Physics Book - User contributions [en]

Daniel Bernoulli

2015-11-30T21:26:00Z

Bmcfarland7:

==Personal Life==
Daniel Bernoulli was born on February 9, 1700 in Groningen, the Netherlands. He came from a family of distinguished mathematicians, but reportedly was the brightest of three children of the family. While growing up in Switzerland, his relationship with his father gradually deteriorated due to competition in academia.

First studying at the University in Basel, he was later invited to study at the Saint Petersburg Academy of Sciences. He studied mathematics, business, medicine, anatomy, and botany, eventually earning his Ph.D. in the latter two. Eventually he returned to Basel as a professor of anatomy, botany, and physics.

He made significant contributions to Physics, most notably '''the Bernoulli Principle''', which is used extensively in aerodynamics and fluid dynamics. His contributions were not limited to only Physics though, he has also been called the founder of mathematical economics and was one of the first people to begin work on a kinetic theory of gases.

==Contributions to Physics==

===''Hydrodynamica''===
Bernoulli published ''Hydrodynamica'' in 1738, and the title eventually gave rise to the name "hydrodynamics" for the field of fluid dynamics. The full title of the text was "Hydrodynamics, or commentaries on the forces and motions of fluids". In the book, Bernoulli characterizes fluid mechanics according to conservation of energy by examining several examples such as fluid coming out of an opening or fluid flowing through a tube. These examples gave the first adequate theory of the motion of incompressible fluids and also hydrodynamic pressure. In the text he also describes work and efficiency of hydraulic machines, the kinetic theory of gases, and several ideas that would eventually be formulated into the Bernoulli Principle.

===The Bernoulli Principle===
The Bernoulli Principle was developed in ''Hydrodynamica'' when he asked the following question: 'Let a very wide vessel ''ACEB'', which is to be kept constantly full of water, be fitted with a horizontal cylindrical tube ''ED''; and at the extremity of the tube let there be an orifice ''o'' emitting water at a uniform velocity; the pressure of the water against the walls of the tube ''ED'' is sought.' To solve this problem, Bernoulli employs his ''principle of equality between the actual descent and potential ascent'', which states that 'If any number of weights begin to move in any way by the force of their own gravity, the velocities of the individual weights will be everywhere such that the products of the squares of these velocities multiplied by the appropriate masses, gathered together, are proportional to the vertical height through which the centre of gravity of the composite of the bodies descends, multiplied by the masses of all of them.' In only considering quasi-one-dimensional fluid motion and by using the principle of conservation of energy, Bernoulli develops the following equation:

<math>{v}{dv \over dx}={(a-v^2) \over 2c}</math>

where:
:<math>v\,</math> is the velocity of the fluid
:<math>dx\,</math> is the length of the cylindrical tube
:<math>a\,</math> is the height of the tube
:<math>c\,</math> is the distance from the entrance of the tube

After making several assumptions such as the pressure is proportional to the ratio of the increase in velocity over time, and that the hole ''o'' is infinitesimal, thus the fluid is virtually motionless which makes the pressure determined by the height of the column, he develops this equation:

<math>{p_1 \over \gamma} + {V_1^2 \over 2g}={p_2 \over \gamma} + {V_2^2 \over 2g}</math>

where:
:<math>p_1\,</math> is the pressure in the tube
:<math>p_2\,</math> is the pressure at the exit of the tube
:<math>V_1\,</math> is the velocity of the fluid in the tube
:<math>V_2\,</math> is the velocity of the fluid exiting the tube
:<math>\gamma\,</math> is the specific weight of the fluid
:<math>g\,</math> is the acceleration due to gravity

A simpler version of Bernoulli's Principle for an incompressible fluid where frictional forces is negligible is:

<math>{v^2 \over 2}+gz+{p \over \rho}=\text{constant}</math>

where:
:<math>v\,</math> is the velocity of the fluid in the tube
:<math>g\,</math> is the acceleration due to gravity
:<math>z\,</math> is the height of the tube
:<math>p\,</math> is the pressure
:<math>\rho\,</math> is the density of the fluid

The main idea of the Bernoulli Principle is that for a steady flow, the sum of all the energies involved will be the same at any point in the tube, therefore, the velocity of the fluid through the tube will increase coinciding with a decrease in pressure or a decrease in the potential energy.

===Euler-Bernoulli Beam Equation===
The Euler-Bernoulli Beam Equation is based on the theory of elasticity, which states that elasticity is the property of solid materials to deform under the application of an external force and to regain their original shape after the force is removed.

The equation is:

<math>{d^2 \over dx^2}[{EI}{d^2w \over dx^2}]=p</math>

where:
:<math>w\,</math> is the displacement of the beam
:<math>p\,</math> is the force per unit length acting in the direction of w
:<math>E\,</math> is the Young's Modulus for the beam
:<math>I\,</math> is the moment of inertia of the beam's cross section
:<math>x\,</math> is the position along the beam

The Euler-Bernoulli Beam Equation relates the displacement, or deflection of the beam (w) to its pressure loading (p). The equation is widely used in engineering applications, such as civil or mechanical to determine the strength of beams when stress is applied.

==References==

Wilkins, D.R. "The Bernoullis." Web. 30 Nov. 2015. <http://www.maths.tcd.ie/pub/HistMath/People/Bernoullis/RouseBall/RB_Bernoullis.html#DanielBernoulli>.

Rothbard, Murray. "Daniel Bernoulli and the Founding of Mathematical Economics." Mises Institute. Mises Institute, 10 Feb. 2011. Web. 30 Nov. 2015. <https://mises.org/library/daniel-bernoulli-and-founding-mathematical-economics>.

Guinness, I. "Daniel Bernoulli, Hydrodynamica (1738)." Landmark Writings in Western Mathematics 1640-1940. Amsterdam: Elsevier, 2005. Print.

Dahr, S. "3.1 Theory of Elasticity." Web. 30 Nov. 2015. <http://www.iue.tuwien.ac.at/phd/dhar/node17.html>.

"Euler-Bernoulli Beam Equation." EFunda, 2015. Web. 30 Nov. 2015. <http://www.efunda.com/formulae/solid_mechanics/beams/theory.cfm>.

''This page was created by Brynn McFarland''

Daniel Bernoulli

2015-11-30T21:24:17Z

Bmcfarland7:

Daniel Bernoulli

2015-11-30T21:23:31Z

Bmcfarland7: /* References */

Claimed by Brynn McFarland, this is a work in progress!

==Personal Life==
Daniel Bernoulli was born on February 9, 1700 in Groningen, the Netherlands. He came from a family of distinguished mathematicians, but reportedly was the brightest of three children of the family. While growing up in Switzerland, his relationship with his father gradually deteriorated due to competition in academia.

First studying at the University in Basel, he was later invited to study at the Saint Petersburg Academy of Sciences. He studied mathematics, business, medicine, anatomy, and botany, eventually earning his Ph.D. in the latter two. Eventually he returned to Basel as a professor of anatomy, botany, and physics.

He made significant contributions to Physics, most notably '''the Bernoulli Principle''', which is used extensively in aerodynamics and fluid dynamics. His contributions were not limited to only Physics though, he has also been called the founder of mathematical economics and was one of the first people to begin work on a kinetic theory of gases.

==Contributions to Physics==

===''Hydrodynamica''===
Bernoulli published ''Hydrodynamica'' in 1738, and the title eventually gave rise to the name "hydrodynamics" for the field of fluid dynamics. The full title of the text was "Hydrodynamics, or commentaries on the forces and motions of fluids". In the book, Bernoulli characterizes fluid mechanics according to conservation of energy by examining several examples such as fluid coming out of an opening or fluid flowing through a tube. These examples gave the first adequate theory of the motion of incompressible fluids and also hydrodynamic pressure. In the text he also describes work and efficiency of hydraulic machines, the kinetic theory of gases, and several ideas that would eventually be formulated into the Bernoulli Principle.

===The Bernoulli Principle===
The Bernoulli Principle was developed in ''Hydrodynamica'' when he asked the following question: 'Let a very wide vessel ''ACEB'', which is to be kept constantly full of water, be fitted with a horizontal cylindrical tube ''ED''; and at the extremity of the tube let there be an orifice ''o'' emitting water at a uniform velocity; the pressure of the water against the walls of the tube ''ED'' is sought.' To solve this problem, Bernoulli employs his ''principle of equality between the actual descent and potential ascent'', which states that 'If any number of weights begin to move in any way by the force of their own gravity, the velocities of the individual weights will be everywhere such that the products of the squares of these velocities multiplied by the appropriate masses, gathered together, are proportional to the vertical height through which the centre of gravity of the composite of the bodies descends, multiplied by the masses of all of them.' In only considering quasi-one-dimensional fluid motion and by using the principle of conservation of energy, Bernoulli develops the following equation:

<math>{v}{dv \over dx}={(a-v^2) \over 2c}</math>

where:
:<math>v\,</math> is the velocity of the fluid
:<math>dx\,</math> is the length of the cylindrical tube
:<math>a\,</math> is the height of the tube
:<math>c\,</math> is the distance from the entrance of the tube

After making several assumptions such as the pressure is proportional to the ratio of the increase in velocity over time, and that the hole ''o'' is infinitesimal, thus the fluid is virtually motionless which makes the pressure determined by the height of the column, he develops this equation:

<math>{p_1 \over \gamma} + {V_1^2 \over 2g}={p_2 \over \gamma} + {V_2^2 \over 2g}</math>

where:
:<math>p_1\,</math> is the pressure in the tube
:<math>p_2\,</math> is the pressure at the exit of the tube
:<math>V_1\,</math> is the velocity of the fluid in the tube
:<math>V_2\,</math> is the velocity of the fluid exiting the tube
:<math>\gamma\,</math> is the specific weight of the fluid
:<math>g\,</math> is the acceleration due to gravity

A simpler version of Bernoulli's Principle for an incompressible fluid where frictional forces is negligible is:

<math>{v^2 \over 2}+gz+{p \over \rho}=\text{constant}</math>

where:
:<math>v\,</math> is the velocity of the fluid in the tube
:<math>g\,</math> is the acceleration due to gravity
:<math>z\,</math> is the height of the tube
:<math>p\,</math> is the pressure
:<math>\rho\,</math> is the density of the fluid

The main idea of the Bernoulli Principle is that for a steady flow, the sum of all the energies involved will be the same at any point in the tube, therefore, the velocity of the fluid through the tube will increase coinciding with a decrease in pressure or a decrease in the potential energy.

===Euler-Bernoulli Beam Equation===
The Euler-Bernoulli Beam Equation is based on the theory of elasticity, which states that elasticity is the property of solid materials to deform under the application of an external force and to regain their original shape after the force is removed.

The equation is:

<math>{d^2 \over dx^2}[{EI}{d^2w \over dx^2}]=p</math>

where:
:<math>w\,</math> is the displacement of the beam
:<math>p\,</math> is the force per unit length acting in the direction of w
:<math>E\,</math> is the Young's Modulus for the beam
:<math>I\,</math> is the moment of inertia of the beam's cross section
:<math>x\,</math> is the position along the beam

The Euler-Bernoulli Beam Equation relates the displacement, or deflection of the beam (w) to its pressure loading (p). The equation is widely used in engineering applications, such as civil or mechanical to determine the strength of beams when stress is applied.

==References==

Wilkins, D.R. "The Bernoullis." Web. 30 Nov. 2015. <http://www.maths.tcd.ie/pub/HistMath/People/Bernoullis/RouseBall/RB_Bernoullis.html#DanielBernoulli>.

Rothbard, Murray. "Daniel Bernoulli and the Founding of Mathematical Economics." Mises Institute. Mises Institute, 10 Feb. 2011. Web. 30 Nov. 2015. <https://mises.org/library/daniel-bernoulli-and-founding-mathematical-economics>.

Guinness, I. "Daniel Bernoulli, Hydrodynamica (1738)." Landmark Writings in Western Mathematics 1640-1940. Amsterdam: Elsevier, 2005. Print.

Dahr, S. "3.1 Theory of Elasticity." Web. 30 Nov. 2015. <http://www.iue.tuwien.ac.at/phd/dhar/node17.html>.

"Euler-Bernoulli Beam Equation." EFunda, 2015. Web. 30 Nov. 2015. <http://www.efunda.com/formulae/solid_mechanics/beams/theory.cfm>.

Daniel Bernoulli

2015-11-30T21:13:19Z

Bmcfarland7: /* Euler-Bernoulli Beam Equation */

Daniel Bernoulli

2015-11-30T20:51:36Z

Bmcfarland7: /* Elasticity */

Daniel Bernoulli

2015-11-30T20:11:28Z

Bmcfarland7:

Claimed by Brynn McFarland, this is a work in progress!

==Personal Life==
Daniel Bernoulli was born on February 9, 1700 in Groningen, the Netherlands. He came from a family of distinguished mathematicians, but reportedly was the brightest of three children of the family. While growing up in Switzerland, his relationship with his father gradually deteriorated due to competition in academia.

First studying at the University in Basel, he was later invited to study at the Saint Petersburg Academy of Sciences. He studied mathematics, business, medicine, anatomy, and botany, eventually earning his Ph.D. in the latter two. Eventually he returned to Basel as a professor of anatomy, botany, and physics.

He made significant contributions to Physics, most notably '''the Bernoulli Principle''', which is used extensively in aerodynamics and fluid dynamics. His contributions were not limited to only Physics though, he has also been called the founder of mathematical economics and was one of the first people to begin work on a kinetic theory of gases.

==Contributions to Physics==

===''Hydrodynamica''===
Bernoulli published ''Hydrodynamica'' in 1738, and the title eventually gave rise to the name "hydrodynamics" for the field of fluid dynamics. The full title of the text was "Hydrodynamics, or commentaries on the forces and motions of fluids". In the book, Bernoulli characterizes fluid mechanics according to conservation of energy by examining several examples such as fluid coming out of an opening or fluid flowing through a tube. These examples gave the first adequate theory of the motion of incompressible fluids and also hydrodynamic pressure. In the text he also describes work and efficiency of hydraulic machines, the kinetic theory of gases, and several ideas that would eventually be formulated into the Bernoulli Principle.

===The Bernoulli Principle===
The Bernoulli Principle was developed in ''Hydrodynamica'' when he asked the following question: 'Let a very wide vessel ''ACEB'', which is to be kept constantly full of water, be fitted with a horizontal cylindrical tube ''ED''; and at the extremity of the tube let there be an orifice ''o'' emitting water at a uniform velocity; the pressure of the water against the walls of the tube ''ED'' is sought.' To solve this problem, Bernoulli employs his ''principle of equality between the actual descent and potential ascent'', which states that 'If any number of weights begin to move in any way by the force of their own gravity, the velocities of the individual weights will be everywhere such that the products of the squares of these velocities multiplied by the appropriate masses, gathered together, are proportional to the vertical height through which the centre of gravity of the composite of the bodies descends, multiplied by the masses of all of them.' In only considering quasi-one-dimensional fluid motion and by using the principle of conservation of energy, Bernoulli develops the following equation:

<math>{v}{dv \over dx}={(a-v^2) \over 2c}</math>

where:
:<math>v\,</math> is the velocity of the fluid
:<math>dx\,</math> is the length of the cylindrical tube
:<math>a\,</math> is the height of the tube
:<math>c\,</math> is the distance from the entrance of the tube

After making several assumptions such as the pressure is proportional to the ratio of the increase in velocity over time, and that the hole ''o'' is infinitesimal, thus the fluid is virtually motionless which makes the pressure determined by the height of the column, he develops this equation:

<math>{p_1 \over \gamma} + {V_1^2 \over 2g}={p_2 \over \gamma} + {V_2^2 \over 2g}</math>

where:
:<math>p_1\,</math> is the pressure in the tube
:<math>p_2\,</math> is the pressure at the exit of the tube
:<math>V_1\,</math> is the velocity of the fluid in the tube
:<math>V_2\,</math> is the velocity of the fluid exiting the tube
:<math>\gamma\,</math> is the specific weight of the fluid
:<math>g\,</math> is the acceleration due to gravity

A simpler version of Bernoulli's Principle for an incompressible fluid where frictional forces is negligible is:

<math>{v^2 \over 2}+gz+{p \over \rho}=\text{constant}</math>

where:
:<math>v\,</math> is the velocity of the fluid in the tube
:<math>g\,</math> is the acceleration due to gravity
:<math>z\,</math> is the height of the tube
:<math>p\,</math> is the pressure
:<math>\rho\,</math> is the density of the fluid

The main idea of the Bernoulli Principle is that for a steady flow, the sum of all the energies involved will be the same at any point in the tube, therefore, the velocity of the fluid through the tube will increase coinciding with a decrease in pressure or a decrease in the potential energy.

===Elasticity===

===Euler-Bernoulli Beam Equation===

==References==

Daniel Bernoulli

2015-11-30T20:10:51Z

Bmcfarland7: /* The Bernoulli Principle */

Daniel Bernoulli

2015-11-30T16:59:35Z

Bmcfarland7:

Daniel Bernoulli

2015-11-30T05:38:56Z

Bmcfarland7:

Daniel Bernoulli

2015-11-30T05:04:43Z

Bmcfarland7: Created page with "Claimed by Brynn McFarland, this is a work in progress!"

Claimed by Brynn McFarland, this is a work in progress!

Main Page

2015-11-30T05:04:03Z

Bmcfarland7: /* Notable Scientists */

__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]]
*[[Josiah Willard Gibbs]]
*[[Richard Feynman]]
*[[Sir David Brewster]]
*[[Daniel Bernoulli]]
</div>
</div>

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

===Properties of Matter===
<div class="mw-collapsible-content">
*[[Mass]]
*[[Velocity]]
*[[Density]]
*[[Charge]]
*[[Spin]]
*[[SI Units]]
*[[Heat Capacity]]
</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]]
* [[Length and Stiffness of an Interatomic Bond]]
</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]]
*[[Systems with Nonzero 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]]
*[[Photons]]
*[[Air Resistance]]
</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]]
*[[Daniel Chung was here]]
</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]]
**[[Potential Difference in an Insulator]]
*[[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]]
*[[Feedback]]
</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]]
**[[Magnetic Field of Coaxial Cable Using Ampere's Law]]
*[[Faraday's Law]]
**[[Curly Electric Fields]]
**[[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]]
*[[Snell's Law]]
</div>
</div>
<div class="toccolours mw-collapsible mw-collapsed">

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