction of the magnetic field. This is always along the axis for a solenoid.

[[File:Righthand.png]]

==Examples==

===Easy===
Find the magnetic field produced by a 40 cm long solenoid if the number of loops is 400 and current passing through it is 5 A.

For this example all of the variables are given so it is just a simple math calculation using Ampere's Law, as given above, but for reiteration.

<math>{\oint\,\vec{B}•d\vec{l} = μ_{0}∑I_{inside path}}</math>

<math>B = ((400*5)/.4)</math>
<math>B = 5,000 </math>

Once you have solved for <math>B</math> all you have to do is find the direction of the magnetic field using the Right Hand Rule.

===Middling===
A solenoid has a magnetic field of 5x10-4 T, 3000 turns, and is 30 cm long. What is the current through the solenoid?
For this example you are solving for I. Very similar to the above question, just rearranging the calculation of Ampere's Law.

<math>{I = \frac{LB}{μ_{0}N}}</math>

===Difficult===
A long, tightly wound solenoid has a circular cross section of radius 0.02 m. The solenoid is connected to a power supply (not shown), and this current changes with time, so the magnetic field inside the solenoid also changes with time. At time t = 0 s, the magnitude of the magnetic field inside the solenoid is 1.8 T. At time t = 0.3 s, the magnitude of the magnetic field inside the solenoid is 0.5 T. The direction of the magnetic field inside the solenoid is shown in the diagram. The solenoid passes through a coil of wire, which has 45 turns of radius 0.15 m. The coil is connected to a voltmeter (not shown).

[[File:hardexdigram.png]]

a.) At the same instant (t = 0.3 seconds), what will the absolute value of the reading on the
voltmeter be?
[[File:harda.jpg|700x900px]]

b.) The resistance of the coil is 2 ohms. At time t = 0.3 seconds, what is the conventional current
in the coil?
[[File:hardb.jpg|700x900px]]

c.) At time t = 0.3 seconds, what is the magnitude of the non-coulomb electric field ENC in
the coil?
[[File:hardc.jpg|700x900px]]

==Connectedness==
#Solenoids are important because they can create controlled magnetic fields making them useful for a variety of applications
#As a Biology major this relates to my major because solenoids are very important in the medical field. An example of solenoids is that they are very beneficial when it comes to controlling the flow of medicine that enters the bloodstream of individuals.

==See Also==
[[Ampere's Law]]

[[Magnetic Field of a Long Thick Wire Using Ampere's Law]]

[[Magnetic Field of Coaxial Cable Using Ampere's Law]]

[[Magnetic Field of a Toroid Using Ampere's Law]]

===Further Reading===

Chabay, Sherwood. (2015). Matter and Interactions (4th ed., Vol. 2). Raleigh, North Carolina: Wiley.

===External Links===
*http://www.one-school.net/Malaysia/UniversityandCollege/SPM/revisioncard/physics/electromagnetism/electromagnet.html

*http://www.physicstutorials.org/home/magnetism/magnetic-field-around-a-solenoid

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

==References==
Chabay, Sherwood. (2015). Matter and Interactions (4th ed., Vol. 2). Raleigh, North Carolina: Wiley. Pg 887-888.
Physics 2212 Spring 2016 Lab Quiz 8

[[Category:Maxwell's Equations]]

Magnetic Field of a Solenoid Using Ampere's Law

2016-11-28T04:17:57Z

Mchandler30: /* Connection */

Claimed by Mary Jane Chandler Fall 2016

This page explains how to use Ampere's Law to solve for the magnetic field of a solenoid.

==The Main Idea==

A solenoid is a cylindrical coil of wire that produces a uniform magnetic field when it is carrying an electric current. A solenoid is a form of an electromagnet that can create strong controlled magnetic fields throughout the coil except at the ends. Ampere's Law states that the magnetic field in space around an electric current is proportional to the source of the electric current. This can be applied to solve the magnetic field of a Solenoid.

[[File:solenoidfrombook.png]]

As you can see in this model, in the middle of the solenoid the field is constant throughout the entirety of the interior and is parallel to the axis. At the ends of a solenoid the magnetic field starts to point outward at varying angles.

===Equation===

If there are <math>N</math> loops of wire that compose a solenoid of length <math>L</math>, and we know that Ampere's Law gives us the form:

<math>{\oint\,\vec{B}•d\vec{l} = μ_{0}∑I_{inside path}}</math>

We can then solve for <math>B</math>:

<math>{B = \frac{μ_{0}NI}{L}}</math>

The Right Hand Rule can be used to find the direction of the magnetic field by using your right hand and curling your fingers in the direction of the current with your thumb pointing in the direction of the magnetic field. This is always along the axis for a solenoid.

[[File:Righthand.png]]

==Easy==
Find the magnetic field produced by a 40 cm long solenoid if the number of loops is 400 and current passing through it is 5 A.

For this example all of the variables are given so it is just a simple math calculation using Ampere's Law, as given above, but for reiteration.

<math>{\oint\,\vec{B}•d\vec{l} = μ_{0}∑I_{inside path}}</math>

Once you have solved for <math>B</math> all you have to do is find the direction of the magnetic field using the Right Hand Rule.

===Middling===
A solenoid has a magnetic field of 5x10-4 T, 3000 turns, and is 30 cm long. What is the current through the solenoid?
For this example you are solving for I. Very similar to the above question, just rearranging the calculation of Ampere's Law.

<math>{I = \frac{LB}{μ_{0}N}}</math>

===Difficult===
A long, tightly wound solenoid has a circular cross section of radius 0.02 m. The solenoid is connected to a power supply (not shown), and this current changes with time, so the magnetic field inside the solenoid also changes with time. At time t = 0 s, the magnitude of the magnetic field inside the solenoid is 1.8 T. At time t = 0.3 s, the magnitude of the magnetic field inside the solenoid is 0.5 T. The direction of the magnetic field inside the solenoid is shown in the diagram. The solenoid passes through a coil of wire, which has 45 turns of radius 0.15 m. The coil is connected to a voltmeter (not shown).

[[File:hardexdigram.png]]

a.) At the same instant (t = 0.3 seconds), what will the absolute value of the reading on the
voltmeter be?
[[File:harda.jpg|700x900px]]

b.) The resistance of the coil is 2 ohms. At time t = 0.3 seconds, what is the conventional current
in the coil?
[[File:hardb.jpg|700x900px]]

c.) At time t = 0.3 seconds, what is the magnitude of the non-coulomb electric field ENC in
the coil?
[[File:hardc.jpg|700x900px]]

==Connectedness==
#Solenoids are important because they can create controlled magnetic fields making them useful for a variety of applications
#As a Biology major this relates to my major because solenoids are very important in the medical field. An example of solenoids is that they are very beneficial when it comes to controlling the flow of medicine that enters the bloodstream of individuals.

==See Also==
[[Ampere's Law]]

[[Magnetic Field of a Long Thick Wire Using Ampere's Law]]

[[Magnetic Field of Coaxial Cable Using Ampere's Law]]

[[Magnetic Field of a Toroid Using Ampere's Law]]

===Further Reading===

Chabay, Sherwood. (2015). Matter and Interactions (4th ed., Vol. 2). Raleigh, North Carolina: Wiley.

===External Links===
*http://www.one-school.net/Malaysia/UniversityandCollege/SPM/revisioncard/physics/electromagnetism/electromagnet.html

*http://www.physicstutorials.org/home/magnetism/magnetic-field-around-a-solenoid

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

==References==
Chabay, Sherwood. (2015). Matter and Interactions (4th ed., Vol. 2). Raleigh, North Carolina: Wiley. Pg 887-888.
Physics 2212 Spring 2016 Lab Quiz 8

[[Category:Maxwell's Equations]]

Magnetic Field of a Solenoid Using Ampere's Law

2016-11-28T04:07:42Z

Mchandler30: /* Examples */

Claimed by Mary Jane Chandler Fall 2016

This page explains how to use Ampere's Law to solve for the magnetic field of a solenoid.

==The Main Idea==

A solenoid is a cylindrical coil of wire that produces a uniform magnetic field when it is carrying an electric current. A solenoid is a form of an electromagnet that can create strong controlled magnetic fields throughout the coil except at the ends. Ampere's Law states that the magnetic field in space around an electric current is proportional to the source of the electric current. This can be applied to solve the magnetic field of a Solenoid.

[[File:solenoidfrombook.png]]

As you can see in this model, in the middle of the solenoid the field is constant throughout the entirety of the interior and is parallel to the axis. At the ends of a solenoid the magnetic field starts to point outward at varying angles.

===Equation===

If there are <math>N</math> loops of wire that compose a solenoid of length <math>L</math>, and we know that Ampere's Law gives us the form:

<math>{\oint\,\vec{B}•d\vec{l} = μ_{0}∑I_{inside path}}</math>

We can then solve for <math>B</math>:

<math>{B = \frac{μ_{0}NI}{L}}</math>

The Right Hand Rule can be used to find the direction of the magnetic field by using your right hand and curling your fingers in the direction of the current with your thumb pointing in the direction of the magnetic field. This is always along the axis for a solenoid.

[[File:Righthand.png]]

==Easy==
Find the magnetic field produced by a 40 cm long solenoid if the number of loops is 400 and current passing through it is 5 A.

For this example all of the variables are given so it is just a simple math calculation using Ampere's Law, as given above, but for reiteration.

<math>{\oint\,\vec{B}•d\vec{l} = μ_{0}∑I_{inside path}}</math>

Once you have solved for <math>B</math> all you have to do is find the direction of the magnetic field using the Right Hand Rule.

===Middling===
A solenoid has a magnetic field of 5x10-4 T, 3000 turns, and is 30 cm long. What is the current through the solenoid?
For this example you are solving for I. Very similar to the above question, just rearranging the calculation of Ampere's Law.

<math>{I = \frac{LB}{μ_{0}N}}</math>

===Difficult===
A long, tightly wound solenoid has a circular cross section of radius 0.02 m. The solenoid is connected to a power supply (not shown), and this current changes with time, so the magnetic field inside the solenoid also changes with time. At time t = 0 s, the magnitude of the magnetic field inside the solenoid is 1.8 T. At time t = 0.3 s, the magnitude of the magnetic field inside the solenoid is 0.5 T. The direction of the magnetic field inside the solenoid is shown in the diagram. The solenoid passes through a coil of wire, which has 45 turns of radius 0.15 m. The coil is connected to a voltmeter (not shown).

[[File:hardexdigram.png]]

a.) At the same instant (t = 0.3 seconds), what will the absolute value of the reading on the
voltmeter be?
[[File:harda.jpg|700x900px]]

b.) The resistance of the coil is 2 ohms. At time t = 0.3 seconds, what is the conventional current
in the coil?
[[File:hardb.jpg|700x900px]]

c.) At time t = 0.3 seconds, what is the magnitude of the non-coulomb electric field ENC in
the coil?
[[File:hardc.jpg|700x900px]]

==Connectedness==
#Solenoids are important because they are the easiest way to create electromagnets and are an important piece in transformers.
#As a Computer Engineering major, solenoids are important, at least for the EE parts of my major, because as stated above they are used to create transformers which are a major piece in large and small scale power grids.

==See Also==
[[Ampere's Law]]

[[Magnetic Field of a Long Thick Wire Using Ampere's Law]]

[[Magnetic Field of Coaxial Cable Using Ampere's Law]]

[[Magnetic Field of a Toroid Using Ampere's Law]]

===Further Reading===

Chabay, Sherwood. (2015). Matter and Interactions (4th ed., Vol. 2). Raleigh, North Carolina: Wiley.

===External Links===
*http://www.one-school.net/Malaysia/UniversityandCollege/SPM/revisioncard/physics/electromagnetism/electromagnet.html

*http://www.physicstutorials.org/home/magnetism/magnetic-field-around-a-solenoid

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

==References==
Chabay, Sherwood. (2015). Matter and Interactions (4th ed., Vol. 2). Raleigh, North Carolina: Wiley. Pg 887-888.
Physics 2212 Spring 2016 Lab Quiz 8

[[Category:Maxwell's Equations]]

Magnetic Field of a Solenoid Using Ampere's Law

2016-11-28T04:07:32Z

Mchandler30: /* Examples */

Claimed by Mary Jane Chandler Fall 2016

This page explains how to use Ampere's Law to solve for the magnetic field of a solenoid.

==The Main Idea==

A solenoid is a cylindrical coil of wire that produces a uniform magnetic field when it is carrying an electric current. A solenoid is a form of an electromagnet that can create strong controlled magnetic fields throughout the coil except at the ends. Ampere's Law states that the magnetic field in space around an electric current is proportional to the source of the electric current. This can be applied to solve the magnetic field of a Solenoid.

[[File:solenoidfrombook.png]]

As you can see in this model, in the middle of the solenoid the field is constant throughout the entirety of the interior and is parallel to the axis. At the ends of a solenoid the magnetic field starts to point outward at varying angles.

===Equation===

If there are <math>N</math> loops of wire that compose a solenoid of length <math>L</math>, and we know that Ampere's Law gives us the form:

<math>{\oint\,\vec{B}•d\vec{l} = μ_{0}∑I_{inside path}}</math>

We can then solve for <math>B</math>:

<math>{B = \frac{μ_{0}NI}{L}}</math>

The Right Hand Rule can be used to find the direction of the magnetic field by using your right hand and curling your fingers in the direction of the current with your thumb pointing in the direction of the magnetic field. This is always along the axis for a solenoid.

[[File:Righthand.png]]

==Examples==

==Easy==
Find the magnetic field produced by a 40 cm long solenoid if the number of loops is 400 and current passing through it is 5 A.

For this example all of the variables are given so it is just a simple math calculation using Ampere's Law, as given above, but for reiteration.

<math>{\oint\,\vec{B}•d\vec{l} = μ_{0}∑I_{inside path}}</math>

Once you have solved for <math>B</math> all you have to do is find the direction of the magnetic field using the Right Hand Rule.

===Middling===
A solenoid has a magnetic field of 5x10-4 T, 3000 turns, and is 30 cm long. What is the current through the solenoid?
For this example you are solving for I. Very similar to the above question, just rearranging the calculation of Ampere's Law.

<math>{I = \frac{LB}{μ_{0}N}}</math>

===Difficult===
A long, tightly wound solenoid has a circular cross section of radius 0.02 m. The solenoid is connected to a power supply (not shown), and this current changes with time, so the magnetic field inside the solenoid also changes with time. At time t = 0 s, the magnitude of the magnetic field inside the solenoid is 1.8 T. At time t = 0.3 s, the magnitude of the magnetic field inside the solenoid is 0.5 T. The direction of the magnetic field inside the solenoid is shown in the diagram. The solenoid passes through a coil of wire, which has 45 turns of radius 0.15 m. The coil is connected to a voltmeter (not shown).

[[File:hardexdigram.png]]

a.) At the same instant (t = 0.3 seconds), what will the absolute value of the reading on the
voltmeter be?
[[File:harda.jpg|700x900px]]

b.) The resistance of the coil is 2 ohms. At time t = 0.3 seconds, what is the conventional current
in the coil?
[[File:hardb.jpg|700x900px]]

c.) At time t = 0.3 seconds, what is the magnitude of the non-coulomb electric field ENC in
the coil?
[[File:hardc.jpg|700x900px]]

==Connectedness==
#Solenoids are important because they are the easiest way to create electromagnets and are an important piece in transformers.
#As a Computer Engineering major, solenoids are important, at least for the EE parts of my major, because as stated above they are used to create transformers which are a major piece in large and small scale power grids.

==See Also==
[[Ampere's Law]]

[[Magnetic Field of a Long Thick Wire Using Ampere's Law]]

[[Magnetic Field of Coaxial Cable Using Ampere's Law]]

[[Magnetic Field of a Toroid Using Ampere's Law]]

===Further Reading===

Chabay, Sherwood. (2015). Matter and Interactions (4th ed., Vol. 2). Raleigh, North Carolina: Wiley.

===External Links===
*http://www.one-school.net/Malaysia/UniversityandCollege/SPM/revisioncard/physics/electromagnetism/electromagnet.html

*http://www.physicstutorials.org/home/magnetism/magnetic-field-around-a-solenoid

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

==References==
Chabay, Sherwood. (2015). Matter and Interactions (4th ed., Vol. 2). Raleigh, North Carolina: Wiley. Pg 887-888.
Physics 2212 Spring 2016 Lab Quiz 8

[[Category:Maxwell's Equations]]

Magnetic Field of a Solenoid Using Ampere's Law

2016-11-28T04:07:20Z

Mchandler30: /* Easy */

Claimed by Mary Jane Chandler Fall 2016

This page explains how to use Ampere's Law to solve for the magnetic field of a solenoid.

==The Main Idea==

A solenoid is a cylindrical coil of wire that produces a uniform magnetic field when it is carrying an electric current. A solenoid is a form of an electromagnet that can create strong controlled magnetic fields throughout the coil except at the ends. Ampere's Law states that the magnetic field in space around an electric current is proportional to the source of the electric current. This can be applied to solve the magnetic field of a Solenoid.

[[File:solenoidfrombook.png]]

As you can see in this model, in the middle of the solenoid the field is constant throughout the entirety of the interior and is parallel to the axis. At the ends of a solenoid the magnetic field starts to point outward at varying angles.

===Equation===

If there are <math>N</math> loops of wire that compose a solenoid of length <math>L</math>, and we know that Ampere's Law gives us the form:

<math>{\oint\,\vec{B}•d\vec{l} = μ_{0}∑I_{inside path}}</math>

We can then solve for <math>B</math>:

<math>{B = \frac{μ_{0}NI}{L}}</math>

The Right Hand Rule can be used to find the direction of the magnetic field by using your right hand and curling your fingers in the direction of the current with your thumb pointing in the direction of the magnetic field. This is always along the axis for a solenoid.

[[File:Righthand.png]]

==Examples==

==Examples==

==Easy==
Find the magnetic field produced by a 40 cm long solenoid if the number of loops is 400 and current passing through it is 5 A.

For this example all of the variables are given so it is just a simple math calculation using Ampere's Law, as given above, but for reiteration.

<math>{\oint\,\vec{B}•d\vec{l} = μ_{0}∑I_{inside path}}</math>

Once you have solved for <math>B</math> all you have to do is find the direction of the magnetic field using the Right Hand Rule.

===Middling===
A solenoid has a magnetic field of 5x10-4 T, 3000 turns, and is 30 cm long. What is the current through the solenoid?
For this example you are solving for I. Very similar to the above question, just rearranging the calculation of Ampere's Law.

<math>{I = \frac{LB}{μ_{0}N}}</math>

===Difficult===
A long, tightly wound solenoid has a circular cross section of radius 0.02 m. The solenoid is connected to a power supply (not shown), and this current changes with time, so the magnetic field inside the solenoid also changes with time. At time t = 0 s, the magnitude of the magnetic field inside the solenoid is 1.8 T. At time t = 0.3 s, the magnitude of the magnetic field inside the solenoid is 0.5 T. The direction of the magnetic field inside the solenoid is shown in the diagram. The solenoid passes through a coil of wire, which has 45 turns of radius 0.15 m. The coil is connected to a voltmeter (not shown).

[[File:hardexdigram.png]]

a.) At the same instant (t = 0.3 seconds), what will the absolute value of the reading on the
voltmeter be?
[[File:harda.jpg|700x900px]]

b.) The resistance of the coil is 2 ohms. At time t = 0.3 seconds, what is the conventional current
in the coil?
[[File:hardb.jpg|700x900px]]

c.) At time t = 0.3 seconds, what is the magnitude of the non-coulomb electric field ENC in
the coil?
[[File:hardc.jpg|700x900px]]

==Connectedness==
#Solenoids are important because they are the easiest way to create electromagnets and are an important piece in transformers.
#As a Computer Engineering major, solenoids are important, at least for the EE parts of my major, because as stated above they are used to create transformers which are a major piece in large and small scale power grids.

==See Also==
[[Ampere's Law]]

[[Magnetic Field of a Long Thick Wire Using Ampere's Law]]

[[Magnetic Field of Coaxial Cable Using Ampere's Law]]

[[Magnetic Field of a Toroid Using Ampere's Law]]

===Further Reading===

Chabay, Sherwood. (2015). Matter and Interactions (4th ed., Vol. 2). Raleigh, North Carolina: Wiley.

===External Links===
*http://www.one-school.net/Malaysia/UniversityandCollege/SPM/revisioncard/physics/electromagnetism/electromagnet.html

*http://www.physicstutorials.org/home/magnetism/magnetic-field-around-a-solenoid

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

==References==
Chabay, Sherwood. (2015). Matter and Interactions (4th ed., Vol. 2). Raleigh, North Carolina: Wiley. Pg 887-888.
Physics 2212 Spring 2016 Lab Quiz 8

[[Category:Maxwell's Equations]]

Magnetic Field of a Solenoid Using Ampere's Law

2016-11-28T04:06:54Z

Mchandler30: /* Examples */

Claimed by Mary Jane Chandler Fall 2016

This page explains how to use Ampere's Law to solve for the magnetic field of a solenoid.

==The Main Idea==

A solenoid is a cylindrical coil of wire that produces a uniform magnetic field when it is carrying an electric current. A solenoid is a form of an electromagnet that can create strong controlled magnetic fields throughout the coil except at the ends. Ampere's Law states that the magnetic field in space around an electric current is proportional to the source of the electric current. This can be applied to solve the magnetic field of a Solenoid.

[[File:solenoidfrombook.png]]

As you can see in this model, in the middle of the solenoid the field is constant throughout the entirety of the interior and is parallel to the axis. At the ends of a solenoid the magnetic field starts to point outward at varying angles.

===Equation===

If there are <math>N</math> loops of wire that compose a solenoid of length <math>L</math>, and we know that Ampere's Law gives us the form:

<math>{\oint\,\vec{B}•d\vec{l} = μ_{0}∑I_{inside path}}</math>

We can then solve for <math>B</math>:

<math>{B = \frac{μ_{0}NI}{L}}</math>

The Right Hand Rule can be used to find the direction of the magnetic field by using your right hand and curling your fingers in the direction of the current with your thumb pointing in the direction of the magnetic field. This is always along the axis for a solenoid.

[[File:Righthand.png]]

==Examples==

==Easy==
Find the magnetic field produced by a 40 cm long solenoid if the number of loops is 400 and current passing through it is 5 A.

For this example all of the variables are given so it is just a simple math calculation using Ampere's Law, as given above, but for reiteration.

<math>{\oint\,\vec{B}•d\vec{l} = μ_{0}∑I_{inside path}}</math>

Once you have solved for <math>B</math> all you have to do is find the direction of the magnetic field using the Right Hand Rule.

===Middling===
A solenoid has a magnetic field of 5x10-4 T, 3000 turns, and is 30 cm long. What is the current through the solenoid?
For this example you are solving for I. Very similar to the above question, just rearranging the calculation of Ampere's Law.

<math>{I = \frac{LB}{μ_{0}N}}</math>

===Difficult===
A long, tightly wound solenoid has a circular cross section of radius 0.02 m. The solenoid is connected to a power supply (not shown), and this current changes with time, so the magnetic field inside the solenoid also changes with time. At time t = 0 s, the magnitude of the magnetic field inside the solenoid is 1.8 T. At time t = 0.3 s, the magnitude of the magnetic field inside the solenoid is 0.5 T. The direction of the magnetic field inside the solenoid is shown in the diagram. The solenoid passes through a coil of wire, which has 45 turns of radius 0.15 m. The coil is connected to a voltmeter (not shown).

[[File:hardexdigram.png]]

a.) At the same instant (t = 0.3 seconds), what will the absolute value of the reading on the
voltmeter be?
[[File:harda.jpg|700x900px]]

b.) The resistance of the coil is 2 ohms. At time t = 0.3 seconds, what is the conventional current
in the coil?
[[File:hardb.jpg|700x900px]]

c.) At time t = 0.3 seconds, what is the magnitude of the non-coulomb electric field ENC in
the coil?
[[File:hardc.jpg|700x900px]]

==Connectedness==
#Solenoids are important because they are the easiest way to create electromagnets and are an important piece in transformers.
#As a Computer Engineering major, solenoids are important, at least for the EE parts of my major, because as stated above they are used to create transformers which are a major piece in large and small scale power grids.

==See Also==
[[Ampere's Law]]

[[Magnetic Field of a Long Thick Wire Using Ampere's Law]]

[[Magnetic Field of Coaxial Cable Using Ampere's Law]]

[[Magnetic Field of a Toroid Using Ampere's Law]]

===Further Reading===

Chabay, Sherwood. (2015). Matter and Interactions (4th ed., Vol. 2). Raleigh, North Carolina: Wiley.

===External Links===
*http://www.one-school.net/Malaysia/UniversityandCollege/SPM/revisioncard/physics/electromagnetism/electromagnet.html

*http://www.physicstutorials.org/home/magnetism/magnetic-field-around-a-solenoid

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

==References==
Chabay, Sherwood. (2015). Matter and Interactions (4th ed., Vol. 2). Raleigh, North Carolina: Wiley. Pg 887-888.
Physics 2212 Spring 2016 Lab Quiz 8

[[Category:Maxwell's Equations]]

Magnetic Field of a Solenoid Using Ampere's Law

2016-11-28T04:06:35Z

Mchandler30: Examples using Ampere's Law

Claimed by Mary Jane Chandler Fall 2016

This page explains how to use Ampere's Law to solve for the magnetic field of a solenoid.

==The Main Idea==

A solenoid is a cylindrical coil of wire that produces a uniform magnetic field when it is carrying an electric current. A solenoid is a form of an electromagnet that can create strong controlled magnetic fields throughout the coil except at the ends. Ampere's Law states that the magnetic field in space around an electric current is proportional to the source of the electric current. This can be applied to solve the magnetic field of a Solenoid.

[[File:solenoidfrombook.png]]

As you can see in this model, in the middle of the solenoid the field is constant throughout the entirety of the interior and is parallel to the axis. At the ends of a solenoid the magnetic field starts to point outward at varying angles.

===Equation===

If there are <math>N</math> loops of wire that compose a solenoid of length <math>L</math>, and we know that Ampere's Law gives us the form:

<math>{\oint\,\vec{B}•d\vec{l} = μ_{0}∑I_{inside path}}</math>

We can then solve for <math>B</math>:

<math>{B = \frac{μ_{0}NI}{L}}</math>

The Right Hand Rule can be used to find the direction of the magnetic field by using your right hand and curling your fingers in the direction of the current with your thumb pointing in the direction of the magnetic field. This is always along the axis for a solenoid.

[[File:Righthand.png]]

==Examples==

==Easy==
Find the magnetic field produced by a 40 cm long solenoid if the number of loops is 400 and current passing through it is 5 A.

For this example all of the variables are given so it is just a simple math calculation using Ampere's Law, as given above, but for reiteration.

<math>{\oint\,\vec{B}•d\vec{l} = μ_{0}∑I_{inside path}}</math>

Once you have solved for <math>B</math> all you have to do is find the direction of the magnetic field using the Right Hand Rule.

===Middling===
A solenoid has a magnetic field of 5x10-4 T, 3000 turns, and is 30 cm long. What is the current through the solenoid?
For this example you are solving for I. Very similar to the above question, just rearranging the calculation of Ampere's Law.

<math>{I = \frac{LB}{μ_{0}N}}</math>

===Difficult===
A long, tightly wound solenoid has a circular cross section of radius 0.02 m. The solenoid is connected to a power supply (not shown), and this current changes with time, so the magnetic field inside the solenoid also changes with time. At time t = 0 s, the magnitude of the magnetic field inside the solenoid is 1.8 T. At time t = 0.3 s, the magnitude of the magnetic field inside the solenoid is 0.5 T. The direction of the magnetic field inside the solenoid is shown in the diagram. The solenoid passes through a coil of wire, which has 45 turns of radius 0.15 m. The coil is connected to a voltmeter (not shown).

[[File:hardexdigram.png]]

a.) At the same instant (t = 0.3 seconds), what will the absolute value of the reading on the
voltmeter be?
[[File:harda.jpg|700x900px]]

b.) The resistance of the coil is 2 ohms. At time t = 0.3 seconds, what is the conventional current
in the coil?
[[File:hardb.jpg|700x900px]]

c.) At time t = 0.3 seconds, what is the magnitude of the non-coulomb electric field ENC in
the coil?
[[File:hardc.jpg|700x900px]]

==Connectedness==
#Solenoids are important because they are the easiest way to create electromagnets and are an important piece in transformers.
#As a Computer Engineering major, solenoids are important, at least for the EE parts of my major, because as stated above they are used to create transformers which are a major piece in large and small scale power grids.

==See Also==
[[Ampere's Law]]

[[Magnetic Field of a Long Thick Wire Using Ampere's Law]]

[[Magnetic Field of Coaxial Cable Using Ampere's Law]]

[[Magnetic Field of a Toroid Using Ampere's Law]]

===Further Reading===

Chabay, Sherwood. (2015). Matter and Interactions (4th ed., Vol. 2). Raleigh, North Carolina: Wiley.

===External Links===
*http://www.one-school.net/Malaysia/UniversityandCollege/SPM/revisioncard/physics/electromagnetism/electromagnet.html

*http://www.physicstutorials.org/home/magnetism/magnetic-field-around-a-solenoid

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

==References==
Chabay, Sherwood. (2015). Matter and Interactions (4th ed., Vol. 2). Raleigh, North Carolina: Wiley. Pg 887-888.
Physics 2212 Spring 2016 Lab Quiz 8

[[Category:Maxwell's Equations]]

Magnetic Field of a Solenoid Using Ampere's Law

2016-11-28T03:58:54Z

Mchandler30: /* Examples */

Claimed by Mary Jane Chandler Fall 2016

This page explains how to use Ampere's Law to solve for the magnetic field of a solenoid.

==The Main Idea==

A solenoid is a cylindrical coil of wire that produces a uniform magnetic field when it is carrying an electric current. A solenoid is a form of an electromagnet that can create strong controlled magnetic fields throughout the coil except at the ends. Ampere's Law states that the magnetic field in space around an electric current is proportional to the source of the electric current. This can be applied to solve the magnetic field of a Solenoid.

[[File:solenoidfrombook.png]]

As you can see in this model, in the middle of the solenoid the field is constant throughout the entirety of the interior and is parallel to the axis. At the ends of a solenoid the magnetic field starts to point outward at varying angles.

===Equation===

If there are <math>N</math> loops of wire that compose a solenoid of length <math>L</math>, and we know that Ampere's Law gives us the form:

<math>{\oint\,\vec{B}•d\vec{l} = μ_{0}∑I_{inside path}}</math>

We can then solve for <math>B</math>:

<math>{B = \frac{μ_{0}NI}{L}}</math>

The Right Hand Rule can be used to find the direction of the magnetic field by using your right hand and curling your fingers in the direction of the current with your thumb pointing in the direction of the magnetic field. This is always along the axis for a solenoid.

[[File:Righthand.png]]

==Examples==

-Easy-
Find the magnetic field produced by a 40 cm long solenoid if the number of loops is 400 and current passing through it is 5 A.

For this example all of the variables are given so it is just a simple math calculation using Ampere's Law, as given above, but for reiteration.

<math>{\oint\,\vec{B}•d\vec{l} = μ_{0}∑I_{inside path}}</math>

Once you have solved for <math>B</> all you have to do is find the direction of the magnetic field using the Right Hand Rule.

===Middling===
A solenoid has a magnetic field of 5x10-4 T, 3000 turns, and is 30 cm long. What is the current through the solenoid?
[[File:example2solenoid.jpg|700x900px]]

This example is just a reverse solving of the equation derived above for the magnetic field of a solenoid. It is not munch more difficult than the previous example.
===Difficult===
A long, tightly wound solenoid has a circular cross section of radius 0.02 m. The solenoid is connected to a power supply (not shown), and this current changes with time, so the magnetic field inside the solenoid also changes with time. At time t = 0 s, the magnitude of the magnetic field inside the solenoid is 1.8 T. At time t = 0.3 s, the magnitude of the magnetic field inside the solenoid is 0.5 T. The direction of the magnetic field inside the solenoid is shown in the diagram. The solenoid passes through a coil of wire, which has 45 turns of radius 0.15 m. The coil is connected to a voltmeter (not shown).

[[File:hardexdigram.png]]

a.) At the same instant (t = 0.3 seconds), what will the absolute value of the reading on the
voltmeter be?
[[File:harda.jpg|700x900px]]

b.) The resistance of the coil is 2 ohms. At time t = 0.3 seconds, what is the conventional current
in the coil?
[[File:hardb.jpg|700x900px]]

c.) At time t = 0.3 seconds, what is the magnitude of the non-coulomb electric field ENC in
the coil?
[[File:hardc.jpg|700x900px]]

==Connectedness==
#Solenoids are important because they are the easiest way to create electromagnets and are an important piece in transformers.
#As a Computer Engineering major, solenoids are important, at least for the EE parts of my major, because as stated above they are used to create transformers which are a major piece in large and small scale power grids.

==See Also==
[[Ampere's Law]]

[[Magnetic Field of a Long Thick Wire Using Ampere's Law]]

[[Magnetic Field of Coaxial Cable Using Ampere's Law]]

[[Magnetic Field of a Toroid Using Ampere's Law]]

===Further Reading===

Chabay, Sherwood. (2015). Matter and Interactions (4th ed., Vol. 2). Raleigh, North Carolina: Wiley.

===External Links===
*http://www.one-school.net/Malaysia/UniversityandCollege/SPM/revisioncard/physics/electromagnetism/electromagnet.html

*http://www.physicstutorials.org/home/magnetism/magnetic-field-around-a-solenoid

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

==References==
Chabay, Sherwood. (2015). Matter and Interactions (4th ed., Vol. 2). Raleigh, North Carolina: Wiley. Pg 887-888.
Physics 2212 Spring 2016 Lab Quiz 8

[[Category:Maxwell's Equations]]

Magnetic Field of a Solenoid Using Ampere's Law

2016-11-28T03:57:13Z

Mchandler30: /* Easy */

Claimed by Mary Jane Chandler Fall 2016

This page explains how to use Ampere's Law to solve for the magnetic field of a solenoid.

==The Main Idea==

A solenoid is a cylindrical coil of wire that produces a uniform magnetic field when it is carrying an electric current. A solenoid is a form of an electromagnet that can create strong controlled magnetic fields throughout the coil except at the ends. Ampere's Law states that the magnetic field in space around an electric current is proportional to the source of the electric current. This can be applied to solve the magnetic field of a Solenoid.

[[File:solenoidfrombook.png]]

As you can see in this model, in the middle of the solenoid the field is constant throughout the entirety of the interior and is parallel to the axis. At the ends of a solenoid the magnetic field starts to point outward at varying angles.

===Equation===

If there are <math>N</math> loops of wire that compose a solenoid of length <math>L</math>, and we know that Ampere's Law gives us the form:

<math>{\oint\,\vec{B}•d\vec{l} = μ_{0}∑I_{inside path}}</math>

We can then solve for <math>B</math>:

<math>{B = \frac{μ_{0}NI}{L}}</math>

The Right Hand Rule can be used to find the direction of the magnetic field by using your right hand and curling your fingers in the direction of the current with your thumb pointing in the direction of the magnetic field. This is always along the axis for a solenoid.

[[File:Righthand.png]]

==Examples==

===Simple===
Find the magnetic field produced by a 40 cm long solenoid if the number of loops is 400 and current passing through it is 5 A.

For this example all of the variables are given so it is just a simple math calculation using Ampere's Law, as given above, but for reiteration.

<math>{\oint\,\vec{B}•d\vec{l} = μ_{0}∑I_{inside path}}</math>

Once you have solved for <math>B</> all you have to do is find the direction of the magnetic field using the Right Hand Rule.

===Middling===
A solenoid has a magnetic field of 5x10-4 T, 3000 turns, and is 30 cm long. What is the current through the solenoid?
[[File:example2solenoid.jpg|700x900px]]

This example is just a reverse solving of the equation derived above for the magnetic field of a solenoid. It is not munch more difficult than the previous example.
===Difficult===
A long, tightly wound solenoid has a circular cross section of radius 0.02 m. The solenoid is connected to a power supply (not shown), and this current changes with time, so the magnetic field inside the solenoid also changes with time. At time t = 0 s, the magnitude of the magnetic field inside the solenoid is 1.8 T. At time t = 0.3 s, the magnitude of the magnetic field inside the solenoid is 0.5 T. The direction of the magnetic field inside the solenoid is shown in the diagram. The solenoid passes through a coil of wire, which has 45 turns of radius 0.15 m. The coil is connected to a voltmeter (not shown).

[[File:hardexdigram.png]]

a.) At the same instant (t = 0.3 seconds), what will the absolute value of the reading on the
voltmeter be?
[[File:harda.jpg|700x900px]]

b.) The resistance of the coil is 2 ohms. At time t = 0.3 seconds, what is the conventional current
in the coil?
[[File:hardb.jpg|700x900px]]

c.) At time t = 0.3 seconds, what is the magnitude of the non-coulomb electric field ENC in
the coil?
[[File:hardc.jpg|700x900px]]

==Connectedness==
#Solenoids are important because they are the easiest way to create electromagnets and are an important piece in transformers.
#As a Computer Engineering major, solenoids are important, at least for the EE parts of my major, because as stated above they are used to create transformers which are a major piece in large and small scale power grids.

==See Also==
[[Ampere's Law]]

[[Magnetic Field of a Long Thick Wire Using Ampere's Law]]

[[Magnetic Field of Coaxial Cable Using Ampere's Law]]

[[Magnetic Field of a Toroid Using Ampere's Law]]

===Further Reading===

Chabay, Sherwood. (2015). Matter and Interactions (4th ed., Vol. 2). Raleigh, North Carolina: Wiley.

===External Links===
*http://www.one-school.net/Malaysia/UniversityandCollege/SPM/revisioncard/physics/electromagnetism/electromagnet.html

*http://www.physicstutorials.org/home/magnetism/magnetic-field-around-a-solenoid

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

==References==
Chabay, Sherwood. (2015). Matter and Interactions (4th ed., Vol. 2). Raleigh, North Carolina: Wiley. Pg 887-888.
Physics 2212 Spring 2016 Lab Quiz 8

[[Category:Maxwell's Equations]]

Magnetic Field of a Solenoid Using Ampere's Law

2016-11-28T03:55:31Z

Mchandler30: /* Simple */

Claimed by Mary Jane Chandler Fall 2016

This page explains how to use Ampere's Law to solve for the magnetic field of a solenoid.

==The Main Idea==

A solenoid is a cylindrical coil of wire that produces a uniform magnetic field when it is carrying an electric current. A solenoid is a form of an electromagnet that can create strong controlled magnetic fields throughout the coil except at the ends. Ampere's Law states that the magnetic field in space around an electric current is proportional to the source of the electric current. This can be applied to solve the magnetic field of a Solenoid.

[[File:solenoidfrombook.png]]

As you can see in this model, in the middle of the solenoid the field is constant throughout the entirety of the interior and is parallel to the axis. At the ends of a solenoid the magnetic field starts to point outward at varying angles.

===Equation===

If there are <math>N</math> loops of wire that compose a solenoid of length <math>L</math>, and we know that Ampere's Law gives us the form:

<math>{\oint\,\vec{B}•d\vec{l} = μ_{0}∑I_{inside path}}</math>

We can then solve for <math>B</math>:

<math>{B = \frac{μ_{0}NI}{L}}</math>

The Right Hand Rule can be used to find the direction of the magnetic field by using your right hand and curling your fingers in the direction of the current with your thumb pointing in the direction of the magnetic field. This is always along the axis for a solenoid.

[[File:Righthand.png]]

==Examples==

===Simple===
Find the magnetic field produced by a 40 cm long solenoid if the number of loops is 400 and current passing through it is 5 A.

For this example all of the variables are given so it is just a simple math calculation using Ampere's Law, as given above, but for reiteration.

===Middling===
A solenoid has a magnetic field of 5x10-4 T, 3000 turns, and is 30 cm long. What is the current through the solenoid?
[[File:example2solenoid.jpg|700x900px]]

This example is just a reverse solving of the equation derived above for the magnetic field of a solenoid. It is not munch more difficult than the previous example.
===Difficult===
A long, tightly wound solenoid has a circular cross section of radius 0.02 m. The solenoid is connected to a power supply (not shown), and this current changes with time, so the magnetic field inside the solenoid also changes with time. At time t = 0 s, the magnitude of the magnetic field inside the solenoid is 1.8 T. At time t = 0.3 s, the magnitude of the magnetic field inside the solenoid is 0.5 T. The direction of the magnetic field inside the solenoid is shown in the diagram. The solenoid passes through a coil of wire, which has 45 turns of radius 0.15 m. The coil is connected to a voltmeter (not shown).

[[File:hardexdigram.png]]

a.) At the same instant (t = 0.3 seconds), what will the absolute value of the reading on the
voltmeter be?
[[File:harda.jpg|700x900px]]

b.) The resistance of the coil is 2 ohms. At time t = 0.3 seconds, what is the conventional current
in the coil?
[[File:hardb.jpg|700x900px]]

c.) At time t = 0.3 seconds, what is the magnitude of the non-coulomb electric field ENC in
the coil?
[[File:hardc.jpg|700x900px]]

==Connectedness==
#Solenoids are important because they are the easiest way to create electromagnets and are an important piece in transformers.
#As a Computer Engineering major, solenoids are important, at least for the EE parts of my major, because as stated above they are used to create transformers which are a major piece in large and small scale power grids.

==See Also==
[[Ampere's Law]]

[[Magnetic Field of a Long Thick Wire Using Ampere's Law]]

[[Magnetic Field of Coaxial Cable Using Ampere's Law]]

[[Magnetic Field of a Toroid Using Ampere's Law]]

===Further Reading===

Chabay, Sherwood. (2015). Matter and Interactions (4th ed., Vol. 2). Raleigh, North Carolina: Wiley.

===External Links===
*http://www.one-school.net/Malaysia/UniversityandCollege/SPM/revisioncard/physics/electromagnetism/electromagnet.html

*http://www.physicstutorials.org/home/magnetism/magnetic-field-around-a-solenoid

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

==References==
Chabay, Sherwood. (2015). Matter and Interactions (4th ed., Vol. 2). Raleigh, North Carolina: Wiley. Pg 887-888.
Physics 2212 Spring 2016 Lab Quiz 8

[[Category:Maxwell's Equations]]

Magnetic Field of a Solenoid Using Ampere's Law

2016-11-28T03:49:00Z

Mchandler30: /* Equation */

Claimed by Mary Jane Chandler Fall 2016

This page explains how to use Ampere's Law to solve for the magnetic field of a solenoid.

==The Main Idea==

A solenoid is a cylindrical coil of wire that produces a uniform magnetic field when it is carrying an electric current. A solenoid is a form of an electromagnet that can create strong controlled magnetic fields throughout the coil except at the ends. Ampere's Law states that the magnetic field in space around an electric current is proportional to the source of the electric current. This can be applied to solve the magnetic field of a Solenoid.

[[File:solenoidfrombook.png]]

As you can see in this model, in the middle of the solenoid the field is constant throughout the entirety of the interior and is parallel to the axis. At the ends of a solenoid the magnetic field starts to point outward at varying angles.

===Equation===

If there are <math>N</math> loops of wire that compose a solenoid of length <math>L</math>, and we know that Ampere's Law gives us the form:

<math>{\oint\,\vec{B}•d\vec{l} = μ_{0}∑I_{inside path}}</math>

We can then solve for <math>B</math>:

<math>{B = \frac{μ_{0}NI}{L}}</math>

The Right Hand Rule can be used to find the direction of the magnetic field by using your right hand and curling your fingers in the direction of the current with your thumb pointing in the direction of the magnetic field. This is always along the axis for a solenoid.

[[File:Righthand.png]]

==Examples==

===Simple===
Find the magnetic field produced by a 40 cm long solenoid if the number of loops is 400 and current passing through it is 5 A.
[[File:Examplesolenoid.jpg|700x900px]]

This example is very simple, as all of the variables of the equation are provided. All you need to do is plug them in and find the direction using the right hand rule.
===Middling===
A solenoid has a magnetic field of 5x10-4 T, 3000 turns, and is 30 cm long. What is the current through the solenoid?
[[File:example2solenoid.jpg|700x900px]]

This example is just a reverse solving of the equation derived above for the magnetic field of a solenoid. It is not munch more difficult than the previous example.
===Difficult===
A long, tightly wound solenoid has a circular cross section of radius 0.02 m. The solenoid is connected to a power supply (not shown), and this current changes with time, so the magnetic field inside the solenoid also changes with time. At time t = 0 s, the magnitude of the magnetic field inside the solenoid is 1.8 T. At time t = 0.3 s, the magnitude of the magnetic field inside the solenoid is 0.5 T. The direction of the magnetic field inside the solenoid is shown in the diagram. The solenoid passes through a coil of wire, which has 45 turns of radius 0.15 m. The coil is connected to a voltmeter (not shown).

[[File:hardexdigram.png]]

a.) At the same instant (t = 0.3 seconds), what will the absolute value of the reading on the
voltmeter be?
[[File:harda.jpg|700x900px]]

b.) The resistance of the coil is 2 ohms. At time t = 0.3 seconds, what is the conventional current
in the coil?
[[File:hardb.jpg|700x900px]]

c.) At time t = 0.3 seconds, what is the magnitude of the non-coulomb electric field ENC in
the coil?
[[File:hardc.jpg|700x900px]]

==Connectedness==
#Solenoids are important because they are the easiest way to create electromagnets and are an important piece in transformers.
#As a Computer Engineering major, solenoids are important, at least for the EE parts of my major, because as stated above they are used to create transformers which are a major piece in large and small scale power grids.

==See Also==
[[Ampere's Law]]

[[Magnetic Field of a Long Thick Wire Using Ampere's Law]]

[[Magnetic Field of Coaxial Cable Using Ampere's Law]]

[[Magnetic Field of a Toroid Using Ampere's Law]]

===Further Reading===

Chabay, Sherwood. (2015). Matter and Interactions (4th ed., Vol. 2). Raleigh, North Carolina: Wiley.

===External Links===
*http://www.one-school.net/Malaysia/UniversityandCollege/SPM/revisioncard/physics/electromagnetism/electromagnet.html

*http://www.physicstutorials.org/home/magnetism/magnetic-field-around-a-solenoid

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

==References==
Chabay, Sherwood. (2015). Matter and Interactions (4th ed., Vol. 2). Raleigh, North Carolina: Wiley. Pg 887-888.
Physics 2212 Spring 2016 Lab Quiz 8

[[Category:Maxwell's Equations]]

Magnetic Field of a Solenoid Using Ampere's Law

2016-11-28T03:47:59Z

Mchandler30: /* Equation */

Claimed by Mary Jane Chandler Fall 2016

This page explains how to use Ampere's Law to solve for the magnetic field of a solenoid.

==The Main Idea==

A solenoid is a cylindrical coil of wire that produces a uniform magnetic field when it is carrying an electric current. A solenoid is a form of an electromagnet that can create strong controlled magnetic fields throughout the coil except at the ends. Ampere's Law states that the magnetic field in space around an electric current is proportional to the source of the electric current. This can be applied to solve the magnetic field of a Solenoid.

[[File:solenoidfrombook.png]]

As you can see in this model, in the middle of the solenoid the field is constant throughout the entirety of the interior and is parallel to the axis. At the ends of a solenoid the magnetic field starts to point outward at varying angles.

===Equation===

If there are <math>N</math> loops of wire that compose a solenoid of length <math>L</math>, and we know that Ampere's Law gives us the form:

<math>{\oint\,\vec{B}•d\vec{l} = μ_{0}∑I_{inside path}}</math>

[[File:mchandlersolenoid.png|frame|Solenoid with variables]]

We can then solve for <math>B</math>:

<math>{B = \frac{μ_{0}NI}{L}}</math>

The Right Hand Rule can be used to find the direction of the magnetic field by using your right hand and curling your fingers in the direction of the current with your thumb pointing in the direction of the magnetic field. This is always along the axis for a solenoid.

[[File:Righthand.png]]

==Examples==

===Simple===
Find the magnetic field produced by a 40 cm long solenoid if the number of loops is 400 and current passing through it is 5 A.
[[File:Examplesolenoid.jpg|700x900px]]

This example is very simple, as all of the variables of the equation are provided. All you need to do is plug them in and find the direction using the right hand rule.
===Middling===
A solenoid has a magnetic field of 5x10-4 T, 3000 turns, and is 30 cm long. What is the current through the solenoid?
[[File:example2solenoid.jpg|700x900px]]

This example is just a reverse solving of the equation derived above for the magnetic field of a solenoid. It is not munch more difficult than the previous example.
===Difficult===
A long, tightly wound solenoid has a circular cross section of radius 0.02 m. The solenoid is connected to a power supply (not shown), and this current changes with time, so the magnetic field inside the solenoid also changes with time. At time t = 0 s, the magnitude of the magnetic field inside the solenoid is 1.8 T. At time t = 0.3 s, the magnitude of the magnetic field inside the solenoid is 0.5 T. The direction of the magnetic field inside the solenoid is shown in the diagram. The solenoid passes through a coil of wire, which has 45 turns of radius 0.15 m. The coil is connected to a voltmeter (not shown).

[[File:hardexdigram.png]]

a.) At the same instant (t = 0.3 seconds), what will the absolute value of the reading on the
voltmeter be?
[[File:harda.jpg|700x900px]]

b.) The resistance of the coil is 2 ohms. At time t = 0.3 seconds, what is the conventional current
in the coil?
[[File:hardb.jpg|700x900px]]

c.) At time t = 0.3 seconds, what is the magnitude of the non-coulomb electric field ENC in
the coil?
[[File:hardc.jpg|700x900px]]

==Connectedness==
#Solenoids are important because they are the easiest way to create electromagnets and are an important piece in transformers.
#As a Computer Engineering major, solenoids are important, at least for the EE parts of my major, because as stated above they are used to create transformers which are a major piece in large and small scale power grids.

==See Also==
[[Ampere's Law]]

[[Magnetic Field of a Long Thick Wire Using Ampere's Law]]

[[Magnetic Field of Coaxial Cable Using Ampere's Law]]

[[Magnetic Field of a Toroid Using Ampere's Law]]

===Further Reading===

Chabay, Sherwood. (2015). Matter and Interactions (4th ed., Vol. 2). Raleigh, North Carolina: Wiley.

===External Links===
*http://www.one-school.net/Malaysia/UniversityandCollege/SPM/revisioncard/physics/electromagnetism/electromagnet.html

*http://www.physicstutorials.org/home/magnetism/magnetic-field-around-a-solenoid

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

==References==
Chabay, Sherwood. (2015). Matter and Interactions (4th ed., Vol. 2). Raleigh, North Carolina: Wiley. Pg 887-888.
Physics 2212 Spring 2016 Lab Quiz 8

[[Category:Maxwell's Equations]]

Magnetic Field of a Solenoid Using Ampere's Law

2016-11-28T03:47:23Z

Mchandler30: /* A Mathematical Model */

Claimed by Mary Jane Chandler Fall 2016

This page explains how to use Ampere's Law to solve for the magnetic field of a solenoid.

==The Main Idea==

A solenoid is a cylindrical coil of wire that produces a uniform magnetic field when it is carrying an electric current. A solenoid is a form of an electromagnet that can create strong controlled magnetic fields throughout the coil except at the ends. Ampere's Law states that the magnetic field in space around an electric current is proportional to the source of the electric current. This can be applied to solve the magnetic field of a Solenoid.

[[File:solenoidfrombook.png]]

As you can see in this model, in the middle of the solenoid the field is constant throughout the entirety of the interior and is parallel to the axis. At the ends of a solenoid the magnetic field starts to point outward at varying angles.

===Equation===

If there are <math>N</math> loops of wire that compose a solenoid of length <math>L</math>, and we know that Ampere's Law gives us the form:

<math>{\oint\,\vec{B}•d\vec{l} = μ_{0}∑I_{inside path}}</math>

[[File:sol.png|frame|Solenoid with variables]]

We can then solve for <math>B</math>:

<math>{B = \frac{μ_{0}NI}{L}}</math>

The Right Hand Rule can be used to find the direction of the magnetic field by using your right hand and curling your fingers in the direction of the current with your thumb pointing in the direction of the magnetic field. This is always along the axis for a solenoid.

[[File:Righthand.png]]

==Examples==

===Simple===
Find the magnetic field produced by a 40 cm long solenoid if the number of loops is 400 and current passing through it is 5 A.
[[File:Examplesolenoid.jpg|700x900px]]

This example is very simple, as all of the variables of the equation are provided. All you need to do is plug them in and find the direction using the right hand rule.
===Middling===
A solenoid has a magnetic field of 5x10-4 T, 3000 turns, and is 30 cm long. What is the current through the solenoid?
[[File:example2solenoid.jpg|700x900px]]

This example is just a reverse solving of the equation derived above for the magnetic field of a solenoid. It is not munch more difficult than the previous example.
===Difficult===
A long, tightly wound solenoid has a circular cross section of radius 0.02 m. The solenoid is connected to a power supply (not shown), and this current changes with time, so the magnetic field inside the solenoid also changes with time. At time t = 0 s, the magnitude of the magnetic field inside the solenoid is 1.8 T. At time t = 0.3 s, the magnitude of the magnetic field inside the solenoid is 0.5 T. The direction of the magnetic field inside the solenoid is shown in the diagram. The solenoid passes through a coil of wire, which has 45 turns of radius 0.15 m. The coil is connected to a voltmeter (not shown).

[[File:hardexdigram.png]]

a.) At the same instant (t = 0.3 seconds), what will the absolute value of the reading on the
voltmeter be?
[[File:harda.jpg|700x900px]]

b.) The resistance of the coil is 2 ohms. At time t = 0.3 seconds, what is the conventional current
in the coil?
[[File:hardb.jpg|700x900px]]

c.) At time t = 0.3 seconds, what is the magnitude of the non-coulomb electric field ENC in
the coil?
[[File:hardc.jpg|700x900px]]

==Connectedness==
#Solenoids are important because they are the easiest way to create electromagnets and are an important piece in transformers.
#As a Computer Engineering major, solenoids are important, at least for the EE parts of my major, because as stated above they are used to create transformers which are a major piece in large and small scale power grids.

==See Also==
[[Ampere's Law]]

[[Magnetic Field of a Long Thick Wire Using Ampere's Law]]

[[Magnetic Field of Coaxial Cable Using Ampere's Law]]

[[Magnetic Field of a Toroid Using Ampere's Law]]

===Further Reading===

Chabay, Sherwood. (2015). Matter and Interactions (4th ed., Vol. 2). Raleigh, North Carolina: Wiley.

===External Links===
*http://www.one-school.net/Malaysia/UniversityandCollege/SPM/revisioncard/physics/electromagnetism/electromagnet.html

*http://www.physicstutorials.org/home/magnetism/magnetic-field-around-a-solenoid

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

==References==
Chabay, Sherwood. (2015). Matter and Interactions (4th ed., Vol. 2). Raleigh, North Carolina: Wiley. Pg 887-888.
Physics 2212 Spring 2016 Lab Quiz 8

[[Category:Maxwell's Equations]]

Magnetic Field of a Solenoid Using Ampere's Law

2016-11-28T03:45:42Z

Mchandler30:

Claimed by Mary Jane Chandler Fall 2016

This page explains how to use Ampere's Law to solve for the magnetic field of a solenoid.

==The Main Idea==

A solenoid is a cylindrical coil of wire that produces a uniform magnetic field when it is carrying an electric current. A solenoid is a form of an electromagnet that can create strong controlled magnetic fields throughout the coil except at the ends. Ampere's Law states that the magnetic field in space around an electric current is proportional to the source of the electric current. This can be applied to solve the magnetic field of a Solenoid.

[[File:solenoidfrombook.png]]

As you can see in this model, in the middle of the solenoid the field is constant throughout the entirety of the interior and is parallel to the axis. At the ends of a solenoid the magnetic field starts to point outward at varying angles.

===A Mathematical Model===

If there are <math>N</math> loops of wire that compose a solenoid of length <math>L</math>, and we know that Ampere's Law gives us the form:

<math>{\oint\,\vec{B}•d\vec{l} = μ_{0}∑I_{inside path}}</math>

[[File:sol.png|frame|Solenoid with variables]]

We can then solve for <math>B</math>:

<math>{B = \frac{μ_{0}NI}{L}}</math>

The Right Hand Rule can be used to find the direction of the magnetic field by using your right hand and curling your fingers in the direction of the current with your thumb pointing in the direction of the magnetic field. This is always along the axis for a solenoid.

[[File:Righthand.png]]

==Examples==

===Simple===
Find the magnetic field produced by a 40 cm long solenoid if the number of loops is 400 and current passing through it is 5 A.
[[File:Examplesolenoid.jpg|700x900px]]

This example is very simple, as all of the variables of the equation are provided. All you need to do is plug them in and find the direction using the right hand rule.
===Middling===
A solenoid has a magnetic field of 5x10-4 T, 3000 turns, and is 30 cm long. What is the current through the solenoid?
[[File:example2solenoid.jpg|700x900px]]

This example is just a reverse solving of the equation derived above for the magnetic field of a solenoid. It is not munch more difficult than the previous example.
===Difficult===
A long, tightly wound solenoid has a circular cross section of radius 0.02 m. The solenoid is connected to a power supply (not shown), and this current changes with time, so the magnetic field inside the solenoid also changes with time. At time t = 0 s, the magnitude of the magnetic field inside the solenoid is 1.8 T. At time t = 0.3 s, the magnitude of the magnetic field inside the solenoid is 0.5 T. The direction of the magnetic field inside the solenoid is shown in the diagram. The solenoid passes through a coil of wire, which has 45 turns of radius 0.15 m. The coil is connected to a voltmeter (not shown).

[[File:hardexdigram.png]]

a.) At the same instant (t = 0.3 seconds), what will the absolute value of the reading on the
voltmeter be?
[[File:harda.jpg|700x900px]]

b.) The resistance of the coil is 2 ohms. At time t = 0.3 seconds, what is the conventional current
in the coil?
[[File:hardb.jpg|700x900px]]

c.) At time t = 0.3 seconds, what is the magnitude of the non-coulomb electric field ENC in
the coil?
[[File:hardc.jpg|700x900px]]

==Connectedness==
#Solenoids are important because they are the easiest way to create electromagnets and are an important piece in transformers.
#As a Computer Engineering major, solenoids are important, at least for the EE parts of my major, because as stated above they are used to create transformers which are a major piece in large and small scale power grids.

==See Also==
[[Ampere's Law]]

[[Magnetic Field of a Long Thick Wire Using Ampere's Law]]

[[Magnetic Field of Coaxial Cable Using Ampere's Law]]

[[Magnetic Field of a Toroid Using Ampere's Law]]

===Further Reading===

Chabay, Sherwood. (2015). Matter and Interactions (4th ed., Vol. 2). Raleigh, North Carolina: Wiley.

===External Links===
*http://www.one-school.net/Malaysia/UniversityandCollege/SPM/revisioncard/physics/electromagnetism/electromagnet.html

*http://www.physicstutorials.org/home/magnetism/magnetic-field-around-a-solenoid

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

==References==
Chabay, Sherwood. (2015). Matter and Interactions (4th ed., Vol. 2). Raleigh, North Carolina: Wiley. Pg 887-888.
Physics 2212 Spring 2016 Lab Quiz 8

[[Category:Maxwell's Equations]]

Magnetic Field of a Solenoid Using Ampere's Law

2016-11-28T03:30:24Z

Mchandler30: /* A Computational Model */

---- CREATED BY JAKE WEBB ----

This page explains how to use Ampere's Law to solve for the magnetic field of a solenoid.

==The Main Idea==

A solenoid is a cylindrical coil of wire that produces a uniform magnetic field when it is carrying an electric current. A solenoid is a form of an electromagnet that can create strong controlled magnetic fields throughout the coil except at the ends. Ampere's Law states that the magnetic field in space around an electric current is proportional to the source of the electric current. This can be applied to solve the magnetic field of a Solenoid.

[[File:solenoidfrombook.png]]

As you can see in this model, in the middle of the solenoid the field is constant throughout the entirety of the interior and is parallel to the axis. At the ends of a solenoid the magnetic field starts to point outward at varying angles.

===A Mathematical Model===

If there are <math>N</math> loops of wire that compose a solenoid of length <math>L</math>, and we know that Ampere's Law gives us the form:

<math>{\oint\,\vec{B}•d\vec{l} = μ_{0}∑I_{inside path}}</math>

[[File:solenoidwithvars.png|frame|Solenoid with variables labeled]]

We can then solve for <math>B</math>:

<math>{B = \frac{μ_{0}NI}{L}}</math>

The Right Hand Rule can be used to find the direction of the magnetic field by using your right hand and curling your fingers in the direction of the current with your thumb pointing in the direction of the magnetic field. This is always along the axis for a solenoid.

[[File:Righthand.png]]

==Examples==

===Simple===
Find the magnetic field produced by a 40 cm long solenoid if the number of loops is 400 and current passing through it is 5 A.
[[File:Examplesolenoid.jpg|700x900px]]

This example is very simple, as all of the variables of the equation are provided. All you need to do is plug them in and find the direction using the right hand rule.
===Middling===
A solenoid has a magnetic field of 5x10-4 T, 3000 turns, and is 30 cm long. What is the current through the solenoid?
[[File:example2solenoid.jpg|700x900px]]

This example is just a reverse solving of the equation derived above for the magnetic field of a solenoid. It is not munch more difficult than the previous example.
===Difficult===
A long, tightly wound solenoid has a circular cross section of radius 0.02 m. The solenoid is connected to a power supply (not shown), and this current changes with time, so the magnetic field inside the solenoid also changes with time. At time t = 0 s, the magnitude of the magnetic field inside the solenoid is 1.8 T. At time t = 0.3 s, the magnitude of the magnetic field inside the solenoid is 0.5 T. The direction of the magnetic field inside the solenoid is shown in the diagram. The solenoid passes through a coil of wire, which has 45 turns of radius 0.15 m. The coil is connected to a voltmeter (not shown).

[[File:hardexdigram.png]]

a.) At the same instant (t = 0.3 seconds), what will the absolute value of the reading on the
voltmeter be?
[[File:harda.jpg|700x900px]]

b.) The resistance of the coil is 2 ohms. At time t = 0.3 seconds, what is the conventional current
in the coil?
[[File:hardb.jpg|700x900px]]

c.) At time t = 0.3 seconds, what is the magnitude of the non-coulomb electric field ENC in
the coil?
[[File:hardc.jpg|700x900px]]

==Connectedness==
#Solenoids are important because they are the easiest way to create electromagnets and are an important piece in transformers.
#As a Computer Engineering major, solenoids are important, at least for the EE parts of my major, because as stated above they are used to create transformers which are a major piece in large and small scale power grids.

==See Also==
[[Ampere's Law]]

[[Magnetic Field of a Long Thick Wire Using Ampere's Law]]

[[Magnetic Field of Coaxial Cable Using Ampere's Law]]

[[Magnetic Field of a Toroid Using Ampere's Law]]

===Further Reading===

Chabay, Sherwood. (2015). Matter and Interactions (4th ed., Vol. 2). Raleigh, North Carolina: Wiley.

===External Links===
*http://www.one-school.net/Malaysia/UniversityandCollege/SPM/revisioncard/physics/electromagnetism/electromagnet.html

*http://www.physicstutorials.org/home/magnetism/magnetic-field-around-a-solenoid

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

==References==
Chabay, Sherwood. (2015). Matter and Interactions (4th ed., Vol. 2). Raleigh, North Carolina: Wiley. Pg 887-888.
Physics 2212 Spring 2016 Lab Quiz 8

[[Category:Maxwell's Equations]]

Magnetic Field of a Solenoid Using Ampere's Law

2016-11-28T03:30:03Z

Mchandler30: /* The Main Idea */

---- CREATED BY JAKE WEBB ----

This page explains how to use Ampere's Law to solve for the magnetic field of a solenoid.

==The Main Idea==

A solenoid is a cylindrical coil of wire that produces a uniform magnetic field when it is carrying an electric current. A solenoid is a form of an electromagnet that can create strong controlled magnetic fields throughout the coil except at the ends. Ampere's Law states that the magnetic field in space around an electric current is proportional to the source of the electric current. This can be applied to solve the magnetic field of a Solenoid.

[[File:solenoidfrombook.png]]

As you can see in this model, in the middle of the solenoid the field is constant throughout the entirety of the interior and is parallel to the axis. At the ends of a solenoid the magnetic field starts to point outward at varying angles.

===A Mathematical Model===

If there are <math>N</math> loops of wire that compose a solenoid of length <math>L</math>, and we know that Ampere's Law gives us the form:

<math>{\oint\,\vec{B}•d\vec{l} = μ_{0}∑I_{inside path}}</math>

[[File:solenoidwithvars.png|frame|Solenoid with variables labeled]]

We can then solve for <math>B</math>:

<math>{B = \frac{μ_{0}NI}{L}}</math>

The Right Hand Rule can be used to find the direction of the magnetic field by using your right hand and curling your fingers in the direction of the current with your thumb pointing in the direction of the magnetic field. This is always along the axis for a solenoid.

[[File:Righthand.png]]

===A Computational Model===
This gif shows how the magnetic field forms in the solenoid when there is a current running through it.
[[File:solenoid-o.gif]]

==Examples==

===Simple===
Find the magnetic field produced by a 40 cm long solenoid if the number of loops is 400 and current passing through it is 5 A.
[[File:Examplesolenoid.jpg|700x900px]]

This example is very simple, as all of the variables of the equation are provided. All you need to do is plug them in and find the direction using the right hand rule.
===Middling===
A solenoid has a magnetic field of 5x10-4 T, 3000 turns, and is 30 cm long. What is the current through the solenoid?
[[File:example2solenoid.jpg|700x900px]]

This example is just a reverse solving of the equation derived above for the magnetic field of a solenoid. It is not munch more difficult than the previous example.
===Difficult===
A long, tightly wound solenoid has a circular cross section of radius 0.02 m. The solenoid is connected to a power supply (not shown), and this current changes with time, so the magnetic field inside the solenoid also changes with time. At time t = 0 s, the magnitude of the magnetic field inside the solenoid is 1.8 T. At time t = 0.3 s, the magnitude of the magnetic field inside the solenoid is 0.5 T. The direction of the magnetic field inside the solenoid is shown in the diagram. The solenoid passes through a coil of wire, which has 45 turns of radius 0.15 m. The coil is connected to a voltmeter (not shown).

[[File:hardexdigram.png]]

a.) At the same instant (t = 0.3 seconds), what will the absolute value of the reading on the
voltmeter be?
[[File:harda.jpg|700x900px]]

b.) The resistance of the coil is 2 ohms. At time t = 0.3 seconds, what is the conventional current
in the coil?
[[File:hardb.jpg|700x900px]]

c.) At time t = 0.3 seconds, what is the magnitude of the non-coulomb electric field ENC in
the coil?
[[File:hardc.jpg|700x900px]]

==Connectedness==
#Solenoids are important because they are the easiest way to create electromagnets and are an important piece in transformers.
#As a Computer Engineering major, solenoids are important, at least for the EE parts of my major, because as stated above they are used to create transformers which are a major piece in large and small scale power grids.

==See Also==
[[Ampere's Law]]

[[Magnetic Field of a Long Thick Wire Using Ampere's Law]]

[[Magnetic Field of Coaxial Cable Using Ampere's Law]]

[[Magnetic Field of a Toroid Using Ampere's Law]]

===Further Reading===

Chabay, Sherwood. (2015). Matter and Interactions (4th ed., Vol. 2). Raleigh, North Carolina: Wiley.

===External Links===
*http://www.one-school.net/Malaysia/UniversityandCollege/SPM/revisioncard/physics/electromagnetism/electromagnet.html

*http://www.physicstutorials.org/home/magnetism/magnetic-field-around-a-solenoid

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

==References==
Chabay, Sherwood. (2015). Matter and Interactions (4th ed., Vol. 2). Raleigh, North Carolina: Wiley. Pg 887-888.
Physics 2212 Spring 2016 Lab Quiz 8

[[Category:Maxwell's Equations]]

Magnetic Field of a Solenoid Using Ampere's Law

2016-11-28T03:13:25Z

Mchandler30: /* The Main Idea */

---- CREATED BY JAKE WEBB ----

This page explains how to use Ampere's Law to solve for the magnetic field of a solenoid.

==The Main Idea==

A solenoid is a cylindrical coil of wire that produces a uniform magnetic field when it is carrying an electric current. A solenoid is a form of an electromagnet that can create strong controlled magnetic fields throughout the coil except at the ends.

[[File:solenoidfrombook.png]]

As you can see in this model, in the middle of the solenoid the field is constant throughout the entirety of the interior and is parallel to the axis. At the ends of a solenoid the magnetic field starts to point outward at varying angles.

===A Mathematical Model===

If there are <math>N</math> loops of wire that compose a solenoid of length <math>L</math>, and we know that Ampere's Law for Magnetism gives us the form:

<math>{\oint\,\vec{B}•d\vec{l} = μ_{0}∑I_{inside path}}</math>

[[File:solenoidwithvars.png|frame|Solenoid with variables labeled]]

As stated above, the magnetic field inside a solenoid is constant and parallel to <math>dl⃗</math>, therefore Ampere's Law can be simplified to:

<math>BL=μ0NI</math>

By simply solving for <math>B</math> we can find the equation for the magnetic field of a solenoid:

<math>{B = \frac{μ_{0}NI}{L}}</math>

The direction can be found using the Right Hand Rule with your fingers curling around in the direction of the current and your thumb pointing in the direction of the magnetic field. It will always be along the axis for a solenoid.

[[File:Righthand.png]]

===A Computational Model===
This gif shows how the magnetic field forms in the solenoid when there is a current running through it.
[[File:solenoid-o.gif]]

==Examples==

===Simple===
Find the magnetic field produced by a 40 cm long solenoid if the number of loops is 400 and current passing through it is 5 A.
[[File:Examplesolenoid.jpg|700x900px]]

This example is very simple, as all of the variables of the equation are provided. All you need to do is plug them in and find the direction using the right hand rule.
===Middling===
A solenoid has a magnetic field of 5x10-4 T, 3000 turns, and is 30 cm long. What is the current through the solenoid?
[[File:example2solenoid.jpg|700x900px]]

This example is just a reverse solving of the equation derived above for the magnetic field of a solenoid. It is not munch more difficult than the previous example.
===Difficult===
A long, tightly wound solenoid has a circular cross section of radius 0.02 m. The solenoid is connected to a power supply (not shown), and this current changes with time, so the magnetic field inside the solenoid also changes with time. At time t = 0 s, the magnitude of the magnetic field inside the solenoid is 1.8 T. At time t = 0.3 s, the magnitude of the magnetic field inside the solenoid is 0.5 T. The direction of the magnetic field inside the solenoid is shown in the diagram. The solenoid passes through a coil of wire, which has 45 turns of radius 0.15 m. The coil is connected to a voltmeter (not shown).

[[File:hardexdigram.png]]

a.) At the same instant (t = 0.3 seconds), what will the absolute value of the reading on the
voltmeter be?
[[File:harda.jpg|700x900px]]

b.) The resistance of the coil is 2 ohms. At time t = 0.3 seconds, what is the conventional current
in the coil?
[[File:hardb.jpg|700x900px]]

c.) At time t = 0.3 seconds, what is the magnitude of the non-coulomb electric field ENC in
the coil?
[[File:hardc.jpg|700x900px]]

==Connectedness==
#Solenoids are important because they are the easiest way to create electromagnets and are an important piece in transformers.
#As a Computer Engineering major, solenoids are important, at least for the EE parts of my major, because as stated above they are used to create transformers which are a major piece in large and small scale power grids.

==See Also==
[[Ampere's Law]]

[[Magnetic Field of a Long Thick Wire Using Ampere's Law]]

[[Magnetic Field of Coaxial Cable Using Ampere's Law]]

[[Magnetic Field of a Toroid Using Ampere's Law]]

===Further Reading===

Chabay, Sherwood. (2015). Matter and Interactions (4th ed., Vol. 2). Raleigh, North Carolina: Wiley.

===External Links===
*http://www.one-school.net/Malaysia/UniversityandCollege/SPM/revisioncard/physics/electromagnetism/electromagnet.html

*http://www.physicstutorials.org/home/magnetism/magnetic-field-around-a-solenoid

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

==References==
Chabay, Sherwood. (2015). Matter and Interactions (4th ed., Vol. 2). Raleigh, North Carolina: Wiley. Pg 887-888.
Physics 2212 Spring 2016 Lab Quiz 8

[[Category:Maxwell's Equations]]