Physics Book - User contributions [en]

Right-Hand Rule

2015-11-10T18:45:16Z

Cjacobson7:

Short Description of Topic

==The Main Idea==

The Right-Hand Rule is an easy way to find the direction of a cross product interaction before doing the math.

===A Mathematical Model===

The Right-Hand Rule is mathamatically modeled by the cross product:
:<math>\mathbf{u\times v}=(u_2v_3\mathbf{i}+u_3v_1\mathbf{j}+u_1v_2\mathbf{k})
-(u_3v_2\mathbf{i}+u_1v_3\mathbf{j}+u_2v_1\mathbf{k})
</math>

===A Computational Model===

The cross product is used to describe many magnetic interactions, for example, magnetic field created by a moving charge or a current and magnetic force on a particle by a magnetic field. Because of this, using the right hand rule, to determine the direction of a cross product, can be a useful to check behind the math for sign errors.

Follow the chart bellow to find which fingers correspond to which vectors.

:<math>\mathbf{A\times B}=\mathbf{C}</math>

{| class=wikitable
|-
! Vector !! Right-hand !! Right-hand (alternative)
|-
| A || First or index || Thumb
|-
| B || Second finger or palm || First or index
|-
| C || Thumb || Second finger or palm
|}

==Examples==

===Magnetic Force on a Moving Particle===
:<math>\mathbf{F} = q\mathbf{v} \times \mathbf{B}</math>

The direction of the cross product may be found by application of the right hand rule as follows:
# The index finger points in the direction of the momentum vector qv.
# The middle finger points in the direction of the magnetic field vector B.
# The thumb points in the direction of magnetic force F.

For example, for a positively charged particle moving to the right, in a region where the magnetic field points up, the resultant force points out of the page.

===Magnetic Field made by a Current===
:<math> \mathbf{B} = \frac{\mu_0I}{4\pi}\int_{\mathrm{wire}}\frac{\mathrm{d}\boldsymbol{\ell} \times \mathbf{\hat r}}{r^2},</math>

The direction of the cross product may be found by application of the right hand rule as follows:
# The thumb points in the direction of current I.
# The index finger points in the direction of the observation vector r.
# The middle finger points in the direction of the magnetic field vector B.

For example, for a current moving out of the page, the magnetic field points up, when the observation location is to the right of the current.

===Force on a Current from a Magnetic Field===
:<math> \mathbf{F} = mathbf{I} \times \mathbf{B}</math>

The direction of the cross product may be found by application of the right hand rule as follows:
# The index finger points in the direction of the current I.
# The middle finger points in the direction of the magnetic field vector B.
# The thumb points in the direction of magnetic force F.

For example, for a current moving into the page, in a region where the magnetic field points up, then the force is to the right of the current.

==References==

#https://en.wikipedia.org/wiki/Right-hand_rule
#https://en.wikipedia.org/wiki/Magnetic_field

--[[User:Cjacobson7|Cjacobson7]] ([[User talk:Cjacobson7|talk]]) 13:45, 10 November 2015 (EST)

[[Category:Fields]]

Right-Hand Rule

2015-11-10T18:43:22Z

Cjacobson7: Right hand rule for cross product

Right-Hand Rule

2015-11-10T18:04:00Z

Cjacobson7: Created page with "Short Description of Topic ==The Main Idea== The Right-Hand Rule is an easy way to find the direction of a cross product interaction before doing the math. ===A Mathematica..."

Main Page

2015-11-10T17:23:20Z

Cjacobson7: /* 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 Catagories ==
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">
*[[Fundamental Interactions]]
*[[System & Surroundings]]
*[[Newton's First Law of Motion]]

</div>
</div>

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

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

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

===Notable Scientists===
<div class="mw-collapsible-content">
*[[Albert Einstein]]
*[[Ernest Rutherford]]
</div>
</div>
<div class="toccolours mw-collapsible mw-collapsed">

===Properties of Matter===
<div class="mw-collapsible-content">
*[[Mass]]
*[[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]]
</div>
</div>

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

===Momentum===
<div class="mw-collapsible-content">
* [[Vectors]]
* [[Kinematics]]
* Predicting Change in one dimension
* [[Predicting Change in multiple dimensions]]
* [[Momentum Principle]]
* [[Curving Motion]]
</div>
</div>

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

===Angular Momentum===
<div class="mw-collapsible-content">
* [[The Moments of Inertia]]
* [[Rotation]]
* [[Torque]]
* Predicting a Change in Rotation
</div>
</div>

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

===Energy===
<div class="mw-collapsible-content">
*[[Predicting Change]]
*[[Rest Mass Energy]]
*[[Kinetic Energy]]
*[[Potential Energy]]
*[[Work]]
*[[Thermal Energy]]
*[[Conservation of Energy]]
*[[Electric Potential]]
*[[Energy Transfer due to a Temperature Difference]]
</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]]
*[[Electric Potential]]
**[[Potential Difference in a Uniform Field]]
*[[Polarization]]
*[[Magnetic Field]]
**[[Right-Hand Rule]]
**[[Direction of Magnetic Field]]
**[[Bar Magnet]]
**[[Magnetic Force]]
**[[Hall Effect]]
**[[Lorentz Force]]
**[[Biot-Savart Law]]
**[[Integration Techniques for Magnetic Field]]
**[[Sparks in Air]]
**[[Motional Emf]]
</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]]
</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]]
*[[Faraday's Law]]
**[[Inductance]]
*[[Ampere-Maxwell Law]]
</div>
</div>

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

===Radiation===
<div class="mw-collapsible-content">
</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]]

Main Page

2015-11-10T17:23:00Z

Cjacobson7: /* 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 Catagories ==
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">
*[[Fundamental Interactions]]
*[[System & Surroundings]]
*[[Newton's First Law of Motion]]

</div>
</div>

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

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

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

===Notable Scientists===
<div class="mw-collapsible-content">
*[[Albert Einstein]]
*[[Ernest Rutherford]]
</div>
</div>
<div class="toccolours mw-collapsible mw-collapsed">

===Properties of Matter===
<div class="mw-collapsible-content">
*[[Mass]]
*[[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]]
</div>
</div>

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

===Momentum===
<div class="mw-collapsible-content">
* [[Vectors]]
* [[Kinematics]]
* Predicting Change in one dimension
* [[Predicting Change in multiple dimensions]]
* [[Momentum Principle]]
* [[Curving Motion]]
</div>
</div>

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

===Angular Momentum===
<div class="mw-collapsible-content">
* [[The Moments of Inertia]]
* [[Rotation]]
* [[Torque]]
* Predicting a Change in Rotation
</div>
</div>

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

===Energy===
<div class="mw-collapsible-content">
*[[Predicting Change]]
*[[Rest Mass Energy]]
*[[Kinetic Energy]]
*[[Potential Energy]]
*[[Work]]
*[[Thermal Energy]]
*[[Conservation of Energy]]
*[[Electric Potential]]
*[[Energy Transfer due to a Temperature Difference]]
</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]]
*[[Electric Potential]]
**[[Potential Difference in a Uniform Field]]
*[[Polarization]]
*[[Magnetic Field]]
**[[Right-Hand Rule[]
**[[Direction of Magnetic Field]]
**[[Bar Magnet]]
**[[Magnetic Force]]
**[[Hall Effect]]
**[[Lorentz Force]]
**[[Biot-Savart Law]]
**[[Integration Techniques for Magnetic Field]]
**[[Sparks in Air]]
**[[Motional Emf]]
</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]]
</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]]
*[[Faraday's Law]]
**[[Inductance]]
*[[Ampere-Maxwell Law]]
</div>
</div>

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

===Radiation===
<div class="mw-collapsible-content">
</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]]