Physics Book - User contributions [en]

Biot-Savart Law for Currents

2015-11-29T23:30:36Z

David Medrano: /* A Computational Model */

Claimed by David Medrano
==Biot-Savart Law==

The Biot-Savart Law can be used for more than just single moving charges; it can also be used to calculate the magnetic field for a large number of charges. One notable reason to do so is to find the magnetic field of a portion of a wire where there can be many moving charges. When we use Biot-Savart Law to find the magnetic field of a short wire, we can apply it to a variety of shapes.

====A Mathematical Model====
First We start off with the original version of the Biot-Savart Law.
<math>\vec B=\frac{\mu_0}{4 \pi } \frac{q\vec v\times\hat r}{r^2}.</math>

Because we are dealing with a portion of wire <math>\mathrm{d}\boldsymbol{\ell}</math> long with an Area A containing n moving particles with charge q, we find that the total number of moving charges is equal to |q|(nAv) which is also equal to I, the current in the wire.
<math>B = \frac{\mu_0I}{4\pi}\frac{\mathrm{d}\boldsymbol{\ell} \times \mathbf{\hat r}}{r^2},</math>

Because the shape of the current carrying wire can vary from a straight wire to a loop, we must integrate over the region of the wire.

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

==Example==
====For a long wire of length L positioned along the x axis with current flowing in the positive x direction====
First, we start off with our adjusted Biot-Savart Formula for a slice of wire.

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

Second, we must find <math>r</math>, the vector pointing from the source to the observation location. In this case, we will choose an observation location y above the rod.

<math> r = obs - source = <0,y,0> - < x,0,0> = <-x,y,0> </math>. which has a magnitude of <math>\sqrt(x^2+y^2)</math>

We see that <math>\hat r = \frac{r}{|r|} </math> .

<math>\hat r = \frac{<-x,y,0>}{\sqrt(x^2+y^2))}</math>

We then have to express <math> \Delta \boldsymbol{\ell}</math> in terms of our variable of integration, x.
<math> \Delta \boldsymbol{\ell}</math> = <math> \Delta x<1,0,0,></math>

Our new equation after substituting our new variables is
<math> \Delta B = \frac{\mu_0I\Delta x<1,0,0,>}{4\pi(x^2+y^2)} \times \frac{<-x,y,0>}{\sqrt(x^2+y^2))} </math>

Finding the cross product of the above vectors gives us a product in the +z direction.
<math> \Delta B = \frac{\mu_0I\Delta x}{4\pi(x^2+y^2)^(\frac{3}{2})} </math>

We are finally ready to integrate. Because we are integrating the entire rod our limits are
<math> \int\limits_{-L/2}^{L/2}\ </math>

<math> \int\limits_{-L/2}^{L/2}\ = \frac{\mu_0I\Delta x}{4\pi(x^2+y^2)^(\frac{3}{2})} </math>

We find that our final answer is <math> B= \frac{\mu_0}{4\pi}\frac{LI}{y\sqrt(y^2+(L/2)^2)}\hat z </math>

==A Computational Model==
The following link shows the magnetic field produced by small segments of wire in a loop individually.
For a long straight wire, we see that there is a circular magnetic field surrounding the wire with current. The following link does a stepwise visual of the contributions of each part of the wire at an observation location a distance r from the wire.

http://www.glowscript.org/#/user/matterandinteractions/folder/matterandinteractions/program/17-Bwire-with-r

We see that along the axis of the wire, each contribution not on the axis is negated due to symmetry and the resulting magnetic field is all along the wire.

http://www.glowscript.org/#/user/matterandinteractions/folder/matterandinteractions/program/17-B-loop-with-r-dB.

== See also ==
[Right Hand Rule[http://www.physicsbook.gatech.edu/Right-Hand_Rule]]

[Direction of magnetic fields[http://www.physicsbook.gatech.edu/Direction_of_Magnetic_Field]]
Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?

==External Links==
[[Category:Which Category did you place this in?]]

Biot-Savart Law for Currents

2015-11-29T23:28:40Z

David Medrano: /* See also */

Claimed by David Medrano
==Biot-Savart Law==

The Biot-Savart Law can be used for more than just single moving charges; it can also be used to calculate the magnetic field for a large number of charges. One notable reason to do so is to find the magnetic field of a portion of a wire where there can be many moving charges. When we use Biot-Savart Law to find the magnetic field of a short wire, we can apply it to a variety of shapes.

====A Mathematical Model====
First We start off with the original version of the Biot-Savart Law.
<math>\vec B=\frac{\mu_0}{4 \pi } \frac{q\vec v\times\hat r}{r^2}.</math>

Because we are dealing with a portion of wire <math>\mathrm{d}\boldsymbol{\ell}</math> long with an Area A containing n moving particles with charge q, we find that the total number of moving charges is equal to |q|(nAv) which is also equal to I, the current in the wire.
<math>B = \frac{\mu_0I}{4\pi}\frac{\mathrm{d}\boldsymbol{\ell} \times \mathbf{\hat r}}{r^2},</math>

Because the shape of the current carrying wire can vary from a straight wire to a loop, we must integrate over the region of the wire.

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

==Example==
====For a long wire of length L positioned along the x axis with current flowing in the positive x direction====
First, we start off with our adjusted Biot-Savart Formula for a slice of wire.

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

Second, we must find <math>r</math>, the vector pointing from the source to the observation location. In this case, we will choose an observation location y above the rod.

<math> r = obs - source = <0,y,0> - < x,0,0> = <-x,y,0> </math>. which has a magnitude of <math>\sqrt(x^2+y^2)</math>

We see that <math>\hat r = \frac{r}{|r|} </math> .

<math>\hat r = \frac{<-x,y,0>}{\sqrt(x^2+y^2))}</math>

We then have to express <math> \Delta \boldsymbol{\ell}</math> in terms of our variable of integration, x.
<math> \Delta \boldsymbol{\ell}</math> = <math> \Delta x<1,0,0,></math>

Our new equation after substituting our new variables is
<math> \Delta B = \frac{\mu_0I\Delta x<1,0,0,>}{4\pi(x^2+y^2)} \times \frac{<-x,y,0>}{\sqrt(x^2+y^2))} </math>

Finding the cross product of the above vectors gives us a product in the +z direction.
<math> \Delta B = \frac{\mu_0I\Delta x}{4\pi(x^2+y^2)^(\frac{3}{2})} </math>

We are finally ready to integrate. Because we are integrating the entire rod our limits are
<math> \int\limits_{-L/2}^{L/2}\ </math>

<math> \int\limits_{-L/2}^{L/2}\ = \frac{\mu_0I\Delta x}{4\pi(x^2+y^2)^(\frac{3}{2})} </math>

We find that our final answer is <math> B= \frac{\mu_0}{4\pi}\frac{LI}{y\sqrt(y^2+(L/2)^2)}\hat z </math>

==A Computational Model==
The following link shows the magnetic field produced by small segments of wire in a loop individually.
For a long straight wire, we see that there is a circular magnetic field surrounding the wire with current. The following link does a stepwise visual of the contributions of each part of the wire at an observation location a distance r from the wire.

http://www.glowscript.org/#/user/matterandinteractions/folder/matterandinteractions/program/17-Bwire-with-r

We see that along the axis of the wire, each contribution not on the axis is negated due to symmetry and the resulting magnetic field is all along the wire.

http://www.glowscript.org/#/user/matterandinteractions/folder/matterandinteractions/program/17-B-loop-with-r-dB.

==Applications==

== See also ==
[Right Hand Rule[http://www.physicsbook.gatech.edu/Right-Hand_Rule]]

[Direction of magnetic fields[http://www.physicsbook.gatech.edu/Direction_of_Magnetic_Field]]
Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?

==External Links==
[[Category:Which Category did you place this in?]]

Biot-Savart Law for Currents

2015-11-29T23:26:49Z

David Medrano:

Claimed by David Medrano
==Biot-Savart Law==

The Biot-Savart Law can be used for more than just single moving charges; it can also be used to calculate the magnetic field for a large number of charges. One notable reason to do so is to find the magnetic field of a portion of a wire where there can be many moving charges. When we use Biot-Savart Law to find the magnetic field of a short wire, we can apply it to a variety of shapes.

====A Mathematical Model====
First We start off with the original version of the Biot-Savart Law.
<math>\vec B=\frac{\mu_0}{4 \pi } \frac{q\vec v\times\hat r}{r^2}.</math>

Because we are dealing with a portion of wire <math>\mathrm{d}\boldsymbol{\ell}</math> long with an Area A containing n moving particles with charge q, we find that the total number of moving charges is equal to |q|(nAv) which is also equal to I, the current in the wire.
<math>B = \frac{\mu_0I}{4\pi}\frac{\mathrm{d}\boldsymbol{\ell} \times \mathbf{\hat r}}{r^2},</math>

Because the shape of the current carrying wire can vary from a straight wire to a loop, we must integrate over the region of the wire.

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

==Example==
====For a long wire of length L positioned along the x axis with current flowing in the positive x direction====
First, we start off with our adjusted Biot-Savart Formula for a slice of wire.

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

Second, we must find <math>r</math>, the vector pointing from the source to the observation location. In this case, we will choose an observation location y above the rod.

<math> r = obs - source = <0,y,0> - < x,0,0> = <-x,y,0> </math>. which has a magnitude of <math>\sqrt(x^2+y^2)</math>

We see that <math>\hat r = \frac{r}{|r|} </math> .

<math>\hat r = \frac{<-x,y,0>}{\sqrt(x^2+y^2))}</math>

We then have to express <math> \Delta \boldsymbol{\ell}</math> in terms of our variable of integration, x.
<math> \Delta \boldsymbol{\ell}</math> = <math> \Delta x<1,0,0,></math>

Our new equation after substituting our new variables is
<math> \Delta B = \frac{\mu_0I\Delta x<1,0,0,>}{4\pi(x^2+y^2)} \times \frac{<-x,y,0>}{\sqrt(x^2+y^2))} </math>

Finding the cross product of the above vectors gives us a product in the +z direction.
<math> \Delta B = \frac{\mu_0I\Delta x}{4\pi(x^2+y^2)^(\frac{3}{2})} </math>

We are finally ready to integrate. Because we are integrating the entire rod our limits are
<math> \int\limits_{-L/2}^{L/2}\ </math>

<math> \int\limits_{-L/2}^{L/2}\ = \frac{\mu_0I\Delta x}{4\pi(x^2+y^2)^(\frac{3}{2})} </math>

We find that our final answer is <math> B= \frac{\mu_0}{4\pi}\frac{LI}{y\sqrt(y^2+(L/2)^2)}\hat z </math>

==A Computational Model==
The following link shows the magnetic field produced by small segments of wire in a loop individually.
For a long straight wire, we see that there is a circular magnetic field surrounding the wire with current. The following link does a stepwise visual of the contributions of each part of the wire at an observation location a distance r from the wire.

http://www.glowscript.org/#/user/matterandinteractions/folder/matterandinteractions/program/17-Bwire-with-r

We see that along the axis of the wire, each contribution not on the axis is negated due to symmetry and the resulting magnetic field is all along the wire.

http://www.glowscript.org/#/user/matterandinteractions/folder/matterandinteractions/program/17-B-loop-with-r-dB.

==Applications==

== See also ==
[Right Hand Rule[http://www.physicsbook.gatech.edu/Right-Hand_Rule]]
[Direction of magnetic fields[http://www.physicsbook.gatech.edu/Direction_of_Magnetic_Field]]
Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?

==External Links==
[[Category:Which Category did you place this in?]]

Biot-Savart Law for Currents

2015-11-29T23:20:24Z

David Medrano: /* History */

Claimed by David Medrano
==Biot-Savart Law==

The Biot-Savart Law can be used for more than just single moving charges; it can also be used to calculate the magnetic field for a large number of charges. One notable reason to do so is to find the magnetic field of a portion of a wire where there can be many moving charges. When we use Biot-Savart Law to find the magnetic field of a short wire, we can apply it to a variety of shapes.

====A Mathematical Model====
First We start off with the original version of the Biot-Savart Law.
<math>\vec B=\frac{\mu_0}{4 \pi } \frac{q\vec v\times\hat r}{r^2}.</math>

Because we are dealing with a portion of wire <math>\mathrm{d}\boldsymbol{\ell}</math> long with an Area A containing n moving particles with charge q, we find that the total number of moving charges is equal to |q|(nAv) which is also equal to I, the current in the wire.
<math>B = \frac{\mu_0I}{4\pi}\frac{\mathrm{d}\boldsymbol{\ell} \times \mathbf{\hat r}}{r^2},</math>

Because the shape of the current carrying wire can vary from a straight wire to a loop, we must integrate over the region of the wire.

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

==Example==
====For a long wire of length L positioned along the x axis with current flowing in the positive x direction====
First, we start off with our adjusted Biot-Savart Formula for a slice of wire.

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

Second, we must find <math>r</math>, the vector pointing from the source to the observation location. In this case, we will choose an observation location y above the rod.

<math> r = obs - source = <0,y,0> - < x,0,0> = <-x,y,0> </math>. which has a magnitude of <math>\sqrt(x^2+y^2)</math>

We see that <math>\hat r = \frac{r}{|r|} </math> .

<math>\hat r = \frac{<-x,y,0>}{\sqrt(x^2+y^2))}</math>

We then have to express <math> \Delta \boldsymbol{\ell}</math> in terms of our variable of integration, x.
<math> \Delta \boldsymbol{\ell}</math> = <math> \Delta x<1,0,0,></math>

Our new equation after substituting our new variables is
<math> \Delta B = \frac{\mu_0I\Delta x<1,0,0,>}{4\pi(x^2+y^2)} \times \frac{<-x,y,0>}{\sqrt(x^2+y^2))} </math>

Finding the cross product of the above vectors gives us a product in the +z direction.
<math> \Delta B = \frac{\mu_0I\Delta x}{4\pi(x^2+y^2)^(\frac{3}{2})} </math>

We are finally ready to integrate. Because we are integrating the entire rod our limits are
<math> \int\limits_{-L/2}^{L/2}\ </math>

<math> \int\limits_{-L/2}^{L/2}\ = \frac{\mu_0I\Delta x}{4\pi(x^2+y^2)^(\frac{3}{2})} </math>

We find that our final answer is <math> B= \frac{\mu_0}{4\pi}\frac{LI}{y\sqrt(y^2+(L/2)^2)}\hat z </math>

==A Computational Model==
The following link shows the magnetic field produced by small segments of wire in a loop individually.
For a long straight wire, we see that there is a circular magnetic field surrounding the wire with current. The following link does a stepwise visual of the contributions of each part of the wire at an observation location a distance r from the wire.

http://www.glowscript.org/#/user/matterandinteractions/folder/matterandinteractions/program/17-Bwire-with-r

We see that along the axis of the wire, each contribution not on the axis is negated due to symmetry and the resulting magnetic field is all along the wire.

http://www.glowscript.org/#/user/matterandinteractions/folder/matterandinteractions/program/17-B-loop-with-r-dB.

==Connectedness==
==Applications==

== See also ==

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

===Further reading===

Books, Articles or other print media on this topic

===External links===

Internet resources on this topic

==References==

https://www.grc.nasa.gov/www/k-12/airplane/thermo0.html
http://hyperphysics.phy-astr.gsu.edu/hbase/thermo/thereq.html
https://www.grc.nasa.gov/www/k-12/airplane/thermo2.html
http://www.phys.nthu.edu.tw/~thschang/notes/GP21.pdf
http://www.eoearth.org/view/article/153532/

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

Biot-Savart Law for Currents

2015-11-29T23:20:02Z

David Medrano: /* Example */

Claimed by David Medrano
==Biot-Savart Law==

The Biot-Savart Law can be used for more than just single moving charges; it can also be used to calculate the magnetic field for a large number of charges. One notable reason to do so is to find the magnetic field of a portion of a wire where there can be many moving charges. When we use Biot-Savart Law to find the magnetic field of a short wire, we can apply it to a variety of shapes.

====A Mathematical Model====
First We start off with the original version of the Biot-Savart Law.
<math>\vec B=\frac{\mu_0}{4 \pi } \frac{q\vec v\times\hat r}{r^2}.</math>

Because we are dealing with a portion of wire <math>\mathrm{d}\boldsymbol{\ell}</math> long with an Area A containing n moving particles with charge q, we find that the total number of moving charges is equal to |q|(nAv) which is also equal to I, the current in the wire.
<math>B = \frac{\mu_0I}{4\pi}\frac{\mathrm{d}\boldsymbol{\ell} \times \mathbf{\hat r}}{r^2},</math>

Because the shape of the current carrying wire can vary from a straight wire to a loop, we must integrate over the region of the wire.

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

==Example==
====For a long wire of length L positioned along the x axis with current flowing in the positive x direction====
First, we start off with our adjusted Biot-Savart Formula for a slice of wire.

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

Second, we must find <math>r</math>, the vector pointing from the source to the observation location. In this case, we will choose an observation location y above the rod.

<math> r = obs - source = <0,y,0> - < x,0,0> = <-x,y,0> </math>. which has a magnitude of <math>\sqrt(x^2+y^2)</math>

We see that <math>\hat r = \frac{r}{|r|} </math> .

<math>\hat r = \frac{<-x,y,0>}{\sqrt(x^2+y^2))}</math>

We then have to express <math> \Delta \boldsymbol{\ell}</math> in terms of our variable of integration, x.
<math> \Delta \boldsymbol{\ell}</math> = <math> \Delta x<1,0,0,></math>

Our new equation after substituting our new variables is
<math> \Delta B = \frac{\mu_0I\Delta x<1,0,0,>}{4\pi(x^2+y^2)} \times \frac{<-x,y,0>}{\sqrt(x^2+y^2))} </math>

Finding the cross product of the above vectors gives us a product in the +z direction.
<math> \Delta B = \frac{\mu_0I\Delta x}{4\pi(x^2+y^2)^(\frac{3}{2})} </math>

We are finally ready to integrate. Because we are integrating the entire rod our limits are
<math> \int\limits_{-L/2}^{L/2}\ </math>

<math> \int\limits_{-L/2}^{L/2}\ = \frac{\mu_0I\Delta x}{4\pi(x^2+y^2)^(\frac{3}{2})} </math>

We find that our final answer is <math> B= \frac{\mu_0}{4\pi}\frac{LI}{y\sqrt(y^2+(L/2)^2)}\hat z </math>

==A Computational Model==
The following link shows the magnetic field produced by small segments of wire in a loop individually.
For a long straight wire, we see that there is a circular magnetic field surrounding the wire with current. The following link does a stepwise visual of the contributions of each part of the wire at an observation location a distance r from the wire.

http://www.glowscript.org/#/user/matterandinteractions/folder/matterandinteractions/program/17-Bwire-with-r

We see that along the axis of the wire, each contribution not on the axis is negated due to symmetry and the resulting magnetic field is all along the wire.

http://www.glowscript.org/#/user/matterandinteractions/folder/matterandinteractions/program/17-B-loop-with-r-dB.

==Connectedness==
==Applications==

==History==

== See also ==

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

===Further reading===

Books, Articles or other print media on this topic

===External links===

Internet resources on this topic

==References==

https://www.grc.nasa.gov/www/k-12/airplane/thermo0.html
http://hyperphysics.phy-astr.gsu.edu/hbase/thermo/thereq.html
https://www.grc.nasa.gov/www/k-12/airplane/thermo2.html
http://www.phys.nthu.edu.tw/~thschang/notes/GP21.pdf
http://www.eoearth.org/view/article/153532/

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

Biot-Savart Law for Currents

2015-11-29T23:19:30Z

David Medrano: /* Example */

Claimed by David Medrano
==Biot-Savart Law==

The Biot-Savart Law can be used for more than just single moving charges; it can also be used to calculate the magnetic field for a large number of charges. One notable reason to do so is to find the magnetic field of a portion of a wire where there can be many moving charges. When we use Biot-Savart Law to find the magnetic field of a short wire, we can apply it to a variety of shapes.

====A Mathematical Model====
First We start off with the original version of the Biot-Savart Law.
<math>\vec B=\frac{\mu_0}{4 \pi } \frac{q\vec v\times\hat r}{r^2}.</math>

Because we are dealing with a portion of wire <math>\mathrm{d}\boldsymbol{\ell}</math> long with an Area A containing n moving particles with charge q, we find that the total number of moving charges is equal to |q|(nAv) which is also equal to I, the current in the wire.
<math>B = \frac{\mu_0I}{4\pi}\frac{\mathrm{d}\boldsymbol{\ell} \times \mathbf{\hat r}}{r^2},</math>

Because the shape of the current carrying wire can vary from a straight wire to a loop, we must integrate over the region of the wire.

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

==Example==
====For a long wire of length L positioned along the x axis with current flowing in the positive x direction====
First, we start off with our adjusted Biot-Savart Formula for a slice of wire.

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

Second, we must find <math>r</math>, the vector pointing from the source to the observation location. In this case, we will choose an observation location y above the rod.

<math> r = obs - source = <0,y,0> - < x,0,0> = <-x,y,0> </math>. which has a magnitude of <math>\sqrt(x^2+y^2)</math>

We see that <math>\hat r = \frac{r}{|r|} </math> .

<math>\hat r = \frac{<-x,y,0>}{\sqrt(x^2+y^2))}</math>

We then have to express <math> \Delta \boldsymbol{\ell}</math> in terms of our variable of integration, x.
<math> \Delta \boldsymbol{\ell}</math> = <math> \Delta x<1,0,0,></math>

Our new equation after substituting our new variables is
<math> \Delta B = \frac{\mu_0I\Delta x<1,0,0,>}{4\pi(x^2+y^2)} \times \frac{<-x,y,0>}{\sqrt(x^2+y^2))} </math>

Finding the cross product of the above vectors gives us a product in the +z direction.
<math> \Delta B = \frac{\mu_0I\Delta x}{4\pi(x^2+y^2)^(\frac{3}{2})} </math>

We are finally ready to integrate. Because we are integrating the entire rod our limits are
<math> \int\limits_{-L/2}^{L/2}\ </math>

<math> \int\limits_{-L/2}^{L/2}\ = \frac{\mu_0I\Delta x}{4\pi(x^2+y^2)^(\frac{3}{2})} </math>

We find that our final answer is <math> B= \frac{\mu_0}{4\pi}\frac{LI}{y\sqrt(y^2+(L/2)^2)}\hatz </math>

==A Computational Model==
The following link shows the magnetic field produced by small segments of wire in a loop individually.
For a long straight wire, we see that there is a circular magnetic field surrounding the wire with current. The following link does a stepwise visual of the contributions of each part of the wire at an observation location a distance r from the wire.

http://www.glowscript.org/#/user/matterandinteractions/folder/matterandinteractions/program/17-Bwire-with-r

We see that along the axis of the wire, each contribution not on the axis is negated due to symmetry and the resulting magnetic field is all along the wire.

http://www.glowscript.org/#/user/matterandinteractions/folder/matterandinteractions/program/17-B-loop-with-r-dB.

==Connectedness==
==Applications==

==History==

== See also ==

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

===Further reading===

Books, Articles or other print media on this topic

===External links===

Internet resources on this topic

==References==

https://www.grc.nasa.gov/www/k-12/airplane/thermo0.html
http://hyperphysics.phy-astr.gsu.edu/hbase/thermo/thereq.html
https://www.grc.nasa.gov/www/k-12/airplane/thermo2.html
http://www.phys.nthu.edu.tw/~thschang/notes/GP21.pdf
http://www.eoearth.org/view/article/153532/

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

Biot-Savart Law for Currents

2015-11-29T23:17:59Z

David Medrano: /* For a long wire of length L positioned along the x axis with current flowing in the positive x direction */

Claimed by David Medrano
==Biot-Savart Law==

The Biot-Savart Law can be used for more than just single moving charges; it can also be used to calculate the magnetic field for a large number of charges. One notable reason to do so is to find the magnetic field of a portion of a wire where there can be many moving charges. When we use Biot-Savart Law to find the magnetic field of a short wire, we can apply it to a variety of shapes.

====A Mathematical Model====
First We start off with the original version of the Biot-Savart Law.
<math>\vec B=\frac{\mu_0}{4 \pi } \frac{q\vec v\times\hat r}{r^2}.</math>

Because we are dealing with a portion of wire <math>\mathrm{d}\boldsymbol{\ell}</math> long with an Area A containing n moving particles with charge q, we find that the total number of moving charges is equal to |q|(nAv) which is also equal to I, the current in the wire.
<math>B = \frac{\mu_0I}{4\pi}\frac{\mathrm{d}\boldsymbol{\ell} \times \mathbf{\hat r}}{r^2},</math>

Because the shape of the current carrying wire can vary from a straight wire to a loop, we must integrate over the region of the wire.

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

==Example==
====For a long wire of length L positioned along the x axis with current flowing in the positive x direction====
First, we start off with our adjusted Biot-Savart Formula for a slice of wire.

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

Second, we must find <math>r</math>, the vector pointing from the source to the observation location. In this case, we will choose an observation location y above the rod.

<math> r = obs - source = <0,y,0> - < x,0,0> = <-x,y,0> </math>. which has a magnitude of <math>\sqrt(x^2+y^2)</math>

We see that <math>\hat r = \frac{r}{|r|} </math> .

<math>\hat r = \frac{<-x,y,0>}{\sqrt(x^2+y^2))}</math>

We then have to express <math> \Delta \boldsymbol{\ell}</math> in terms of our variable of integration, x.
<math> \Delta \boldsymbol{\ell}</math> = <math> \Delta x<1,0,0,></math>

Our new equation after substituting our new variables is
<math> \Delta B = \frac{\mu_0I\Delta x<1,0,0,>}{4\pi(x^2+y^2)} \times \frac{<-x,y,0>}{\sqrt(x^2+y^2))} </math>

Finding the cross product of the above vectors gives us a product in the +z direction.
<math> \Delta B = \frac{\mu_0I\Delta x}{4\pi(x^2+y^2)^(\frac{3}{2})} </math>

We are finally ready to integrate. Because we are integrating the entire rod our limits are
<math> \int\limits_{-L/2}^{L/2}\ </math>

<math> \int\limits_{-L/2}^{L/2}\ \Delta B = \frac{\mu_0I\Delta x}{4\pi(x^2+y^2)^(\frac{3}{2})} </math>

We find that our final answer is <math> B= \frac{\mu_0}{4\pi}\frac{LI}{y\sqrt(y^2+(L/2)^2)}\hatz

==A Computational Model==
The following link shows the magnetic field produced by small segments of wire in a loop individually.
For a long straight wire, we see that there is a circular magnetic field surrounding the wire with current. The following link does a stepwise visual of the contributions of each part of the wire at an observation location a distance r from the wire.

http://www.glowscript.org/#/user/matterandinteractions/folder/matterandinteractions/program/17-Bwire-with-r

We see that along the axis of the wire, each contribution not on the axis is negated due to symmetry and the resulting magnetic field is all along the wire.

http://www.glowscript.org/#/user/matterandinteractions/folder/matterandinteractions/program/17-B-loop-with-r-dB.

==Connectedness==
==Applications==

==History==

== See also ==

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

===Further reading===

Books, Articles or other print media on this topic

===External links===

Internet resources on this topic

==References==

https://www.grc.nasa.gov/www/k-12/airplane/thermo0.html
http://hyperphysics.phy-astr.gsu.edu/hbase/thermo/thereq.html
https://www.grc.nasa.gov/www/k-12/airplane/thermo2.html
http://www.phys.nthu.edu.tw/~thschang/notes/GP21.pdf
http://www.eoearth.org/view/article/153532/

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

Biot-Savart Law for Currents

2015-11-29T23:10:14Z

David Medrano: /* Example */

Claimed by David Medrano
==Biot-Savart Law==

The Biot-Savart Law can be used for more than just single moving charges; it can also be used to calculate the magnetic field for a large number of charges. One notable reason to do so is to find the magnetic field of a portion of a wire where there can be many moving charges. When we use Biot-Savart Law to find the magnetic field of a short wire, we can apply it to a variety of shapes.

====A Mathematical Model====
First We start off with the original version of the Biot-Savart Law.
<math>\vec B=\frac{\mu_0}{4 \pi } \frac{q\vec v\times\hat r}{r^2}.</math>

Because we are dealing with a portion of wire <math>\mathrm{d}\boldsymbol{\ell}</math> long with an Area A containing n moving particles with charge q, we find that the total number of moving charges is equal to |q|(nAv) which is also equal to I, the current in the wire.
<math>B = \frac{\mu_0I}{4\pi}\frac{\mathrm{d}\boldsymbol{\ell} \times \mathbf{\hat r}}{r^2},</math>

Because the shape of the current carrying wire can vary from a straight wire to a loop, we must integrate over the region of the wire.

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

==Example==
====For a long wire of length L positioned along the x axis with current flowing in the positive x direction====
First, we start off with our adjusted Biot-Savart Formula for a slice of wire.

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

Second, we must find <math>r</math>, the vector pointing from the source to the observation location. In this case, we will choose an observation location y above the rod.

<math> r = obs - source = <0,y,0> - < x,0,0> = <-x,y,0> </math>. which has a magnitude of <math>\sqrt(x^2+y^2)</math>

We see that <math>\hat r = \frac{r}{|r|} </math> .

<math>\hat r = \frac{<-x,y,0>}{\sqrt(x^2+y^2))}</math>

We then have to express <math> \Delta \boldsymbol{\ell}</math> in terms of our variable of integration, x.
<math> \Delta \boldsymbol{\ell}</math> = <math> \Delta x<1,0,0,></math>

Our new equation after substituting our new variables is
<math> \Delta B = \frac{\mu_0I\Delta x<1,0,0,>}{4\pi(x^2+y^2)} \times \frac{<-x,y,0>}{\sqrt(x^2+y^2))} </math>

Finding the cross product of the above vectors gives us a product in the +z direction.
<math> \Delta B = \frac{\mu_0I\Delta x}{4\pi(x^2+y^2)^(\frac{3}{2})} </math>

We are finally ready to integrate. Because we are integrating the entire rod our limits are
<math> \int\limits_{-L/2}^{L/2}\ </math>
<math> \int\limits_{-L/2}^{L/2}\ \Delta B = \frac{\mu_0I\Delta x}{4\pi(x^2+y^2)^(\frac{3}{2})} </math>

==A Computational Model==
The following link shows the magnetic field produced by small segments of wire in a loop individually.
For a long straight wire, we see that there is a circular magnetic field surrounding the wire with current. The following link does a stepwise visual of the contributions of each part of the wire at an observation location a distance r from the wire.

http://www.glowscript.org/#/user/matterandinteractions/folder/matterandinteractions/program/17-Bwire-with-r

We see that along the axis of the wire, each contribution not on the axis is negated due to symmetry and the resulting magnetic field is all along the wire.

http://www.glowscript.org/#/user/matterandinteractions/folder/matterandinteractions/program/17-B-loop-with-r-dB.

==Connectedness==
==Applications==

==History==

== See also ==

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

===Further reading===

Books, Articles or other print media on this topic

===External links===

Internet resources on this topic

==References==

https://www.grc.nasa.gov/www/k-12/airplane/thermo0.html
http://hyperphysics.phy-astr.gsu.edu/hbase/thermo/thereq.html
https://www.grc.nasa.gov/www/k-12/airplane/thermo2.html
http://www.phys.nthu.edu.tw/~thschang/notes/GP21.pdf
http://www.eoearth.org/view/article/153532/

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

Biot-Savart Law for Currents

2015-11-29T22:53:51Z

David Medrano: /* For a long wire of length L positioned along the x axis with current flowing in the positive x direction */

Claimed by David Medrano
==Biot-Savart Law==

The Biot-Savart Law can be used for more than just single moving charges; it can also be used to calculate the magnetic field for a large number of charges. One notable reason to do so is to find the magnetic field of a portion of a wire where there can be many moving charges. When we use Biot-Savart Law to find the magnetic field of a short wire, we can apply it to a variety of shapes.

====A Mathematical Model====
First We start off with the original version of the Biot-Savart Law.
<math>\vec B=\frac{\mu_0}{4 \pi } \frac{q\vec v\times\hat r}{r^2}.</math>

Because we are dealing with a portion of wire <math>\mathrm{d}\boldsymbol{\ell}</math> long with an Area A containing n moving particles with charge q, we find that the total number of moving charges is equal to |q|(nAv) which is also equal to I, the current in the wire.
<math>B = \frac{\mu_0I}{4\pi}\frac{\mathrm{d}\boldsymbol{\ell} \times \mathbf{\hat r}}{r^2},</math>

Because the shape of the current carrying wire can vary from a straight wire to a loop, we must integrate over the region of the wire.

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

==Example==
====For a long wire of length L positioned along the x axis with current flowing in the positive x direction====
First, we start off with our adjusted Biot-Savart Formula for a slice of wire.

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

Second, we must find <math>r</math>, the vector pointing from the source to the observation location. In this case, we will choose an observation location y above the rod.

<math> r = obs - source = <0,y,0> - < x,0,0> = <-x,y,0> </math>. which has a magnitude of <math>\sqrt(x^2+y^2)</math>

We see that <math>\hat r = \frac{r}{|r|} </math> .

<math>\hat r = \frac{<-x,y,0>}{\sqrt(x^2+y^2))}</math>

We then have to express <math> \Delta \boldsymbol{\ell}</math> in terms of our variable of integration, x.
<math> \Delta \boldsymbol{\ell}</math> = <math> \Delta x<1,0,0,></math>

Our new equation after substituting our new variables is
<math> \Delta B = \frac{\mu_0I\Delta x<1,0,0,>}{4\pi(x^2+y^2)} \times \frac{<-x,y,0>}{\sqrt(x^2+y^2))} </math>

Finding the cross product of the above vectors gives us a product in the +z direction.

==A Computational Model==
The following link shows the magnetic field produced by small segments of wire in a loop individually.
For a long straight wire, we see that there is a circular magnetic field surrounding the wire with current. The following link does a stepwise visual of the contributions of each part of the wire at an observation location a distance r from the wire.

http://www.glowscript.org/#/user/matterandinteractions/folder/matterandinteractions/program/17-Bwire-with-r

We see that along the axis of the wire, each contribution not on the axis is negated due to symmetry and the resulting magnetic field is all along the wire.

http://www.glowscript.org/#/user/matterandinteractions/folder/matterandinteractions/program/17-B-loop-with-r-dB.

==Connectedness==
==Applications==

==History==

== See also ==

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

===Further reading===

Books, Articles or other print media on this topic

===External links===

Internet resources on this topic

==References==

https://www.grc.nasa.gov/www/k-12/airplane/thermo0.html
http://hyperphysics.phy-astr.gsu.edu/hbase/thermo/thereq.html
https://www.grc.nasa.gov/www/k-12/airplane/thermo2.html
http://www.phys.nthu.edu.tw/~thschang/notes/GP21.pdf
http://www.eoearth.org/view/article/153532/

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

Biot-Savart Law for Currents

2015-11-29T22:34:28Z

David Medrano: /* For a long wire of length L */

Claimed by David Medrano
==Biot-Savart Law==

The Biot-Savart Law can be used for more than just single moving charges; it can also be used to calculate the magnetic field for a large number of charges. One notable reason to do so is to find the magnetic field of a portion of a wire where there can be many moving charges. When we use Biot-Savart Law to find the magnetic field of a short wire, we can apply it to a variety of shapes.

====A Mathematical Model====
First We start off with the original version of the Biot-Savart Law.
<math>\vec B=\frac{\mu_0}{4 \pi } \frac{q\vec v\times\hat r}{r^2}.</math>

Because we are dealing with a portion of wire <math>\mathrm{d}\boldsymbol{\ell}</math> long with an Area A containing n moving particles with charge q, we find that the total number of moving charges is equal to |q|(nAv) which is also equal to I, the current in the wire.
<math>B = \frac{\mu_0I}{4\pi}\frac{\mathrm{d}\boldsymbol{\ell} \times \mathbf{\hat r}}{r^2},</math>

Because the shape of the current carrying wire can vary from a straight wire to a loop, we must integrate over the region of the wire.

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

==Example==
====For a long wire of length L positioned along the x axis with current flowing in the positive x direction====
First, we start off with our adjusted Biot-Savart Formula for a slice of wire.

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

Second, we must find <math>r</math>, the vector pointing from the source to the observation location. In this case, we will choose an observation location y above the rod.

<math> r = obs - source = <0,y,0> - < x,0,0> = <-x,y,0></math>.

We see that <math>\hat r = \frac{r}{|r|} </math>
<math>\hat r = \frac{<-x,y,0>}{\sqrt(x^2+y^2))}</math>

We then have to express <math> \Delta \boldsymbol{\ell}</math> in terms of our variable of integration, x.
<math> \Delta \boldsymbol{\ell}</math> = <math> \Delta x<1,0,0,></math>

==A Computational Model==
The following link shows the magnetic field produced by small segments of wire in a loop individually.
For a long straight wire, we see that there is a circular magnetic field surrounding the wire with current. The following link does a stepwise visual of the contributions of each part of the wire at an observation location a distance r from the wire.

http://www.glowscript.org/#/user/matterandinteractions/folder/matterandinteractions/program/17-Bwire-with-r

We see that along the axis of the wire, each contribution not on the axis is negated due to symmetry and the resulting magnetic field is all along the wire.

http://www.glowscript.org/#/user/matterandinteractions/folder/matterandinteractions/program/17-B-loop-with-r-dB.

==Connectedness==
==Applications==

==History==

== See also ==

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

===Further reading===

Books, Articles or other print media on this topic

===External links===

Internet resources on this topic

==References==

https://www.grc.nasa.gov/www/k-12/airplane/thermo0.html
http://hyperphysics.phy-astr.gsu.edu/hbase/thermo/thereq.html
https://www.grc.nasa.gov/www/k-12/airplane/thermo2.html
http://www.phys.nthu.edu.tw/~thschang/notes/GP21.pdf
http://www.eoearth.org/view/article/153532/

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

Biot-Savart Law for Currents

2015-11-29T22:09:44Z

David Medrano:

Biot-Savart Law for Currents

2015-11-29T21:59:18Z

David Medrano: /* Connectedness */

Biot-Savart Law for Currents

2015-11-29T21:55:07Z

David Medrano: /* A Computational Model */

Biot-Savart Law for Currents

2015-11-29T21:54:48Z

David Medrano: /* A Computational Model */

Biot-Savart Law for Currents

2015-11-29T21:50:24Z

David Medrano: /* Example */

Biot-Savart Law for Currents

2015-11-29T21:42:02Z

David Medrano:

Biot-Savart Law for Currents

2015-11-29T20:38:46Z

David Medrano: /* A Mathematical Model */

Claimed by David Medrano
==Biot-Savart Law for Currents==

The Biot-Savart Law can be used for more than just single moving charges; it can also be used to calculate the magnetic field for a large number of charges. One notable reason to do so is to find the magnetic field of a portion of a wire where there can be many moving charges. When we use Biot-Savart Law to find the magnetic field of a short wire, we can apply it to a variety of shapes.

====A Mathematical Model====
First We start off with the original version of the Biot-Savart Law.
<math>\vec B=\frac{\mu_0}{4 \pi } \frac{q\vec v\times\hat r}{r^2}.</math>

Because we are dealing with a portion of wire <math>\mathrm{d}\boldsymbol{\ell}</math> long with an Area A containing n moving particles with charge q, we find that the total number of moving charges is equal to |q|(nAv) which is also equal to I, the current in the wire.
<math>B = \frac{\mu_0I}{4\pi}\frac{\mathrm{d}\boldsymbol{\ell} \times \mathbf{\hat r}}{r^2},</math>

Because the shape of the current carrying wire can vary from a straight wire to a loop, we must integrate over the region of the wire.

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

====A Computational Model====

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

==History==

== See also ==

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

===Further reading===

Books, Articles or other print media on this topic

===External links===

Internet resources on this topic

==References==

https://www.grc.nasa.gov/www/k-12/airplane/thermo0.html
http://hyperphysics.phy-astr.gsu.edu/hbase/thermo/thereq.html
https://www.grc.nasa.gov/www/k-12/airplane/thermo2.html
http://www.phys.nthu.edu.tw/~thschang/notes/GP21.pdf
http://www.eoearth.org/view/article/153532/

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

Biot-Savart Law for Currents

2015-11-29T20:10:13Z

David Medrano: /* Biot-Savart Law for Currents */

Biot-Savart Law for Currents

2015-11-29T20:05:56Z

David Medrano: /* Biot-Savart Law for Currents */

==Biot-Savart Law for Currents==

====A Mathematical Model====

====A Computational Model====

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

==History==

== See also ==

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

===Further reading===

Books, Articles or other print media on this topic

===External links===

Internet resources on this topic

==References==

https://www.grc.nasa.gov/www/k-12/airplane/thermo0.html
http://hyperphysics.phy-astr.gsu.edu/hbase/thermo/thereq.html
https://www.grc.nasa.gov/www/k-12/airplane/thermo2.html
http://www.phys.nthu.edu.tw/~thschang/notes/GP21.pdf
http://www.eoearth.org/view/article/153532/

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

Biot-Savart Law for Currents

2015-11-29T20:05:40Z

David Medrano: /* Zeroth Law */

==Biot-Savart Law for Currents==

This topics focuses on energy work of a system but it can only deal with a large scale response to heat in a system. '''Thermodynamics''' is the study of the work, heat and energy of a system. The smaller scale gas interactions can explained using the kinetic theory of gases. There are three fundamental laws that go along with the topic of thermodynamics. They are the zeroth law, the first law, and the second law. These laws help us understand predict the the operation of the physical system. In order to understand the laws, you must first understand thermal equilibrium. [[Thermal equilibrium]] is reached when a object that is at a higher temperature is in contact with an object that is at a lower temperature and the first object transfers heat to the latter object until they approach the same temperature and maintain that temperature constantly. It is also important to note that any thermodynamic system in thermal equilibrium possesses internal energy.

====A Mathematical Model====

====A Computational Model====

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

==History==

== See also ==

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

===Further reading===

Books, Articles or other print media on this topic

===External links===

Internet resources on this topic

==References==

https://www.grc.nasa.gov/www/k-12/airplane/thermo0.html
http://hyperphysics.phy-astr.gsu.edu/hbase/thermo/thereq.html
https://www.grc.nasa.gov/www/k-12/airplane/thermo2.html
http://www.phys.nthu.edu.tw/~thschang/notes/GP21.pdf
http://www.eoearth.org/view/article/153532/

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

Biot-Savart Law for Currents

2015-11-29T20:05:28Z

David Medrano:

==Biot-Savart Law for Currents==

This topics focuses on energy work of a system but it can only deal with a large scale response to heat in a system. '''Thermodynamics''' is the study of the work, heat and energy of a system. The smaller scale gas interactions can explained using the kinetic theory of gases. There are three fundamental laws that go along with the topic of thermodynamics. They are the zeroth law, the first law, and the second law. These laws help us understand predict the the operation of the physical system. In order to understand the laws, you must first understand thermal equilibrium. [[Thermal equilibrium]] is reached when a object that is at a higher temperature is in contact with an object that is at a lower temperature and the first object transfers heat to the latter object until they approach the same temperature and maintain that temperature constantly. It is also important to note that any thermodynamic system in thermal equilibrium possesses internal energy.

===Zeroth Law===

====A Mathematical Model====

====A Computational Model====

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

==History==

== See also ==

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

===Further reading===

Books, Articles or other print media on this topic

===External links===

Internet resources on this topic

==References==

https://www.grc.nasa.gov/www/k-12/airplane/thermo0.html
http://hyperphysics.phy-astr.gsu.edu/hbase/thermo/thereq.html
https://www.grc.nasa.gov/www/k-12/airplane/thermo2.html
http://www.phys.nthu.edu.tw/~thschang/notes/GP21.pdf
http://www.eoearth.org/view/article/153532/

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

Biot-Savart Law for Currents

2015-11-29T20:04:10Z

David Medrano: Created page with "==Thermodynamics== This topics focuses on energy work of a system but it can only deal with a large scale response to heat in a system. '''Thermodynamics''' is the study of..."

==Thermodynamics==

This topics focuses on energy work of a system but it can only deal with a large scale response to heat in a system. '''Thermodynamics''' is the study of the work, heat and energy of a system. The smaller scale gas interactions can explained using the kinetic theory of gases. There are three fundamental laws that go along with the topic of thermodynamics. They are the zeroth law, the first law, and the second law. These laws help us understand predict the the operation of the physical system. In order to understand the laws, you must first understand thermal equilibrium. [[Thermal equilibrium]] is reached when a object that is at a higher temperature is in contact with an object that is at a lower temperature and the first object transfers heat to the latter object until they approach the same temperature and maintain that temperature constantly. It is also important to note that any thermodynamic system in thermal equilibrium possesses internal energy.

===Zeroth Law===

The zeroth law states that if two systems are at thermal equilibrium at the same time as a third system, then all of the systems are at equilibrium with each other. If systems A and C are in thermal equilibrium with B, then system A and C are also in thermal equilibrium with each other. There are underlying ideas of heat that are also important. The most prominent one is that all heat is of the same kind. As long as the systems are at thermal equilibrium, every unit of internal energy that passes from one system to the other is balanced by the same amount of energy passing back. This also applies when the two systems or objects have different atomic masses or material.

====A Mathematical Model====

If A = B and A = C, then B = C
A = B = C

====A Computational Model====

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

===First Law===

The first law of thermodynamics defines the internal energy (E) as equal to the difference between heat transfer (Q) ''into'' a system and work (W) ''done by'' the system. Heat removed from a system would be given a negative sign and heat applied to the system would be given a positive sign. Internal energy can be converted into other types of energy because it acts like potential energy. Heat and work, however, cannot be stored or conserved independently because they depend on the process. This allows for many different possible states of a system to exist. There can be a process known as the adiabatic process in which there is no heat transfer. This occurs when a system is full insulated from the outside environment. The implementation of this law also brings about another useful state variable, '''enthalpy'''.

====A Mathematical Model====

E2 - E1 = Q - W

==Second Law==

The second law states that there is another useful variable of heat, entropy (S). Entropy can be described as the disorder or chaos of a system, but in physics, we will just refer to it as another variable like enthalpy or temperature. For any given physical process, the combined entropy of a system and the environment remains a constant if the process can be reversed. The second law also states that if the physical process is irreversible, the combined entropy of the system and the environment must increase. Therefore, the final entropy must be greater than the initial entropy.

===Mathematical Models===

delta S = delta Q/T
Sf = Si (reversible process)
Sf > Si (irreversible process)

===Examples===

'''Reversible process''': Ideally forcing a flow through a constricted pipe, where there are no boundary layers. As the flow moves through the constriction, the pressure, volume and temperature change, but they return to their normal values once they hit the downstream. This return to the variables' original values allows there to be no change in entropy. It is often known as an isentropic process.

'''Irreversible process''': When a hot object and cold object are put in contact with each other, eventually the heat from the hot object will transfer to the cold object and the two will reach the same temperature and stay constant at that temperature, reaching equilibrium. However, once those objects are separated, they will remain at that equilibrium temperature until something else acts upon it. The objects do not go back to their original temperatures so there is a change in entropy.

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

==History==

Thermodynamics was brought up as a science in the 18th and 19th centuries. However, it was first brought up by Galilei, who introduced the concept of temperature and invented the first thermometer. G. Black first introduced the word 'thermodynamics'. Later, G. Wilke introduced another unit of measurement known as the calorie that measures heat. The idea of thermodynamics was brought up by Nicolas Leonard Sadi Carnot. He is often known as "the father of thermodynamics". It all began with the development of the steam engine during the Industrial Revolution. He devised an ideal cycle of operation. During his observations and experimentations, he had the incorrect notion that heat is conserved, however he was able to lay down theorems that led to the development of thermodynamics. In the 20th century, the science of thermodynamics became a conventional term and a basic division of physics. Thermodynamics dealt with the study of general properties of physical systems under equilibrium and the conditions necessary to obtain equilibrium.

== See also ==

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

===Further reading===

Books, Articles or other print media on this topic

===External links===

Internet resources on this topic

==References==

https://www.grc.nasa.gov/www/k-12/airplane/thermo0.html
http://hyperphysics.phy-astr.gsu.edu/hbase/thermo/thereq.html
https://www.grc.nasa.gov/www/k-12/airplane/thermo2.html
http://www.phys.nthu.edu.tw/~thschang/notes/GP21.pdf
http://www.eoearth.org/view/article/153532/

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

Main Page

2015-11-29T20:03:18Z

David Medrano: /* Fields */

__NOTOC__
Welcome to the Georgia Tech Wiki for Intro Physics. This resources was created so that students can contribute and curate content to help those with limited or no access to a textbook. When reading this website, please correct any errors you may come across. If you read something that isn't clear, please consider revising it!

Looking to make a contribution?
#Pick a specific topic from intro physics
#Add that topic, as a link to a new page, under the appropriate category listed below by editing this page.
#Copy and paste the default [[Template]] into your new page and start editing.

Please remember that this is not a textbook and you are not limited to expressing your ideas with only text and equations. Whenever possible embed: pictures, videos, diagrams, simulations, computational models (e.g. Glowscript), and whatever content you think makes learning physics easier for other students.

== Source Material ==
All of the content added to this resource must be in the public domain or similar free resource. If you are unsure about a source, contact the original author for permission. That said, there is a surprisingly large amount of introductory physics content scattered across the web. Here is an incomplete list of intro physics resources (please update as needed).
* A physics resource written by experts for an expert audience [https://en.wikipedia.org/wiki/Portal:Physics Physics Portal]
* A wiki book on modern physics [https://en.wikibooks.org/wiki/Modern_Physics Modern Physics Wiki]
* The MIT open courseware for intro physics [http://ocw.mit.edu/resources/res-8-002-a-wikitextbook-for-introductory-mechanics-fall-2009/index.htm MITOCW Wiki]
* An online concept map of intro physics [http://hyperphysics.phy-astr.gsu.edu/hbase/hph.html HyperPhysics]
* Interactive physics simulations [https://phet.colorado.edu/en/simulations/category/physics PhET]
* OpenStax algebra based intro physics textbook [https://openstaxcollege.org/textbooks/college-physics College Physics]
* The Open Source Physics project is a collection of online physics resources [http://www.opensourcephysics.org/ OSP]
* A resource guide compiled by the [http://www.aapt.org/ AAPT] for educators [http://www.compadre.org/ ComPADRE]

== Organizing Categories ==
These are the broad, overarching categories, that we cover in two semester of introductory physics. You can add subcategories or make a new category as needed. A single topic should direct readers to a page in one of these catagories.

<div class="toccolours mw-collapsible mw-collapsed">
===Interactions===
<div class="mw-collapsible-content">
*[[Kinds of Matter]]
*[[Detecting Interactions]]
*[[Fundamental Interactions]]
*[[System & Surroundings]]
*[[Newton's First Law of Motion]]
*[[Newton's Second Law of Motion]]
*[[Newton's Third Law of Motion]]
*[[Gravitational Force]]
*[[Terminal Velocity and Friction Due to Air]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">

===Theory===
<div class="mw-collapsible-content">
*[[Einstein's Theory of Special Relativity]]
*[[Quantum Theory]]

</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">

===Notable Scientists===
<div class="mw-collapsible-content">
*[[Albert Einstein]]
*[[Ernest Rutherford]]
*[[Joseph Henry]]
*[[Michael Faraday]]
*[[J.J. Thomson]]
*[[James Maxwell]]
*[[Robert Hooke]]
*[[Marie Curie]]
*[[Carl Friedrich Gauss]]
*[[Nikola Tesla]]
*[[Andre Marie Ampere]]
*[[Sir Isaac Newton]]
*[[J. Robert Oppenheimer]]
*[[Oliver Heaviside]]
*[[Rosalind Franklin]]
*[[Erwin Schrödinger]]
*[[Enrico Fermi]]
*[[Robert J. Van de Graaff]]
*[[Charles de Coulomb]]
*[[Hans Christian Ørsted]]
*[[Philo Farnsworth]]
*[[Niels Bohr]]
*[[Georg Ohm]]
*[[Galileo Galilei]]
*[[Gustav Kirchhoff]]
*[[Max Planck]]
*[[Heinrich Hertz]]
*[[Edwin Hall]]
*[[James Watt]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">

===Properties of Matter===
<div class="mw-collapsible-content">
*[[Mass]]
*[[Velocity]]
*[[Density]]
*[[Charge]]
*[[Spin]]
*[[SI Units]]

</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">

===Contact Interactions===
<div class="mw-collapsible-content">
* [[Young's Modulus]]
* [[Friction]]
* [[Tension]]
* [[Hooke's Law]]
*[[Centripetal Force and Curving Motion]]
*[[Compression or Normal Force]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">

===Momentum===
<div class="mw-collapsible-content">
* [[Vectors]]
* [[Kinematics]]
* [[Predicting Change in multiple dimensions]]
* [[Momentum Principle]]
* [[Impulse Momentum]]
* [[Curving Motion]]
* [[Multi-particle Analysis of Momentum]]
* [[Iterative Prediction]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">

===Angular Momentum===
<div class="mw-collapsible-content">
* [[The Moments of Inertia]]
* [[Rotation]]
* [[Torque]]
*[[Systems with Zero Torque]]
* [[Right Hand Rule]]
* [[Angular Velocity]]
* [[Predicting a Change in Rotation]]
* [[Conservation of Angular Momentum]]
*[[Rotational Angular Momentum]]
*[[Total Angular Momentum]]

</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">

===Energy===
<div class="mw-collapsible-content">
*[[The Energy Principle]]
*[[Predicting Change]]
*[[Rest Mass Energy]]
*[[Kinetic Energy]]
*[[Potential Energy]]
*[[Work]]
*[[Thermal Energy]]
*[[Conservation of Energy]]
*[[Electric Potential]]
*[[Energy Transfer due to a Temperature Difference]]
*[[Gravitational Potential Energy]]
*[[Point Particle Systems]]
*[[Real Systems]]
*[[Spring Potential Energy]]
*[[Internal Energy]]
*[[Translational, Rotational and Vibrational Energy]]
*[[Franck-Hertz Experiment]]
*[[Power]]
*[[Energy Graphs]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">

===Collisions===
<div class="mw-collapsible-content">
*[[Collisions]]
*[[Maximally Inelastic Collision]]
*[[Elastic Collisions]]
*[[Inelastic Collisions]]
*[[Head-on Collision of Equal Masses]]
*[[Head-on Collision of Unequal Masses]]
*[[Rutherford Experiment and Atomic Collisions]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">

===Fields===
<div class="mw-collapsible-content">
* [[Electric Field]] of a
** [[Point Charge]]
** [[Electric Dipole]]
** [[Capacitor]]
** [[Charged Rod]]
** [[Charged Ring]]
** [[Charged Disk]]
** [[Charged Spherical Shell]]
** [[Charged Cylinder]]
**[[A Solid Sphere Charged Throughout Its Volume]]
*[[Electric Potential]]
**[[Potential Difference in a Uniform Field]]
**[[Potential Difference of point charge in a non-Uniform Field]]
**[[Sign of Potential Difference]]
*[[Electric Force]]
*[[Polarization]]
*[[Charge Motion in Metals]]
*[[Magnetic Field]]
**[[Right-Hand Rule]]
**[[Direction of Magnetic Field]]
**[[Magnetic Field of a Long Straight Wire]]
**[[Magnetic Field of a Loop]]
**[[Bar Magnet]]
**[[Magnetic Force]]
**[[Hall Effect]]
**[[Lorentz Force]]
**[[Biot-Savart Law]]
**[[Biot-Savart Law for Currents]]
**[[Integration Techniques for Magnetic Field]]
**[[Sparks in Air]]
**[[Motional Emf]]
**[[Detecting a Magnetic Field]]
**[[Moving Point Charge]]
**[[Non-Coulomb Electric Field]]
**[[Motors and Generators]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">

===Simple Circuits===
<div class="mw-collapsible-content">
*[[Components]]
*[[Steady State]]
*[[Non Steady State]]
*[[Node Rule]]
*[[Loop Rule]]
*[[Power in a circuit]]
*[[Ammeters,Voltmeters,Ohmmeters]]
*[[Current]]
*[[Ohm's Law]]
*[[RC]]
*[[Circular Loop of Wire]]
*[[RL Circuit]]
*[[LC Circuit]]
*[[Surface Charge Distributions]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">

===Maxwell's Equations===
<div class="mw-collapsible-content">
*[[Gauss's Flux Theorem]]
**[[Electric Fields]]
**[[Magnetic Fields]]
*[[Ampere's Law]]
*[[Faraday's Law]]
**[[Inductance]]
**[[Lenz's Law]]
***[[Lenz Effect and the Jumping Ring]]
*[[Ampere-Maxwell Law]]
**[[Superconducters]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">

===Radiation===
<div class="mw-collapsible-content">
*[[Producing a Radiative Electric Field]]
*[[Sinusoidal Electromagnetic Radiaton]]
*[[Lenses]]
*[[Energy and Momentum Analysis in Radiation]]
*[[Electromagnetic Propagation]]
</div>
</div>
<div class="toccolours mw-collapsible mw-collapsed">

===Sound===
<div class="mw-collapsible-content">
*[[Doppler Effect]]
*[[Nature, Behavior, and Properties of Sound]]
</div>
</div>
*[[blahb]]
</div>
</div>

== Resources ==
* Commonly used wiki commands [https://en.wikipedia.org/wiki/Help:Cheatsheet Wiki Cheatsheet]
* A guide to representing equations in math mode [https://en.wikipedia.org/wiki/Help:Displaying_a_formula Wiki Math Mode]
* A page to keep track of all the physics [[Constants]]
* An overview of [[VPython]]