Physics Book - User contributions [en]

Kirchoff's Laws

2019-11-26T03:03:51Z

Htaghian3:

Edits: Heeva Taghian Fall 2019
Claimed by Abieshek Subramaniam - Fall 2019

[[File:Junction.gif|thumb|The node (or junction) rule states that the current flowing in is equal to the current that flows out.
I<sub>1</sub> + I<sub>4</sub> = I<sub>2</sub> + I<sub>3</sub> + I<sub>5</sub>]]

<b>Kirchoff's Laws</b> are two fundamental principles of electric circuits and are used to determine the behaviors of electric circuits and their components. They serve as a guide for how circuits will behave and are accurate for all DC and low-frequency AC circuits. These principles are used to measure voltage and current in [http://www.physicsbook.gatech.edu/Ammeters,Voltmeters,Ohmmeters voltmeters and ammeters].

<b>Kirchoff's Node Rule</b>, also known as <b>Kirchoff's First Law</b> or <b>Kirchoff's Junction Rule</b>, further exercises the law of Conservation of Charge and states that if current is constant, all the current that flows through one junction must be equal to all the current that flows out of the junction. This rule can be applied both to [[Electron and Conventional Current|conventional]] and [[Electron and Conventional Current|electron currents]]. This rule is not a fundamental principle, but rather a consequence of the fundamental principle of conservation of charge and the definition of steady-state.

[[File:Visual_Model2.png|thumb|The Loop rule states that the sum of voltage around a loop is equal to 0.
LOOP 1: <math> \Delta {V}_{AB} + \Delta {V}_{BC} + \Delta {V}_{CF} + \Delta {V}_{FA} = 0 </math>

LOOP 2: <math> \Delta {V}_{FC} + \Delta {V}_{CD} + \Delta {V}_{DE} + \Delta {V}_{EF} = 0 </math>

LOOP 3: <math> \Delta {V}_{AB} + \Delta {V}_{BC} + \Delta {V}_{CD} + \Delta {V}_{DE} + \Delta {V}_{EF} + \Delta {V}_{FA} = 0 </math>]]

<b>Kirchoff's Second Law</b>, also known as <b>Kirchhoff's Loop Rule</b> or <b>Kirchhoff's Voltage Law</b> states that the sum of potential differences around a closed circuit is equal to zero. More simply, in a completed circuit, the voltages around a loop will sum to 0. This is because voltage is just energy per unit charge, and both energy and charge are conserved by fundamental laws.

Note that this is only true when the magnetic field is neither fluctuating nor time-varying. If a changing magnetic field links the closed loop, then the principle of energy conservation does not apply to the electric field, causing the Loop Rule to be inaccurate in this scenario.

==The Main Idea==

'''Kirchoff's Node Rule'''

The node rule states that at any junction in an electrical circuit, the amount of current flowing into the junction is equal to the amount of current flowing out of the junction in steady-state.

In the steady state, for many electrons flowing into and out of a node,
* electron current: <math> net\ i_{in} = net\ i_{out},</math> where <math>i = nA\mu</math><math>E</math>
* conventional current: <math> net\ I_{in} = net\ I_{out},</math> where <math>I = |q|nA\mu</math><math>E</math>

'''Conservation of Charge'''

This rule is an application of the conservation of electric charge, basically that charge within a circuit cannot be created or lost. During the flow process around the circuit, there is no loss of any charge, thus the total current in any cross-section of the circuit is the same. If there are no nodes in the loop, the conventional current is the same throughout the loop.

'''Kirchoff's Loop Rule'''

The loop rule simply states that in any round trip path in a circuit,
[[Electric Potential]] equals zero. This applies through <i>any</i> round trip path; in more complex circuits, there can be
multiple round trip paths. This principle is an application of the conservation of energy, specifically within a circuit.
This principle is often used to solve for resistance or current passing through of light bulbs and other resistors, as well as the capacitance or charge of capacitors in a circuit.

[[File:loopexample.png]]

LOOP 1: <math> \Delta {V}_1 = emf - I_1R_1 = 0 </math>

LOOP 2: <math> \Delta {V}_2 = -I_1R_1 + I_2R_2 = 0 </math>

LOOP 3: <math> \Delta {V}_3 = emf - I_2R_2 = 0 </math>

To figure out the sign of the voltages, act as an observer walking along the path. Start at the negative end of the emf and continue walking along the path. The emf will be positive in the loop rule because you are moving from low to high voltage. Once you reach a resistor or capacitor, this will be negative in the loop rule equation because it is high to low voltage. Continue along the path until you return to the starting position.

'''Bringing Both Laws Together'''

Find all possible node and loop equations for the following circuit.

[[File:Non_steady_state_image_TWO.png|400 px]]

You should have 3 Loop Equations and 2 Node equations.

Some examples:

<math> I_1= I_2+I_3 </math>

<math> I_1*R_1 + emf_1 + emf_3 + I_3*R_4 = 0 </math>

'''Matrices in Conjunction with Kirchhoff's Laws'''

After creating loop equations for all possible loops in a circuit using the node rule and loop rule, you can input the coefficients of the equations into a matrix. After inputting it into the matrix, you can use linear algebra and row reduction in order to solve for the current or resistances of the different parts of the circuit. This format and method of understanding complex circuits are especially useful for circuits with a large number of loops as it makes the algebra involved in getting the currents much simpler and straightforward. Simply creating the equations for every loop possible and every node and then inputting the coefficients into a row reduction calculator can give you all the values for I and/or R that you might need.

After finding the loop equations you can use a matrix calculator as well to further simplify your task!: [http://www.math.odu.edu/~bogacki/cgi-bin/lat.cgi?c=rref Online Matrix Row Reduction Calculator]

An example of how you would format the matrix of a Kirchhoff's law problem is shown below:

:<math>\mathbf{A} = \begin{bmatrix}
R1 & R2 & R3 & | EMF \\
& & & | EMF \\
& & & | EMF
\end{bmatrix}.</math>

Simply place to coefficients or resistances of each of the different resistors as separate elements in the columns of the matrix while keeping track of which resistance pertains to which part of the loop and place the EMF of that loop as the solution column in the augmented matrix. Then after row reducing, each of the resistors should be simplified so that there is a 1 in at least 1 row for every resistor and the current at the end of that row is the current for the resistor that is in the same column as the 1 in the row of the current.

For example in the matrix below the current going through R2 is 1/15 amps:

:<math>\mathbf{A} = \begin{bmatrix}
R1 & R2 & R3 & | EMF \\
& 1 & & | 1/15 \\
& & & | EMF
\end{bmatrix}.</math>

'''Limitations'''

The Node rule assumes that current flows only in conductors and that whenever current flows into one end of a conductor it immediately flows out the other end. This is not a safe assumption for high-frequency AC circuits. In other words, the node is valid only if the total electric charge, <math>Q</math>, remains constant in the region being considered. In practical cases, this is always so when the node rule is applied at a point.

The Loop rule is based on the assumption that there is no fluctuating magnetic field linking the closed-loop.
This is not a safe assumption for high-frequency AC circuits. In the presence of a changing magnetic field, the electric field is not a conservative vector field. Therefore, the electric field cannot be the gradient of any potential. That is to say, the line integral of the electric field around the loop is not zero, directly contradicting KVL.

Understanding these limitations is essential to understanding how motional emf, motors, and generators work.

===A Mathematical Model===

'''Kirchoff's Node Rule'''

[[File:kircho2.gif|right]]
The node rule can be stated as:
:<math> \sum \Delta{I} = 0 </math> <br/>
where <math>I</math> stands for the current of the individual parts or wires in a circuit and the sign of the current that flows into the junction is opposite of the current that flows out of the junction. This simply supports the idea that charge cannot be created or destroyed because the total current must remain equal regardless of the path it takes.
:<math> \sum_{k=1}^n I_k = 0 </math> <br/>
where <math>n</math> is the total number of branches with current flowing through the node, as well as along any node in a circuit:

:<math> \Delta {I}_{1} + \Delta {I}_{2} + \space.... = 0 </math>

or more generally:

:<math> \sum_{k=1}^n \tilde{I_k}</math> = 0 <br/>

'''Kirchoff's Loop Rule'''

A mathematical representation is:

:<math> \sum \Delta{V} = 0 </math> <br/>
where <math>V</math> stands for the voltage of the individual parts or wires in a circuit and the sign of the voltage that flows clock-wise is opposite of the current that flows counterclockwise. This simply supports the idea that energy cannot be created or destroyed because the total current must remain equal regardless of the path it takes.

:<math> \sum_{i=1}^n {V}_{i} = 0 </math>

where <math>n</math> is the number of voltages being measured in the loop, as well as

:<math> \Delta {V}_{1} + \Delta {V}_{2} + \space.... = 0 </math>

along any closed path in a circuit. The voltages may also be complex:

:<math>\sum_{k=1}^n \tilde{V}_k = 0</math>

'''Matrix Intrepretation'''

Using matrices can simplify the process of using node and loop rules in order to find out different parts of a complex circuit. Simply write out all the loop and node rules for a circuit. Then place coefficients of the equations you created in a matrix in the format below. The matrix should be an augmented matrix with the elements on the left being the resistances and the right being the EMF of that loop.

:<math>\mathbf{A} = \begin{bmatrix}
R1 & R2 & R3 & | EMF \\
& & & | EMF \\
& & & | EMF
\end{bmatrix}.</math>

To row reduce you should add, subtract, multiply, interchange or add a multiple of rows to each other until the matrix is as far simplified as possible. Otherwise, you can simply use a row reduction calculator online ([http://www.math.odu.edu/~bogacki/cgi-bin/lat.cgi?c=rref Online Matrix Row Reduction Calculator]) in order to do it for you and the right hand column will show the currents associated with the different resistors. To figure out which current goes with which resistor look to see which resistor has a 1 in its column and the current at the end of that row is the current of that resistor.

More information on how to row reduce by hand can be found here: [https://www.mathportal.org/algebra/solving-system-of-linear-equations/row-reduction-method.php Row Reduction Methodology]

===A Computational Model===

Click here for an [http://www.falstad.com/circuit/ online circuit simulator]. It opens up with an LRC circuit that has current running through it. The graphs on the bottom show the voltage as the current runs through the circuit. You can see that after a full loop the voltage is 0, verifying the loop rule. You can make all sorts of different circuits and loops and see for yourself.

==Examples==

===Simple===
'''Question'''

[[File: Node_comp.gif|thumb|250 px|Figure 1]]

Figure 1 displays a node in a circuit. I<sub>1</sub> is equal to 10 amps. I<sub>2</sub> is equal to 4 amps. What is I<sub>3</sub>?

'''Solution'''

: The current flowing into the node: <math> I_1 = 10A </math> <br/> The current flowing out of the node: <math> I_2 + I_3 </math> <br/> We know that the current flowing in must equal the current flowing out, so <math>10A = 4A + I_3 </math><br/> Therefore <math>I_3</math> must equal <b>6A</b>.

'''Question'''

[[File:SimpleLoopRule.jpg|300 px]]

The circuit shown above consists of a single battery and a single resistor. The resistance of the wires is negligible for this problem.

If the <math> emf </math> is 5 V and the resistance of the resistor is 10 ohms, what is the current passing through the resistor?

'''Solution'''

Although we can solve this using the <math>V = IR</math> equation for the whole loop, let's examine this problem using the loop rule equation.

The loop rule equation would be <math> {V}_{battery} - {V}_{resistor} = 0 </math>

Since we know the <math> emf </math> of the battery we just need to find the potential difference through the resistor. For this we can use the equation of <math> V = IR </math>.

Thus we now have an loop rule equation of <math> emf - IR = 0 </math>
From here it is a relatively simple process to find the current. We can rewrite the loop rule equation as <math> emf = IR </math> and then plug in 5 for the emf and
10 for the resistance, leaving us with I = .5 amperes.

===Middling===

'''Question'''

[[File:ExampleLoopRule2.png|300 px]]

The circuit shown above consists of a single battery, whose <math> emf </math> is 1.3 V, and three wires made of the same material, but having different cross-sectional areas.
Let the length of the thin wires be <math> {L}_{thick} </math> and the length of the thin wire be <math> {L}_{thin} </math>
Find a loop rule equation that starts at the negative end of the battery and goes counterclockwise through the circuit.

'''Solution'''

When beginning this problem, you must notice that the difference in cross-sectional areas affects the electric field in each wire. Because of this
we will denote the electric field at D. as <math> {E}_{D} </math> and the electric field everywhere else as <math> {E}_{A} </math>.
To begin we will go around the circuit clockwise and add up each component. First, we know that the <math> emf </math> of the battery is 1.3 V. Then, we will add up the potential
voltage of each of the wires.

Remember that the electric potential of a wire is equal to the product of the electric field and the length of the wire. From this we can now find the potential difference
of each section of the wires. The electric potential of location A-C is <math> {E}_{A} * {L}_{thick} </math>. This is the same for the electric potential of locations E - G of the wire.
For the thin section of the wire, the electric potential is <math> {E}_{D} * {L}_{thin} </math>. From here we just go around the circuit counterclockwise and add each potential difference to the loop rule equation.

Thus we can find that a loop rule equation is: <math> emf - 2 ({E}_{A} * {L}_{thick}) - {E}_{D} * {L}_{thin} = 0 </math>

This can also be rewritten as: <math> emf = 2 ({E}_{A} * {L}_{thick}) + {E}_{D} * {L}_{thin} = 0 </math>

===Difficult===
'''Question'''

[[File: Middlenode.gif|thumb|250 px|Figure 2]]

In Figure 2, I<sub>1</sub> equal 23 amps, I<sub>2</sub> equals 5 amps and I<sub>3</sub> equals 42 amps. What is I<sub>4</sub>?

'''Solution'''

:The current flowing into the node: <math> I_1 + I_2 = 23A + 5A = 28A </math> <br/> The current flowing out of the node: <math> I_3 + I_4 = 42A + I_4 </math> <br/> Applying the node rule by using substitution, <math> I_4 = -14A </math> <br/> But how could we get a negative current? This negative current implies that <math> I_4 </math> flows in the opposite direction of what we assumed. A negative current in a loop rule problem implies that a current is in the opposite direction.

'''Question'''

[[File:HardLoopRule.jpg|350 px]]

For the circuit above, imagine a situation where the switch has been closed for a long time.
Calculate the current at a,b,c,d,e and charge Q of the capacitor. Answer these using <math> emf, {R}_{1}, {R}_{2},
and \space C </math>

'''Solution'''

First, write loop rule equations for each of the possible loops in the circuit. There are 3 loop equations that are possible.

<math> emf - {I}_{1}{R}_{1} - {I}_{2}{R}_{2} = 0 </math>

<math> emf - {I}_{1}{R}_{1} - Q/C = 0 </math>

<math> {I}_{2}{R}_{2} - Q/C = 0 </math>

From here, we can then solve for the current passing through a,b,d and e. We also know that the current passing through
these points must be the same so <math> {I}_{1} = {I}_{2} </math>

<math> emf - {I}_{1}{R}_{1} - {I}_{1}{R}_{2} = 0 </math>

<math> emf = {I}_{1}({R}_{1} + {R}_{2}) = 0 </math>

<math> emf/({R}_{1} + {R}_{2}) = {I}_{1} </math>

So the current at <math>a,b,d,e = emf/({R}_{1} + {R}_{2}) </math>

You must also know that once a capacitor is charging for a long time, current no longer flows through the capacitor. We can then
easily solve for c because since current is no longer flowing through the capacitor, the current at c = 0.

We will use the loop rule equation of <math> {I}_{2}{R}_{2} - Q/C = 0 </math> to solve for Q.

<math> {I}_{2}{R}_{2} = Q/C </math>

<math> C*({I}_{2}{R}_{2}) = Q </math> Since <math> {I}_{1} = {I}_{2} </math>

<math> C*({I}_{1}{R}_{2}) = Q </math>

We will plug in what we found {I}_{1} equals from before.

<math> C* (emf/({R}_{1} + {R}_{2})){R}_{2}) = Q </math>

Lastly, <math>Q = C* (emf/({R}_{1} + {R}_{2})){R}_{2}</math> and we have now solved the problem.

Current at <math> a,b,d,e = emf/({R}_{1} + {R}_{2}) </math>

Current at <math> c = 0 </math>

<math> Q = C* (emf/({R}_{1} + {R}_{2})){R}_{2}</math>

'''Question (USING MATRICES)'''

[[File:Phys_Wiki_Image_1.png]]

Six identical resistors and two different batteries are connected in a circuit as shown in the diagram. One of the batteries has a potential difference of 20 V and the other has a potential difference of 5 V. The direction of the currents in the circuit are indicated and labeled. Solve your loop and node equations to determine the current through resistorR6. The resistance of each resistor is 100 Ω.

'''Solution'''

From the diagram, it is evident that this particular problem will require quite a few loop and node rule equations, 11 total to be exact. To figure out the current through resistor R6 we will need to set up the node and loop rule equations in order to have a system of equations that will have enough variables and coefficients in order to be able to solve for this current.

The node equations are:

0 = I1 - I3 - I6

0 = I1 - I2 - I4

0 = I2 - I3 - I5

0 = I4 + I5 - I6

The loop rule equations are:

0 = -emf1 + (R1 + R4)I1 + (R5)I4 + (R4)I6

0 = -emf1 + (R1 + R6)I1 + (R2)I2 + (R3)I3

0 = -emf1 + (R1 + R6)I1 + (R2)I2 + emf2 + (R4)I6

0 = (R2)I2 + (R3)I3 - (R4)I6 - (R5)I4

0 = (R2)I2 - emf2 - (R5)I4

0 = (R3)I3 - (R4)I6 + emf2

0 = -emf1 + (R1 + R6)I1 + (R5)I4 + emf2 + (R3)I3

Now that we have the equations instead of taking the time to solve the system of equations for all 11 of these equations, we can simply use a matrix and row reduce in order to find the current is going through R6 as we should have enough relationships to deduce this. The matrix for this particular problem would be the following:

[[File:Phys_Wiki_Matrix.png]]

In the matrix above, the headers at the top represent what the coefficients in the matrix pertain too, being the emf and the resistances associated with each of the currents form I1 through I6. Now using a row reduction calculator we can make an augmented matrix with the results being the emf column and the currents and associated resistances being on the LHS and we can find the I in the right hand column of the augmented matrix that is associated with the correct part of the circuit we are looking for and that will be our result for the current through the circuit at that resistor. In this case, that ends up being 1/15 amps.

In this particular problem, using traditional system of equation methods would prove problematic and time consuming as there are 11 equations that we have to work with. Thus, by using a matrix and row reduction, we can simply place the coefficients into a matrix, row reduce, and look at the number that is in the column of the resistor we are trying to find the current for and that will be our solution.

==Connectedness==

The Node Rule is connected to a lot of other topics in physics. The loop rule is the most important one, as the node rule and loop rule in conjunction allow us to solve circuits. The node rule is also connected to other concepts such as voltage, current and electricity. The Node Rule also supports the law of conservation of energy because in essence, current is simply the flow of electric charge, and since you cannot (at least as of now) create energy or electrons out of nothing, everything that is put into the system must come out somehow. Therefore, all the current that is applied, must come out the other end.

The Loop Rule is simply an extension of the conservation of energy applied to circuits. Circuits are ubiquitous as they are featured in almost every technology today. Our understanding of these technologies is rooted in the empirical discoveries made in the mid 19th century, and further boosted by the the advancement of theoretical knowledge due to the likes of Faraday and Maxwell.

One interesting note about Loop Rule is that is does not apply universally to all circuits. In particular, AC (alternating current) circuits at high frequencies, have a fluctuating
electric charge that changes direction. This causes the electric potential of a round trip path around the circuit to no longer be zero. However, DC (direct current)
circuits, and low frequency circuits in general, still follow the loop rule.

These laws allow for voltmeters and ammeters to work, with voltmeters having a high resistance and being connected in parallel and ammeters having a low resistance and being connected in series.

Linear algebra is also intertwined with Kirchhoff's laws involving loops and nodes as complex and large circuits with many components can often lead to many different loops and the amount of loop and node equations can often get out of hand very quickly. As a result, we can use matrices to simplify the algebra involved with solving for currents in components that are a part of large circuits with many different loop and node equations. After creating the matrix we need skills from linear algebra in order to find the row reduced form of the augmented matrix that we create. With this reduced version of the matrix, we can find the current or resistances of the different parts of the circuit in a much easier and more timely fashion.

==History==
[[File:KirchoffLoopRule.jpg|thumb|Gustav Kirchhoff]]

Gustav Kirchhoff was a German physicist who lived during the 19th century. There are many equations and laws named after him that he helped to discover. His circuit laws (the node rule and loop rule) were the first laws that he conceived, and discovered this during his time as a student at Albertus University of Königsberg in 1845; he later wrote his doctoral dissertation on these laws. Kirchoff went on to explore the topics of spectroscopy and black body radiation after his graduation from Albertus. In addition to his circuit laws, he is also known for his law of thermochemistry and three laws of spectroscopy, the latter of which helped lead to quantum mechanics.

== See Also ==

===Further Reading===

*[[Components]]

*[[Circular Loop of Wire]]

*[[Resistors and Conductivity]]

*[[Current]]

===External Links===

https://www.boundless.com/physics/textbooks/boundless-physics-textbook/circuits-and-direct-currents-20/kirchhoff-s-rules-152/the-junction-rule-539-6331/

https://en.wikipedia.org/wiki/Kirchhoff%27s_circuit_laws#Kirchhoff.27s

http://www.tutorvista.com/content/physics/physics-iv/current-electricity/kirchhoffs-rules.php

http://physics.bu.edu/~duffy/py106/Kirchoff.html

https://www.mathportal.org/algebra/solving-system-of-linear-equations/row-reduction-method.php

==References==

*Matter & Interactions 4th Edition by Ruth W. Chabay & Bruce A. Sherwood
*http://www.math.odu.edu/~bogacki/cgi-bin/lat.cgi?c=roc
*http://www.regentsprep.org/Regents/physics/phys03/bkirchof1/
*https://www.mathportal.org/algebra/solving-system-of-linear-equations/row-reduction-method.php
*https://en.wikipedia.org/wiki/Kirchhoff%27s_circuit_laws#Kirchhoff.27s
* https://en.wikipedia.org/wiki/Kirchhoff%27s_circuit_laws#Kirchhoff.27s_voltage_law
* https://www.khanacademy.org/science/electrical-engineering/ee-circuit-analysis-topic/ee-dc-circuit-analysis
* http://www.ux1.eiu.edu/~cfadd/1360/28DC/Loop.html
* http://higheredbcs.wiley.com/legacy/college/cutnell/0470223553/concept_sims/sim34/sim34.html
* http://www.falstad.com/circuit/
* Schuster, D. (Producer). (2013). Kirchhoff's Loop and Junction Rules Theory [Motion picture]. United States of America: YouTube.
* Schuster, D. (Producer). (2013). Kirchhoff's Rules (Laws) Worked Example [Motion picture]. United States of America: YouTube.
* Anderson, P. (Producer). (2015). Kirchoff's Loop Rule [Motion picture]. United States of America: YouTube.

[[Category: Electric Fields and energy in circuits]]

Vectors

2018-09-16T05:58:51Z

Htaghian3: /* Middling */ changed title since middling is not a common word

Written by Elizabeth Robelo

Improved by Aparajita Satapathy

Improved by Lichao Tang

Improved by Jimin Yoon

Improved by Sabrina Seibel

Claimed: Sanjana Kumar Fall 2017

Improved by Audrey Suh (Spring 2018)

'''Improved by Heeva Taghian (Fall 2018)'''

In physics, a vector is a quantity with a magnitude and a direction. It helps determine the position of one point relative to another.

==The Main Idea==

A vector <math> \vec A </math> is a quantity with a magnitude <math> |\vec A| </math> and a direction <math> \hat A </math>. The magnitude of a vector is a scalar quantity which represents the length of the vector but does not have a direction. A vector is represented by an arrow. The orientation of the vector represents its direction. The length of the vector represents its magnitude. When a vector is drawn, the starting point is the tail and the ending point is called the head, or the 'tip', of the vector. In physics, a vector always starts at the source and directs to the observation location. In other words, if you are drawing a vector, the tail of the vector will be located at the original location and the tip of the vector will be located at the observation location. Refer to the image below for a visual representation:
[[File:Mathinsight.png|300px|thumb|center|Visual Representation]]

We can also add and subtract vectors. To add two vectors, place the head of one vector at the tail of the other. The sum vector will be the arrow starting from the tail of the first vector to the head of the second vector.

[[File:Addingvectors.jpg|275px|thumb|center|Adding vector A to B]]



To subtract two vectors, reverse the direction of the vector you want to subtract and continue to add them like shown before.



[[File:Subtractingvectors.jpg|350px|thumb|center|Subtracting vector B from A]]

A vector can also be multiplied by a scalar. To multiply a vector by a scalar, we can stretch, compress, or reverse the direction of a vector. If the scalar is between 0 and 1, the vector will be compressed. If the scalar is greater than 1, the vector will get stretched. If the scalar has a negative sign, then the vector reverses its direction as well as any compression or extension.

[[File:Ibguides.png|400px|thumb|center|Scalar Multiplication]]

===A Mathematical Model===

Vectors are given by ''x'', ''y'', and ''z'' coordinates. They are written in the form <math> < X,\ Y,\ Z > </math> or <math> (X\ i + Y\ j + Z\ k) </math>.

The following calculations can be performed on vectors:

'''Finding the Magnitude''': <math> |\vec A| = \sqrt{x^2 + y^2 + z^2} </math>

'''Finding the Unit Vector''': :<math> \hat{A} = \frac{\vec A}{|\vec A|} </math>

'''Dot Product''': <math> |\vec A \cdot \vec B| = |\vec A| \ast |\vec B| \ast \cos\Theta </math>

'''Cross Product''': <math> |\vec A \times \vec B| = |\vec A| \ast |\vec B| \ast \sin\Theta </math>

'''Adding Two Vectors''': <math> < A_1,\ A_2,\ A_3 > + < B_1,\ B_2,\ B_3 >\ =\ < A_1 + B_1,\ A_2 + B_2,\ A_3 + B_3 > </math>

'''Multiplying Two Vectors''': <math> \vec A \times \vec B = < A_1,\ A_2,\ A_3 > \times < B_1,\ B_2,\ B_3 > = < A_2 \ast B_3 - A_3 \ast B_2 >\ i\ +\ < A_1 \ast B_3 - A_3 \ast B_1 >\ j\ +\ < A_1 \ast B_2 - A_2 \ast B_1 >\ k </math>

'''Multiplying a vector and a scalar''': <math> C\ \ast\ < A_1,\ A_2,\ A_3 >\ =\ < C \ast A_1,\ C \ast A_2,\ C \ast A_3 > </math>

<math>\vec A \cdot \vec B\ =\ \sum_{i=1}^n A_iB_i=A_1B_1+A_2B_2+\cdots+A_nB_n</math>

===A Computational Model===

[[File:glowscript_ide11.jpg|200px|thumb|left|Vectors in GlowScript]]

VIDLE is an interactive editor for VPython, a programming language that is commonly used in Physics to create 3D displays and animations. It is also used to perform iterative calculations using fundamental principles. Codes on VIDLE are instructions for a computer to follow to make these calculations.

In VIDLE code, arrow objects usually represent vector components. Arrows can be defined by their position, axis, and color. Each part can be manipulated to achieve different results. The position and axis of arrows are vectors, so they can be scaled by multiplying by a scalar. Arrows are often used to represent relative position vectors, starting at position A and ending at position B or by finding the "final minus initial" (B-A) position vector. In the image, the relative position vector is of the tennis ball with respect to the baseball, so the arrow points from the baseball to the tennis ball. If a relative position vector is in the 3D-plane, three further arrows can be used to denote the x, y, and z components. The ''z'' component vector is referenced using the formula ''vectorname.z''.

In Physics 2, you will learn that a vector always starts at a source and points to the observation location at which physical quantities such as the electric or magnetic fields need to be found. Furthermore, it is important to be able to calculate the magnitude and direction of a vector in 3D space. [https://trinket.io/embed/glowscript/e17d933a59?outputOnly=true Here] is an example of a VPython model that computationally calculates such values. The green arrow represents the position vector which starts from a proton (red ball) to the arbitrary observation location. Click 'Run' on the upper-left corner in order to display the model.

--[[User:Htaghian3|Htaghian3]] ([[User talk:Htaghian3|talk]]) 01:54, 16 September 2018 (EDT)

==Examples==

===Simple===
Which of the following statements is correct? (Can be more than one)

[[File:simproblem.jpg|275px|thumb|center]]

1. <math>\overrightarrow{c} = \overrightarrow{a} + \overrightarrow{b}</math>

2. <math>\overrightarrow{a} = \overrightarrow{b} - \overrightarrow{c}</math>

3. <math>\overrightarrow{a} = \overrightarrow{c} + \overrightarrow{b}</math>

4. <math>\overrightarrow{b} = \overrightarrow{c} + \overrightarrow{a}</math>

The answer is option number 2 and option number 4.

===Intermediate===
1. What is the magnitude of the vector C = A - B if A = <10, 5, 8> and B = <9, 4, 3>?

First we need to find the vector C:
A - B = <math> <(10-9), (5-4), (8-3)> = <1, 1, 5> = C</math>

<math>\sqrt{(1)^2 + 1^2 + 5^2} = 5.196</math>

2. What is the cross product of A = <1,2,3> and B = <9,4,5>?

Use the equation for cross product: a x b= <a1, a2, a3> x <b1, b2, b3> = <a2*b3 - a3*b2> i - <a1*b3 - a3*b1> j + <a1*b2 - a2*b1> k

A x B<math>=<2*5 - 3*4, 1*5 - 3*9, 1*4 - 2*9> = <-2, -22, -14></math>

===Difficult===
What is the unit vector in the direction of the vector <10, 5, 8>?
First you have to find the magnitude of the vector given:
<math>\sqrt{10^2 + (5)^2 + 8^2} = 13.74</math>

Finally divide the vector by its magnitude to get the unit vector:

<math>\tfrac{<10, 5, 8>}{13.74}</math>

= <.727, .364, .582>
Notice that the magnitude of the unit vector is equal to 1

==Connectedness==
1.Vectors will be used in many applications in most calculation based fields when movement and position are involved. Vectors can be two dimensional or three dimensional. Vectors are used to represent forces, fields, and momentum.

2.Vectors has been used in many application problems in engineering majors. In engineering applications, vectors are used to a lot of quantities which have both magnitude and direction. Dividing a magnitude into vector quantities in the x,y, and z directions clarify which components of a vector have quantity. For example, in Biomedical Engineering applications, vectors are used to represent the velocity of a flow to further calculate the flow rate and some other related quantities.

3. Vectors play a huge part in industry. For example, in process flow, vectors play a huge part in most calculations. For example, many calculations in different fields of science and math use vector components and direction. Our car's GPS uses vectors even if we don't realize it!

==History==
The discovery and use of vectors can date back to the ancient philosophers, Aristotle and Heron. The theory can also be found in the first article of Newtons Principia Mathematica. In the early 19th century Caspar Wessel, Jean Robert Argand, Carl Friedrich Gauss, and a few more depicted and worked with complex numbers as points on a 2D plane. in 1827, August Ferdinand published a book introducing line segments labelled with letters. he wrote about vectors without the name "vector".

In 1835, Giusto Bellavitis abstracted the basic idea of a vector while establishing the concept of equipollence. He called any pair of line segments of the same length and orientation equipollent (meaning equal length). He found a relationship and created the first set of vectors.
Also in 1835 Hamilton founded "quaternions", which were 4D planes and equations with vectors.

William Rowan Hamilton devised the name "vector" as part of his system of quaternions consisting of three dimensional vectors.

Several other mathematicians developed similar vector systems to those of Bellavitis and Hamilton in the 19th century. The system used by Herman Grassman is the one that is most similar to the one used today.

VPython was released by David Scherer in the year 2000. He came up with the idea after taking a physics class at Carnegie Mellon University. Previous programs only allowed for 2D modeling, so he took it upon himself to make something better. VPython, also known as Visual Python, allows for 3D modeling.
== See also ==

===External links===
Here is a link on more mathematical computations on vectors:
[http://ocw.mit.edu/courses/mathematics/18-02sc-multivariable-calculus-fall-2010/1.-vectors-and-matrices/part-a-vectors-determinants-and-planes/session-1-vectors/MIT18_02SC_notes_0.pdf]

Here is a link on more computational work with vectors:
[http://vpython.org/contents/docs/vector.html]

Here is a link detailing the basics of vectors:
[https://www.physics.uoguelph.ca/tutorials/vectors/vectors.html]

===Further Reading===

Vector Analysis by Josiah Willard Gibbs

Introduction to Matrices and Vectors by Jacob T. Schwartz

==References==
[https://www.mathsisfun.com/algebra/vectors.html https://www.mathsisfun.com/algebra/vectors.html]

[http://ocw.mit.edu/courses/mathematics/18-02sc-multivariable-calculus-fall-2010/1.-vectors-and-matrices/part-a-vectors-determinants-and-planes/session-1-vectors/MIT18_02SC_notes_0.pdf http://ocw.mit.edu/courses/mathematics/18-02sc-multivariable-calculus-fall-2010/1.-vectors-and-matrices/part-a-vectors-determinants-and-planes/session-1-vectors/MIT18_02SC_notes_0.pdf ]

[http://mathinsight.org/vector_introduction]

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

[https://hijabersea.com/posts/intro-to-glowscript.html]

Vectors

2018-09-16T05:56:59Z

Htaghian3: Name and time stamped

Written by Elizabeth Robelo

Improved by Aparajita Satapathy

Improved by Lichao Tang

Improved by Jimin Yoon

Improved by Sabrina Seibel

Claimed: Sanjana Kumar Fall 2017

Improved by Audrey Suh (Spring 2018)

'''Improved by Heeva Taghian (Fall 2018)'''

In physics, a vector is a quantity with a magnitude and a direction. It helps determine the position of one point relative to another.

==The Main Idea==

A vector <math> \vec A </math> is a quantity with a magnitude <math> |\vec A| </math> and a direction <math> \hat A </math>. The magnitude of a vector is a scalar quantity which represents the length of the vector but does not have a direction. A vector is represented by an arrow. The orientation of the vector represents its direction. The length of the vector represents its magnitude. When a vector is drawn, the starting point is the tail and the ending point is called the head, or the 'tip', of the vector. In physics, a vector always starts at the source and directs to the observation location. In other words, if you are drawing a vector, the tail of the vector will be located at the original location and the tip of the vector will be located at the observation location. Refer to the image below for a visual representation:
[[File:Mathinsight.png|300px|thumb|center|Visual Representation]]

We can also add and subtract vectors. To add two vectors, place the head of one vector at the tail of the other. The sum vector will be the arrow starting from the tail of the first vector to the head of the second vector.

[[File:Addingvectors.jpg|275px|thumb|center|Adding vector A to B]]



To subtract two vectors, reverse the direction of the vector you want to subtract and continue to add them like shown before.



[[File:Subtractingvectors.jpg|350px|thumb|center|Subtracting vector B from A]]

A vector can also be multiplied by a scalar. To multiply a vector by a scalar, we can stretch, compress, or reverse the direction of a vector. If the scalar is between 0 and 1, the vector will be compressed. If the scalar is greater than 1, the vector will get stretched. If the scalar has a negative sign, then the vector reverses its direction as well as any compression or extension.

[[File:Ibguides.png|400px|thumb|center|Scalar Multiplication]]

===A Mathematical Model===

Vectors are given by ''x'', ''y'', and ''z'' coordinates. They are written in the form <math> < X,\ Y,\ Z > </math> or <math> (X\ i + Y\ j + Z\ k) </math>.

The following calculations can be performed on vectors:

'''Finding the Magnitude''': <math> |\vec A| = \sqrt{x^2 + y^2 + z^2} </math>

'''Finding the Unit Vector''': :<math> \hat{A} = \frac{\vec A}{|\vec A|} </math>

'''Dot Product''': <math> |\vec A \cdot \vec B| = |\vec A| \ast |\vec B| \ast \cos\Theta </math>

'''Cross Product''': <math> |\vec A \times \vec B| = |\vec A| \ast |\vec B| \ast \sin\Theta </math>

'''Adding Two Vectors''': <math> < A_1,\ A_2,\ A_3 > + < B_1,\ B_2,\ B_3 >\ =\ < A_1 + B_1,\ A_2 + B_2,\ A_3 + B_3 > </math>

'''Multiplying Two Vectors''': <math> \vec A \times \vec B = < A_1,\ A_2,\ A_3 > \times < B_1,\ B_2,\ B_3 > = < A_2 \ast B_3 - A_3 \ast B_2 >\ i\ +\ < A_1 \ast B_3 - A_3 \ast B_1 >\ j\ +\ < A_1 \ast B_2 - A_2 \ast B_1 >\ k </math>

'''Multiplying a vector and a scalar''': <math> C\ \ast\ < A_1,\ A_2,\ A_3 >\ =\ < C \ast A_1,\ C \ast A_2,\ C \ast A_3 > </math>

<math>\vec A \cdot \vec B\ =\ \sum_{i=1}^n A_iB_i=A_1B_1+A_2B_2+\cdots+A_nB_n</math>

===A Computational Model===

[[File:glowscript_ide11.jpg|200px|thumb|left|Vectors in GlowScript]]

VIDLE is an interactive editor for VPython, a programming language that is commonly used in Physics to create 3D displays and animations. It is also used to perform iterative calculations using fundamental principles. Codes on VIDLE are instructions for a computer to follow to make these calculations.

In VIDLE code, arrow objects usually represent vector components. Arrows can be defined by their position, axis, and color. Each part can be manipulated to achieve different results. The position and axis of arrows are vectors, so they can be scaled by multiplying by a scalar. Arrows are often used to represent relative position vectors, starting at position A and ending at position B or by finding the "final minus initial" (B-A) position vector. In the image, the relative position vector is of the tennis ball with respect to the baseball, so the arrow points from the baseball to the tennis ball. If a relative position vector is in the 3D-plane, three further arrows can be used to denote the x, y, and z components. The ''z'' component vector is referenced using the formula ''vectorname.z''.

In Physics 2, you will learn that a vector always starts at a source and points to the observation location at which physical quantities such as the electric or magnetic fields need to be found. Furthermore, it is important to be able to calculate the magnitude and direction of a vector in 3D space. [https://trinket.io/embed/glowscript/e17d933a59?outputOnly=true Here] is an example of a VPython model that computationally calculates such values. The green arrow represents the position vector which starts from a proton (red ball) to the arbitrary observation location. Click 'Run' on the upper-left corner in order to display the model.

--[[User:Htaghian3|Htaghian3]] ([[User talk:Htaghian3|talk]]) 01:54, 16 September 2018 (EDT)

==Examples==

===Simple===
Which of the following statements is correct? (Can be more than one)

[[File:simproblem.jpg|275px|thumb|center]]

1. <math>\overrightarrow{c} = \overrightarrow{a} + \overrightarrow{b}</math>

2. <math>\overrightarrow{a} = \overrightarrow{b} - \overrightarrow{c}</math>

3. <math>\overrightarrow{a} = \overrightarrow{c} + \overrightarrow{b}</math>

4. <math>\overrightarrow{b} = \overrightarrow{c} + \overrightarrow{a}</math>

The answer is option number 2 and option number 4.

===Middling===
1. What is the magnitude of the vector C = A - B if A = <10, 5, 8> and B = <9, 4, 3>?

First we need to find the vector C:
A - B = <math> <(10-9), (5-4), (8-3)> = <1, 1, 5> = C</math>

<math>\sqrt{(1)^2 + 1^2 + 5^2} = 5.196</math>

2. What is the cross product of A = <1,2,3> and B = <9,4,5>?

Use the equation for cross product: a x b= <a1, a2, a3> x <b1, b2, b3> = <a2*b3 - a3*b2> i - <a1*b3 - a3*b1> j + <a1*b2 - a2*b1> k

A x B<math>=<2*5 - 3*4, 1*5 - 3*9, 1*4 - 2*9> = <-2, -22, -14></math>

===Difficult===
What is the unit vector in the direction of the vector <10, 5, 8>?
First you have to find the magnitude of the vector given:
<math>\sqrt{10^2 + (5)^2 + 8^2} = 13.74</math>

Finally divide the vector by its magnitude to get the unit vector:

<math>\tfrac{<10, 5, 8>}{13.74}</math>

= <.727, .364, .582>
Notice that the magnitude of the unit vector is equal to 1

==Connectedness==
1.Vectors will be used in many applications in most calculation based fields when movement and position are involved. Vectors can be two dimensional or three dimensional. Vectors are used to represent forces, fields, and momentum.

2.Vectors has been used in many application problems in engineering majors. In engineering applications, vectors are used to a lot of quantities which have both magnitude and direction. Dividing a magnitude into vector quantities in the x,y, and z directions clarify which components of a vector have quantity. For example, in Biomedical Engineering applications, vectors are used to represent the velocity of a flow to further calculate the flow rate and some other related quantities.

3. Vectors play a huge part in industry. For example, in process flow, vectors play a huge part in most calculations. For example, many calculations in different fields of science and math use vector components and direction. Our car's GPS uses vectors even if we don't realize it!

==History==
The discovery and use of vectors can date back to the ancient philosophers, Aristotle and Heron. The theory can also be found in the first article of Newtons Principia Mathematica. In the early 19th century Caspar Wessel, Jean Robert Argand, Carl Friedrich Gauss, and a few more depicted and worked with complex numbers as points on a 2D plane. in 1827, August Ferdinand published a book introducing line segments labelled with letters. he wrote about vectors without the name "vector".

In 1835, Giusto Bellavitis abstracted the basic idea of a vector while establishing the concept of equipollence. He called any pair of line segments of the same length and orientation equipollent (meaning equal length). He found a relationship and created the first set of vectors.
Also in 1835 Hamilton founded "quaternions", which were 4D planes and equations with vectors.

William Rowan Hamilton devised the name "vector" as part of his system of quaternions consisting of three dimensional vectors.

Several other mathematicians developed similar vector systems to those of Bellavitis and Hamilton in the 19th century. The system used by Herman Grassman is the one that is most similar to the one used today.

VPython was released by David Scherer in the year 2000. He came up with the idea after taking a physics class at Carnegie Mellon University. Previous programs only allowed for 2D modeling, so he took it upon himself to make something better. VPython, also known as Visual Python, allows for 3D modeling.
== See also ==

===External links===
Here is a link on more mathematical computations on vectors:
[http://ocw.mit.edu/courses/mathematics/18-02sc-multivariable-calculus-fall-2010/1.-vectors-and-matrices/part-a-vectors-determinants-and-planes/session-1-vectors/MIT18_02SC_notes_0.pdf]

Here is a link on more computational work with vectors:
[http://vpython.org/contents/docs/vector.html]

Here is a link detailing the basics of vectors:
[https://www.physics.uoguelph.ca/tutorials/vectors/vectors.html]

===Further Reading===

Vector Analysis by Josiah Willard Gibbs

Introduction to Matrices and Vectors by Jacob T. Schwartz

==References==
[https://www.mathsisfun.com/algebra/vectors.html https://www.mathsisfun.com/algebra/vectors.html]

[http://ocw.mit.edu/courses/mathematics/18-02sc-multivariable-calculus-fall-2010/1.-vectors-and-matrices/part-a-vectors-determinants-and-planes/session-1-vectors/MIT18_02SC_notes_0.pdf http://ocw.mit.edu/courses/mathematics/18-02sc-multivariable-calculus-fall-2010/1.-vectors-and-matrices/part-a-vectors-determinants-and-planes/session-1-vectors/MIT18_02SC_notes_0.pdf ]

[http://mathinsight.org/vector_introduction]

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

[https://hijabersea.com/posts/intro-to-glowscript.html]

Vectors

2018-09-16T05:54:53Z

Htaghian3: /* The Main Idea */ Sentences edited for improved readability and brevity. Corrected grammar and typos. Edited mathematical formulas for cleaner and cohesive text.

Written by Elizabeth Robelo

Improved by Aparajita Satapathy

'''Improved by Lichao Tang'''

Improved by Jimin Yoon

Improved by Sabrina Seibel

'''Claimed: Sanjana Kumar Fall 2017'''

Improved by Audrey Suh (Spring 2018)

In physics, a vector is a quantity with a magnitude and a direction. It helps determine the position of one point relative to another.

==The Main Idea==

A vector <math> \vec A </math> is a quantity with a magnitude <math> |\vec A| </math> and a direction <math> \hat A </math>. The magnitude of a vector is a scalar quantity which represents the length of the vector but does not have a direction. A vector is represented by an arrow. The orientation of the vector represents its direction. The length of the vector represents its magnitude. When a vector is drawn, the starting point is the tail and the ending point is called the head, or the 'tip', of the vector. In physics, a vector always starts at the source and directs to the observation location. In other words, if you are drawing a vector, the tail of the vector will be located at the original location and the tip of the vector will be located at the observation location. Refer to the image below for a visual representation:
[[File:Mathinsight.png|300px|thumb|center|Visual Representation]]

We can also add and subtract vectors. To add two vectors, place the head of one vector at the tail of the other. The sum vector will be the arrow starting from the tail of the first vector to the head of the second vector.

[[File:Addingvectors.jpg|275px|thumb|center|Adding vector A to B]]



To subtract two vectors, reverse the direction of the vector you want to subtract and continue to add them like shown before.



[[File:Subtractingvectors.jpg|350px|thumb|center|Subtracting vector B from A]]

A vector can also be multiplied by a scalar. To multiply a vector by a scalar, we can stretch, compress, or reverse the direction of a vector. If the scalar is between 0 and 1, the vector will be compressed. If the scalar is greater than 1, the vector will get stretched. If the scalar has a negative sign, then the vector reverses its direction as well as any compression or extension.

[[File:Ibguides.png|400px|thumb|center|Scalar Multiplication]]

===A Mathematical Model===

Vectors are given by ''x'', ''y'', and ''z'' coordinates. They are written in the form <math> < X,\ Y,\ Z > </math> or <math> (X\ i + Y\ j + Z\ k) </math>.

The following calculations can be performed on vectors:

'''Finding the Magnitude''': <math> |\vec A| = \sqrt{x^2 + y^2 + z^2} </math>

'''Finding the Unit Vector''': :<math> \hat{A} = \frac{\vec A}{|\vec A|} </math>

'''Dot Product''': <math> |\vec A \cdot \vec B| = |\vec A| \ast |\vec B| \ast \cos\Theta </math>

'''Cross Product''': <math> |\vec A \times \vec B| = |\vec A| \ast |\vec B| \ast \sin\Theta </math>

'''Adding Two Vectors''': <math> < A_1,\ A_2,\ A_3 > + < B_1,\ B_2,\ B_3 >\ =\ < A_1 + B_1,\ A_2 + B_2,\ A_3 + B_3 > </math>

'''Multiplying Two Vectors''': <math> \vec A \times \vec B = < A_1,\ A_2,\ A_3 > \times < B_1,\ B_2,\ B_3 > = < A_2 \ast B_3 - A_3 \ast B_2 >\ i\ +\ < A_1 \ast B_3 - A_3 \ast B_1 >\ j\ +\ < A_1 \ast B_2 - A_2 \ast B_1 >\ k </math>

'''Multiplying a vector and a scalar''': <math> C\ \ast\ < A_1,\ A_2,\ A_3 >\ =\ < C \ast A_1,\ C \ast A_2,\ C \ast A_3 > </math>

<math>\vec A \cdot \vec B\ =\ \sum_{i=1}^n A_iB_i=A_1B_1+A_2B_2+\cdots+A_nB_n</math>

===A Computational Model===

[[File:glowscript_ide11.jpg|200px|thumb|left|Vectors in GlowScript]]

VIDLE is an interactive editor for VPython, a programming language that is commonly used in Physics to create 3D displays and animations. It is also used to perform iterative calculations using fundamental principles. Codes on VIDLE are instructions for a computer to follow to make these calculations.

In VIDLE code, arrow objects usually represent vector components. Arrows can be defined by their position, axis, and color. Each part can be manipulated to achieve different results. The position and axis of arrows are vectors, so they can be scaled by multiplying by a scalar. Arrows are often used to represent relative position vectors, starting at position A and ending at position B or by finding the "final minus initial" (B-A) position vector. In the image, the relative position vector is of the tennis ball with respect to the baseball, so the arrow points from the baseball to the tennis ball. If a relative position vector is in the 3D-plane, three further arrows can be used to denote the x, y, and z components. The ''z'' component vector is referenced using the formula ''vectorname.z''.

In Physics 2, you will learn that a vector always starts at a source and points to the observation location at which physical quantities such as the electric or magnetic fields need to be found. Furthermore, it is important to be able to calculate the magnitude and direction of a vector in 3D space. [https://trinket.io/embed/glowscript/e17d933a59?outputOnly=true Here] is an example of a VPython model that computationally calculates such values. The green arrow represents the position vector which starts from a proton (red ball) to the arbitrary observation location. Click 'Run' on the upper-left corner in order to display the model.

--[[User:Htaghian3|Htaghian3]] ([[User talk:Htaghian3|talk]]) 01:54, 16 September 2018 (EDT)

==Examples==

===Simple===
Which of the following statements is correct? (Can be more than one)

[[File:simproblem.jpg|275px|thumb|center]]

1. <math>\overrightarrow{c} = \overrightarrow{a} + \overrightarrow{b}</math>

2. <math>\overrightarrow{a} = \overrightarrow{b} - \overrightarrow{c}</math>

3. <math>\overrightarrow{a} = \overrightarrow{c} + \overrightarrow{b}</math>

4. <math>\overrightarrow{b} = \overrightarrow{c} + \overrightarrow{a}</math>

The answer is option number 2 and option number 4.

===Middling===
1. What is the magnitude of the vector C = A - B if A = <10, 5, 8> and B = <9, 4, 3>?

First we need to find the vector C:
A - B = <math> <(10-9), (5-4), (8-3)> = <1, 1, 5> = C</math>

<math>\sqrt{(1)^2 + 1^2 + 5^2} = 5.196</math>

2. What is the cross product of A = <1,2,3> and B = <9,4,5>?

Use the equation for cross product: a x b= <a1, a2, a3> x <b1, b2, b3> = <a2*b3 - a3*b2> i - <a1*b3 - a3*b1> j + <a1*b2 - a2*b1> k

A x B<math>=<2*5 - 3*4, 1*5 - 3*9, 1*4 - 2*9> = <-2, -22, -14></math>

===Difficult===
What is the unit vector in the direction of the vector <10, 5, 8>?
First you have to find the magnitude of the vector given:
<math>\sqrt{10^2 + (5)^2 + 8^2} = 13.74</math>

Finally divide the vector by its magnitude to get the unit vector:

<math>\tfrac{<10, 5, 8>}{13.74}</math>

= <.727, .364, .582>
Notice that the magnitude of the unit vector is equal to 1

==Connectedness==
1.Vectors will be used in many applications in most calculation based fields when movement and position are involved. Vectors can be two dimensional or three dimensional. Vectors are used to represent forces, fields, and momentum.

2.Vectors has been used in many application problems in engineering majors. In engineering applications, vectors are used to a lot of quantities which have both magnitude and direction. Dividing a magnitude into vector quantities in the x,y, and z directions clarify which components of a vector have quantity. For example, in Biomedical Engineering applications, vectors are used to represent the velocity of a flow to further calculate the flow rate and some other related quantities.

3. Vectors play a huge part in industry. For example, in process flow, vectors play a huge part in most calculations. For example, many calculations in different fields of science and math use vector components and direction. Our car's GPS uses vectors even if we don't realize it!

==History==
The discovery and use of vectors can date back to the ancient philosophers, Aristotle and Heron. The theory can also be found in the first article of Newtons Principia Mathematica. In the early 19th century Caspar Wessel, Jean Robert Argand, Carl Friedrich Gauss, and a few more depicted and worked with complex numbers as points on a 2D plane. in 1827, August Ferdinand published a book introducing line segments labelled with letters. he wrote about vectors without the name "vector".

In 1835, Giusto Bellavitis abstracted the basic idea of a vector while establishing the concept of equipollence. He called any pair of line segments of the same length and orientation equipollent (meaning equal length). He found a relationship and created the first set of vectors.
Also in 1835 Hamilton founded "quaternions", which were 4D planes and equations with vectors.

William Rowan Hamilton devised the name "vector" as part of his system of quaternions consisting of three dimensional vectors.

Several other mathematicians developed similar vector systems to those of Bellavitis and Hamilton in the 19th century. The system used by Herman Grassman is the one that is most similar to the one used today.

VPython was released by David Scherer in the year 2000. He came up with the idea after taking a physics class at Carnegie Mellon University. Previous programs only allowed for 2D modeling, so he took it upon himself to make something better. VPython, also known as Visual Python, allows for 3D modeling.
== See also ==

===External links===
Here is a link on more mathematical computations on vectors:
[http://ocw.mit.edu/courses/mathematics/18-02sc-multivariable-calculus-fall-2010/1.-vectors-and-matrices/part-a-vectors-determinants-and-planes/session-1-vectors/MIT18_02SC_notes_0.pdf]

Here is a link on more computational work with vectors:
[http://vpython.org/contents/docs/vector.html]

Here is a link detailing the basics of vectors:
[https://www.physics.uoguelph.ca/tutorials/vectors/vectors.html]

===Further Reading===

Vector Analysis by Josiah Willard Gibbs

Introduction to Matrices and Vectors by Jacob T. Schwartz

==References==
[https://www.mathsisfun.com/algebra/vectors.html https://www.mathsisfun.com/algebra/vectors.html]

[http://ocw.mit.edu/courses/mathematics/18-02sc-multivariable-calculus-fall-2010/1.-vectors-and-matrices/part-a-vectors-determinants-and-planes/session-1-vectors/MIT18_02SC_notes_0.pdf http://ocw.mit.edu/courses/mathematics/18-02sc-multivariable-calculus-fall-2010/1.-vectors-and-matrices/part-a-vectors-determinants-and-planes/session-1-vectors/MIT18_02SC_notes_0.pdf ]

[http://mathinsight.org/vector_introduction]

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

[https://hijabersea.com/posts/intro-to-glowscript.html]

Main Page

2018-09-16T04:09:07Z

Htaghian3: /* Charging and Discharging */

__NOTOC__
= '''Georgia Tech Student Wiki for Introductory Physics.''' =

This resource 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 for future students!

Looking to make a contribution?
#Pick one of the topics from intro physics listed below
#Add content to that topic or improve the quality of what is already there.
#Need to make a new topic? Edit this page and add it to the list under the appropriate category. Then 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 written for students by a physics expert [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes MSU Physics Wiki]
* 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 intro physics textbooks: [https://openstax.org/details/books/university-physics-volume-1 Vol1], [https://openstax.org/details/books/university-physics-volume-2 Vol2], [https://openstax.org/details/books/university-physics-volume-3 Vol3]
* 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]
* The Feynman lectures on physics are free to read [http://www.feynmanlectures.caltech.edu/ Feynman]
* Final Study Guide for Modern Physics II created by a lab TA [https://docs.google.com/document/d/1_6GktDPq5tiNFFYs_ZjgjxBAWVQYaXp_2Imha4_nSyc/edit?usp=sharing Modern Physics II Final Study Guide]

== 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]]
* A page for review of [[Vectors]] and vector operations
* A listing of [[Notable Scientist]] with links to their individual pages

<div style="float:left; width:30%; padding:1%;">
==Physics 1==
===Week 1===
<div class="toccolours mw-collapsible mw-collapsed">
====Help with VPython====
<div class="mw-collapsible-content">
*[[Python Syntax]]
</div>
</div>

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

====Vectors and Units====

<div class="mw-collapsible-content">
*[[Vectors]]
*[[SI Units]]
</div>
</div>

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

====VPython====

<div class="mw-collapsible-content">
*[[VPython]]
*[[VPython basics]]
*[[VPython Common Errors and Troubleshooting]]
*[[VPython Functions]]
*[[VPython Lists]]
*[[VPython Loops]]
*[[VPython Multithreading]]
*[[VPython Animation]]
*[[VPython Objects]]
*[[VPython 3D Objects]]
*[[VPython Reference]]
*[[VPython MapReduceFilter]]
*[[VPython GUIs]]
</div>
</div>

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

====Vectors and Units====
<div class="mw-collapsible-content">
*[[Vectors]]
*[[SI Units]]
</div>
</div>

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

====Interactions====
<div class="mw-collapsible-content">
*[[Types of Interactions and How to Detect Them]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
====Velocity and Momentum====
<div class="mw-collapsible-content">
*[[Newton's First Law of Motion]]
*[[Velocity]]
*[[Mass]]
*[[Speed and Velocity]]
*[[Relative Velocity]]
*[[Derivation of Average Velocity]]
*[[2-Dimensional Motion]]
*[[3-Dimensional Position and Motion]]
</div>
</div>

===Week 2===
<div class="toccolours mw-collapsible mw-collapsed">
====Momentum and the Momentum Principle====
<div class="mw-collapsible-content">
*[[Momentum Principle]]
*[[Inertia]]
*[[Net Force]]
*[[Derivation of the Momentum Principle]]
*[[Impulse Momentum]]
*[[Acceleration]]
*[[Momentum with respect to external Forces]]
*[[Relativistic Momentum]]
</div>
</div>

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

====Iterative Prediction with a Constant Force====
<div class="mw-collapsible-content">
*[[Newton’s Second Law of Motion]]
*[[Iterative Prediction]]
*[[Kinematics]]
*[[Newton’s Laws and Linear Momentum]]
*[[Projectile Motion]]
</div>
</div>

===Week 3===
<div class="toccolours mw-collapsible mw-collapsed">

====Analytic Prediction with a Constant Force====
<div class="mw-collapsible-content">
*[[Analytical Prediction]]
</div>
</div>

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

====Iterative Prediction with a Varying Force====
<div class="mw-collapsible-content">
*[[Predicting Change in multiple dimensions]]
*[[Spring Force]]
*[[Hooke's Law]]
*[[Simple Harmonic Motion]]
*[[Iterative Prediction of Spring-Mass System]]
*[[Terminal Speed]]
*[[Determinism]]
</div>
</div>

===Week 4===
<div class="toccolours mw-collapsible mw-collapsed">
====Fundamental Interactions====
<div class="mw-collapsible-content">

==Main Idea==

*[[Gravitational Force]]
*[[Fluid Mechanics]]
*[[An Application of Gravitational Potential]]
*[[Electric Force]]
*[[Reciprocity]]
</div>
</div>

===Week 5===
<div class="toccolours mw-collapsible mw-collapsed">
====Conservation of Momentum====
<div class="mw-collapsible-content">
*[[Conservation of Momentum]]
</div>
</div>
<div class="toccolours mw-collapsible mw-collapsed">

====Properties of Matter====
<div class="mw-collapsible-content">
*[[Kinds of Matter]]
*[[Ball and Spring Model of Matter]]
*[[Density]]
*[[Length and Stiffness of an Interatomic Bond]]
*[[Young's Modulus]]
*[[Speed of Sound in Solids]]
*[[Malleability]]
*[[Ductility]]
*[[Weight]]
*[[Hardness]]
*[[Boiling Point]]
*[[Melting Point]]
*[[Change of State]]
</div>
</div>

===Week 6===
<div class="toccolours mw-collapsible mw-collapsed">
====Identifying Forces====
<div class="mw-collapsible-content">
*[[Free Body Diagram]]
*[[Inclined Plane]]
*[[Compression or Normal Force]]
*[[Tension]]
</div>
</div>
<div class="toccolours mw-collapsible mw-collapsed">

====Curving Motion====
<div class="mw-collapsible-content">
*[[Curving Motion]]
*[[Centripetal Force and Curving Motion]]
*[[Perpetual Freefall (Orbit)]]
</div>
</div>

===Week 7===
<div class="toccolours mw-collapsible mw-collapsed">
====Energy Principle====
<div class="mw-collapsible-content">
*[[The Energy Principle]]
*[[Conservation of Energy]]
*[[Kinetic Energy]]
*[[Work]]
*[[Power (Mechanical)]]
</div>
</div>

===Week 8===
<div class="toccolours mw-collapsible mw-collapsed">
====Work by Non-Constant Forces====
<div class="mw-collapsible-content">
*[[Work Done By A Nonconstant Force]]
</div>
</div>
<div class="toccolours mw-collapsible mw-collapsed">
====Potential Energy====
<div class="mw-collapsible-content">
*[[Potential Energy]]
*[[Potential Energy of Macroscopic Springs]]
*[[Spring Potential Energy]]
*[[Ball and Spring Model]]
*[[Gravitational Potential Energy]]
*[[Energy Graphs]]
*[[Escape Velocity]]
</div>
</div>

===Week 9===
<div class="toccolours mw-collapsible mw-collapsed">
====Multiparticle Systems====
<div class="mw-collapsible-content">
*[[Center of Mass]]
*[[Multi-particle analysis of Momentum]]
*[[Momentum with respect to external Forces]]
*[[Potential Energy of a Multiparticle System]]
*[[Work and Energy for an Extended System]]
*[[Internal Energy]]
**[[Potential Energy of a Pair of Neutral Atoms]]
</div>
</div>

===Week 10===
<div class="toccolours mw-collapsible mw-collapsed">
====Choice of System====
<div class="mw-collapsible-content">
*[[System & Surroundings]]
</div>
</div>
<div class="toccolours mw-collapsible mw-collapsed">
====Thermal Energy, Dissipation, and Transfer of Energy====
<div class="mw-collapsible-content">
*[[Thermal Energy]]
*[[Specific Heat]]
*[[Heat Capacity]]
*[[Calorific Value(Heat of combustion)]]
*[[Specific Heat Capacity]]
*[[First Law of Thermodynamics]]
*[[Second Law of Thermodynamics and Entropy]]
*[[Temperature]]
*[[Predicting Change]]
*[[Energy Transfer due to a Temperature Difference]]
*[[Transformation of Energy]]
*[[The Maxwell-Boltzmann Distribution]]
*[[Air Resistance]]
</div>
</div>
<div class="toccolours mw-collapsible mw-collapsed">

====Rotational and Vibrational Energy====
<div class="mw-collapsible-content">
*[[Translational, Rotational and Vibrational Energy]]
</div>
</div>

===Week 11===
<div class="toccolours mw-collapsible mw-collapsed">
====Different Models of a System====
<div class="mw-collapsible-content">
*[[Point Particle Systems]]
*[[Real Systems]]
</div>
</div>
<div class="toccolours mw-collapsible mw-collapsed">
====Models of Friction====
<div class="mw-collapsible-content">
*[[Friction]]
*[[Static Friction]]
</div>
</div>

===Week 12===
<div class="toccolours mw-collapsible mw-collapsed">
====Collisions====
<div class="mw-collapsible-content">
*[[Newton's Third Law of Motion]]
*[[Collisions]]
*[[Elastic Collisions]]
*[[Inelastic Collisions]]
*[[Maximally Inelastic Collision]]
*[[Head-on Collision of Equal Masses]]
*[[Head-on Collision of Unequal Masses]]
*[[Scattering: Collisions in 2D and 3D]]
*[[Rutherford Experiment and Atomic Collisions]]
*[[Coefficient of Restitution]]
</div>
</div>

===Week 13===
<div class="toccolours mw-collapsible mw-collapsed">
====Rotations====
<div class="mw-collapsible-content">
*[[Rotation]]
*[[Angular Velocity]]
*[[Eulerian Angles]]
</div>
</div>
<div class="toccolours mw-collapsible mw-collapsed">
====Angular Momentum====
<div class="mw-collapsible-content">
*[[Total Angular Momentum]]
*[[Translational Angular Momentum]]
*[[Rotational Angular Momentum]]
*[[The Angular Momentum Principle]]
*[[Angular Momentum Compared to Linear Momentum]]
*[[Angular Impulse]]
*[[Predicting the Position of a Rotating System]]
*[[Angular Momentum of Multiparticle Systems]]
*[[The Moments of Inertia]]
*[[Moment of Inertia for a cylinder]]
*[[Right Hand Rule]]
</div>
</div>

===Week 14===
<div class="toccolours mw-collapsible mw-collapsed">
====Analyzing Motion with and without Torque====
<div class="mw-collapsible-content">
*[[Torque]]
*[[Torque 2]]
*[[Systems with Zero Torque]]
*[[Systems with Nonzero Torque]]
*[[Torque vs Work]]
*[[Gyroscopes]]
</div>
</div>

===Week 15===
<div class="toccolours mw-collapsible mw-collapsed">
====Introduction to Quantum Concepts====
<div class="mw-collapsible-content">
*[[Bohr Model]]
*[[Energy graphs and the Bohr model]]
*[[Quantized energy levels]]
*[[Quantized energy levels part II]]
*[[Entropy]]
</div>
</div>
</div>

<div style="float:left; width:30%; padding:1%;">

==Physics 2==
===Week 1===
<div class="toccolours mw-collapsible mw-collapsed">
====3D Vectors====
<div class="mw-collapsible-content">
*[[Vectors]]
*[[Right-Hand Rule]]
*[[Right Hand Rule]]
</div>
</div>

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

====Electric field====
<div class="mw-collapsible-content">
*[[Electric Field]]
*[[Electric Field and Electric Potential]]
</div>
</div>

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

====Electric force====
<div class="mw-collapsible-content">
*[[Electric Force]]
*[[Lorentz Force]]
</div>
</div>

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

====Electric field of a point particle====
<div class="mw-collapsible-content">
*[[Point Charge]]
</div>
</div>

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

====Superposition====
<div class="mw-collapsible-content">
*[[Superposition Principle]]
*[[Superposition principle]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
====Dipoles====
<div class="mw-collapsible-content">
*[[Electric Dipole]]
*[[Magnetic Dipole]]
</div>
</div>

===Week 2===
<div class="toccolours mw-collapsible mw-collapsed">
====Interactions of charged objects====
<div class="mw-collapsible-content">
*[[Electric Field]]
*[[Electric Potential]]
*[[Electric Force]]
*[[Lorentz Force]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
====Tape experiments====
<div class="mw-collapsible-content">
*[[Polarization]]
*[[Electric Polarization]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
====Polarization====
<div class="mw-collapsible-content">
*[[Polarization]]
*[[Electric Polarization]]
*[[Polarization of an Atom]]
</div>
</div>

===Week 3===
<div class="toccolours mw-collapsible mw-collapsed">
====Insulators====
<div class="mw-collapsible-content">
*[[Insulators]]
*[[Potential Difference in an Insulator]]
*[[Charged Conductor and Charged Insulator]]
*[[Charged conductor and charged insulator]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
====Conductors====
<div class="mw-collapsible-content">
*[[Conductivity]]
*[[Charge Transfer]]
*[[Resistivity]]
*[[Polarization of a conductor]]
*[[Charged Conductor and Charged Insulator]]
*[[Charged conductor and charged insulator]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
====Charging and Discharging====
<div class="mw-collapsible-content">
*[[Charge Transfer]]
*[[Electrostatic Discharge]]
*[[Charged Conductor and Charged Insulator]]
*[[Charged conductor and charged insulator]]
</div>
</div>

===Week 4===
<div class="toccolours mw-collapsible mw-collapsed">
====Field of a charged rod====
<div class="mw-collapsible-content">
*[[Charged Rod]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
====Field of a charged ring/disk/capacitor====
<div class="mw-collapsible-content">
*[[Charged Ring]]
*[[Charged Disk]]
*[[Charged Capacitor]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
====Field of a charged sphere====
<div class="mw-collapsible-content">
*[[Charged Spherical Shell]]
*[[Field of a Charged Ball]]
</div>
</div>

===Week 5===
<div class="toccolours mw-collapsible mw-collapsed">
====Potential energy====
<div class="mw-collapsible-content">
*[[Potential Energy]]
</div>
</div>

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

====Electric potential====
<div class="mw-collapsible-content">
*[[Electric Potential]]
*[[Path Independence of Electric Potential]]
*[[Potential Difference Path Independence, claimed by Aditya Mohile]]
*[[Potential Difference in a Uniform Field]]
*[[Potential Difference of Point Charge in a Non-Uniform Field]]
</div>
</div>
<div class="toccolours mw-collapsible mw-collapsed">
====Sign of a potential difference====
<div class="mw-collapsible-content">
*[[Sign of a Potential Difference]]
</div>
</div>
<div class="toccolours mw-collapsible mw-collapsed">
====Potential at a single location====
<div class="mw-collapsible-content">
*[[Electric Potential]]
*[[Potential Difference at One Location]]
</div>
</div>

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

====Path independence and round trip potential====
<div class="mw-collapsible-content">
*[[Path Independence of Electric Potential]]
*[[Potential Difference Path Independence, claimed by Aditya Mohile]]
</div>
</div>

===Week 6===
<div class="toccolours mw-collapsible mw-collapsed">
====Electric field and potential in an insulator====
<div class="mw-collapsible-content">
*[[Potential Difference in an Insulator]]
*[[Electric Field in an Insulator]]
</div>
</div>
<div class="toccolours mw-collapsible mw-collapsed">
====Moving charges in a magnetic field====
<div class="mw-collapsible-content">
*[[Magnetic Field]]
*[[Magnetic Force]]
*[[Lorentz Force]]
</div>
</div>
<div class="toccolours mw-collapsible mw-collapsed">
====Biot-Savart Law====
<div class="mw-collapsible-content">
*[[Biot-Savart Law]]
*[[Biot-Savart Law for Currents]]
</div>
</div>
<div class="toccolours mw-collapsible mw-collapsed">
====Moving charges, electron current, and conventional current====
<div class="mw-collapsible-content">
*[[Moving Point Charge]]
*[[Current]]
</div>
</div>

===Week 7===
<div class="toccolours mw-collapsible mw-collapsed">
====Magnetic field of a wire====
<div class="mw-collapsible-content">
*[[Magnetic Field of a Long Straight Wire]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
====Magnetic field of a current-carrying loop====
<div class="mw-collapsible-content">
*[[Magnetic Field of a Loop]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
====Magnetic field of a Charged Disk====
<div class="mw-collapsible-content">
*[[Magnetic Field of a Disk]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
====Magnetic dipoles====
<div class="mw-collapsible-content">
*[[Magnetic Dipole Moment]]
*[[Bar Magnet]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
====Atomic structure of magnets====
<div class="mw-collapsible-content">
*[[Atomic Structure of Magnets]]
</div>
</div>

===Week 8===
<div class="toccolours mw-collapsible mw-collapsed">
====Steady state current====
<div class="mw-collapsible-content">
*[[Steady State]]
*[[Non Steady State]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
====Kirchoff's Laws====
<div class="mw-collapsible-content">
*[[Kirchoff's Laws]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
====Electric fields and energy in circuits====
<div class="mw-collapsible-content">
*[[Series circuit]]
*[[Node Rule]]
*[[Loop Rule]]
*[[Electric Potential Difference]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
====Macroscopic analysis of circuits====
<div class="mw-collapsible-content">
*[[Series Circuits]]
*[[Parallel Circuits]]
*[[Parallel Circuits vs. Series Circuits*]]
*[[Loop Rule]]
*[[Node Rule]]
*[[Fundamentals of Resistance]]
*[[Problem Solving]]
</div>
</div>

===Week 9===
<div class="toccolours mw-collapsible mw-collapsed">
====Electric field and potential in circuits with capacitors====
<div class="mw-collapsible-content">
*[[Charging and Discharging a Capacitor]]
*[[RC Circuit]]
*[[R Circuit]]
*[[AC and DC]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
====Magnetic forces on charges and currents====
<div class="mw-collapsible-content">
*[[Magnetic Force]]
*[[Lorentz Force]]
*[[Motors and Generators]]
*[[Applying Magnetic Force to Currents]]
*[[Magnetic Force in a Moving Reference Frame]]
*[[Right-Hand Rule]]
*[[Analysis of Railgun vs Coil gun technologies]]
</div>
</div>

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

====Electric and magnetic forces====
<div class="mw-collapsible-content">
*[[Electric Force]]
*[[Magnetic Force]]
*[[Lorentz Force]]
*[[VPython Modelling of Electric and Magnetic Forces]]
</div>
</div>

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

====Velocity selector====
<div class="mw-collapsible-content">
*[[Lorentz Force]]
*[[Combining Electric and Magnetic Forces]]
</div>
</div>

===Week 10===
<div class="toccolours mw-collapsible mw-collapsed">

====Hall Effect====
<div class="mw-collapsible-content">
*[[Hall Effect]]
*[[Right-Hand Rule]]
*[[Motional Emf]]
*[[Magnetic Force]]
*[[Magnetic Torque]]
</div>
</div>

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

====Motional EMF====
<div class="mw-collapsible-content">
*[[Motional Emf]]
*[[Motional Emf using Faraday's Law]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
====Magnetic force====
<div class="mw-collapsible-content">
*[[Magnetic Force]]
*[[Lorentz Force]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
====Magnetic torque====
<div class="mw-collapsible-content">
*[[Magnetic Torque]]
*[[Right-Hand Rule]]
</div>
</div>

===Week 12===

<div class="toccolours mw-collapsible mw-collapsed">
====Gauss's Law====
<div class="mw-collapsible-content">
*[[Gauss's Flux Theorem]]
*[[Gauss's Law]]
*[[Magnetic Flux]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
====Ampere's Law====
<div class="mw-collapsible-content">
*[[Ampere's Law]]
*[[Ampere-Maxwell Law]]
*[[Magnetic Field of Coaxial Cable Using Ampere's Law]]
*[[Magnetic Field of a Long Thick Wire Using Ampere's Law]]
*[[Magnetic Field of a Toroid Using Ampere's Law]]
*[[Magnetic Field of a Solenoid Using Ampere's Law]]
*[[The Differential Form of Ampere's Law]]
</div>
</div>

===Week 13===
<div class="toccolours mw-collapsible mw-collapsed">
====Semiconductors====
<div class="mw-collapsible-content">
*[[Semiconductor Devices]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
====Faraday's Law====
<div class="mw-collapsible-content">
*[[Faraday's Law]]
*[[Motional Emf using Faraday's Law]]
*[[Lenz's Law]]

</div>
</div>

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

====Maxwell's equations====
<div class="mw-collapsible-content">
*[[Gauss's Law]]
*[[Magnetic Flux]]
*[[Ampere's Law]]
*[[Faraday's Law]]
*[[Maxwell's Electromagnetic Theory]]
</div>
</div>

===Week 14===
<div class="toccolours mw-collapsible mw-collapsed">
====Circuits revisited====
<div class="mw-collapsible-content">

</div>
</div>

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

====Inductors====
<div class="mw-collapsible-content">
*[[Inductors]]
*[[Current in an LC Circuit]]
*[[Current in an RL Circuit]]
</div>
</div>

===Week 15===
<div class="toccolours mw-collapsible mw-collapsed">
==== Electromagnetic Radiation ====
<div class="mw-collapsible-content">
*[[Electromagnetic Radiation]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
====Sparks in the air====
<div class="mw-collapsible-content">
*[[Sparks in Air]]
*[[Spark Plugs]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
====Superconductors====
<div class="mw-collapsible-content">
*[[Superconducters]]
*[[Superconductors]]
*[[Meissner effect]]
</div>
</div>
</div>

<div style="float:left; width:30%; padding:1%;">

==Physics 3==

===Week 1===
<div class="toccolours mw-collapsible mw-collapsed">
====Classical Physics====
<div class="mw-collapsible-content">
</div>
</div>

===Week 2===
<div class="toccolours mw-collapsible mw-collapsed">
====Special Relativity====
<div class="mw-collapsible-content">
*[[Frame of Reference]]
*[[Einstein's Theory of Special Relativity]]
*[[Time Dilation]]
*[[Einstein's Theory of General Relativity]]
*[[Albert A. Micheleson & Edward W. Morley]]
*[[Magnetic Force in a Moving Reference Frame]]
</div>
</div>

===Week 3===
<div class="toccolours mw-collapsible mw-collapsed">
====Photons====
<div class="mw-collapsible-content">
*[[Spontaneous Photon Emission]]
*[[Light Scattering: Why is the Sky Blue]]
*[[Lasers]]
*[[Electronic Energy Levels and Photons]]
*[[Quantum Properties of Light]]
</div>
</div>

===Week 4===
<div class="toccolours mw-collapsible mw-collapsed">
====Matter Waves====
<div class="mw-collapsible-content">
*[[Wave-Particle Duality]]
</div>
</div>

===Week 5===
<div class="toccolours mw-collapsible mw-collapsed">
====Wave Mechanics====
<div class="mw-collapsible-content">
*[[Standing Waves]]
*[[Wavelength]]
*[[Wavelength and Frequency]]
*[[Mechanical Waves]]
*[[Transverse and Longitudinal Waves]]
</div>
</div>

===Week 6===
<div class="toccolours mw-collapsible mw-collapsed">
====Rutherford-Bohr Model====
<div class="mw-collapsible-content">
*[[Rutherford Experiment and Atomic Collisions]]
*[[Bohr Model]]
*[[Quantized energy levels]]
*[[Energy graphs and the Bohr model]]
</div>
</div>

===Week 7===
<div class="toccolours mw-collapsible mw-collapsed">
====The Hydrogen Atom====
<div class="mw-collapsible-content">
*[[Quantum Theory]]
*[[Atomic Theory]]
</div>
</div>

===Week 8===
<div class="toccolours mw-collapsible mw-collapsed">
====Many-Electron Atoms====
<div class="mw-collapsible-content">
*[[Quantum Theory]]
*[[Atomic Theory]]
*[[Pauli exclusion principle]]
</div>
</div>

===Week 9===
<div class="toccolours mw-collapsible mw-collapsed">
====Molecules====
<div class="mw-collapsible-content">
</div>
</div>

===Week 10===
<div class="toccolours mw-collapsible mw-collapsed">
====Statistical Physics====
<div class="mw-collapsible-content">
</div>
</div>

===Week 11===
<div class="toccolours mw-collapsible mw-collapsed">
====Condensed Matter Physics====
<div class="mw-collapsible-content">
</div>
</div>

===Week 12===
<div class="toccolours mw-collapsible mw-collapsed">
====The Nucleus====
<div class="mw-collapsible-content">
*[[Nucleus]]
</div>
</div>

===Week 13===
<div class="toccolours mw-collapsible mw-collapsed">
====Nuclear Physics====
<div class="mw-collapsible-content">
*[[Nuclear Fission]]
*[[Nuclear Energy from Fission and Fusion]]
</div>
</div>

===Week 14===
<div class="toccolours mw-collapsible mw-collapsed">
====Particle Physics====
<div class="mw-collapsible-content">
*[[Elementary Particles and Particle Physics Theory]]
*[[String Theory]]
</div>
</div>
</div>

Main Page

2018-09-16T04:08:24Z

Htaghian3: /* Thermal Energy, Dissipation, and Transfer of Energy */

__NOTOC__
= '''Georgia Tech Student Wiki for Introductory Physics.''' =

This resource 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 for future students!

Looking to make a contribution?
#Pick one of the topics from intro physics listed below
#Add content to that topic or improve the quality of what is already there.
#Need to make a new topic? Edit this page and add it to the list under the appropriate category. Then 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 written for students by a physics expert [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes MSU Physics Wiki]
* 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 intro physics textbooks: [https://openstax.org/details/books/university-physics-volume-1 Vol1], [https://openstax.org/details/books/university-physics-volume-2 Vol2], [https://openstax.org/details/books/university-physics-volume-3 Vol3]
* 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]
* The Feynman lectures on physics are free to read [http://www.feynmanlectures.caltech.edu/ Feynman]
* Final Study Guide for Modern Physics II created by a lab TA [https://docs.google.com/document/d/1_6GktDPq5tiNFFYs_ZjgjxBAWVQYaXp_2Imha4_nSyc/edit?usp=sharing Modern Physics II Final Study Guide]

== 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]]
* A page for review of [[Vectors]] and vector operations
* A listing of [[Notable Scientist]] with links to their individual pages

<div style="float:left; width:30%; padding:1%;">
==Physics 1==
===Week 1===
<div class="toccolours mw-collapsible mw-collapsed">
====Help with VPython====
<div class="mw-collapsible-content">
*[[Python Syntax]]
</div>
</div>

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

====Vectors and Units====

<div class="mw-collapsible-content">
*[[Vectors]]
*[[SI Units]]
</div>
</div>

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

====VPython====

<div class="mw-collapsible-content">
*[[VPython]]
*[[VPython basics]]
*[[VPython Common Errors and Troubleshooting]]
*[[VPython Functions]]
*[[VPython Lists]]
*[[VPython Loops]]
*[[VPython Multithreading]]
*[[VPython Animation]]
*[[VPython Objects]]
*[[VPython 3D Objects]]
*[[VPython Reference]]
*[[VPython MapReduceFilter]]
*[[VPython GUIs]]
</div>
</div>

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

====Vectors and Units====
<div class="mw-collapsible-content">
*[[Vectors]]
*[[SI Units]]
</div>
</div>

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

====Interactions====
<div class="mw-collapsible-content">
*[[Types of Interactions and How to Detect Them]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
====Velocity and Momentum====
<div class="mw-collapsible-content">
*[[Newton's First Law of Motion]]
*[[Velocity]]
*[[Mass]]
*[[Speed and Velocity]]
*[[Relative Velocity]]
*[[Derivation of Average Velocity]]
*[[2-Dimensional Motion]]
*[[3-Dimensional Position and Motion]]
</div>
</div>

===Week 2===
<div class="toccolours mw-collapsible mw-collapsed">
====Momentum and the Momentum Principle====
<div class="mw-collapsible-content">
*[[Momentum Principle]]
*[[Inertia]]
*[[Net Force]]
*[[Derivation of the Momentum Principle]]
*[[Impulse Momentum]]
*[[Acceleration]]
*[[Momentum with respect to external Forces]]
*[[Relativistic Momentum]]
</div>
</div>

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

====Iterative Prediction with a Constant Force====
<div class="mw-collapsible-content">
*[[Newton’s Second Law of Motion]]
*[[Iterative Prediction]]
*[[Kinematics]]
*[[Newton’s Laws and Linear Momentum]]
*[[Projectile Motion]]
</div>
</div>

===Week 3===
<div class="toccolours mw-collapsible mw-collapsed">

====Analytic Prediction with a Constant Force====
<div class="mw-collapsible-content">
*[[Analytical Prediction]]
</div>
</div>

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

====Iterative Prediction with a Varying Force====
<div class="mw-collapsible-content">
*[[Predicting Change in multiple dimensions]]
*[[Spring Force]]
*[[Hooke's Law]]
*[[Simple Harmonic Motion]]
*[[Iterative Prediction of Spring-Mass System]]
*[[Terminal Speed]]
*[[Determinism]]
</div>
</div>

===Week 4===
<div class="toccolours mw-collapsible mw-collapsed">
====Fundamental Interactions====
<div class="mw-collapsible-content">

==Main Idea==

*[[Gravitational Force]]
*[[Fluid Mechanics]]
*[[An Application of Gravitational Potential]]
*[[Electric Force]]
*[[Reciprocity]]
</div>
</div>

===Week 5===
<div class="toccolours mw-collapsible mw-collapsed">
====Conservation of Momentum====
<div class="mw-collapsible-content">
*[[Conservation of Momentum]]
</div>
</div>
<div class="toccolours mw-collapsible mw-collapsed">

====Properties of Matter====
<div class="mw-collapsible-content">
*[[Kinds of Matter]]
*[[Ball and Spring Model of Matter]]
*[[Density]]
*[[Length and Stiffness of an Interatomic Bond]]
*[[Young's Modulus]]
*[[Speed of Sound in Solids]]
*[[Malleability]]
*[[Ductility]]
*[[Weight]]
*[[Hardness]]
*[[Boiling Point]]
*[[Melting Point]]
*[[Change of State]]
</div>
</div>

===Week 6===
<div class="toccolours mw-collapsible mw-collapsed">
====Identifying Forces====
<div class="mw-collapsible-content">
*[[Free Body Diagram]]
*[[Inclined Plane]]
*[[Compression or Normal Force]]
*[[Tension]]
</div>
</div>
<div class="toccolours mw-collapsible mw-collapsed">

====Curving Motion====
<div class="mw-collapsible-content">
*[[Curving Motion]]
*[[Centripetal Force and Curving Motion]]
*[[Perpetual Freefall (Orbit)]]
</div>
</div>

===Week 7===
<div class="toccolours mw-collapsible mw-collapsed">
====Energy Principle====
<div class="mw-collapsible-content">
*[[The Energy Principle]]
*[[Conservation of Energy]]
*[[Kinetic Energy]]
*[[Work]]
*[[Power (Mechanical)]]
</div>
</div>

===Week 8===
<div class="toccolours mw-collapsible mw-collapsed">
====Work by Non-Constant Forces====
<div class="mw-collapsible-content">
*[[Work Done By A Nonconstant Force]]
</div>
</div>
<div class="toccolours mw-collapsible mw-collapsed">
====Potential Energy====
<div class="mw-collapsible-content">
*[[Potential Energy]]
*[[Potential Energy of Macroscopic Springs]]
*[[Spring Potential Energy]]
*[[Ball and Spring Model]]
*[[Gravitational Potential Energy]]
*[[Energy Graphs]]
*[[Escape Velocity]]
</div>
</div>

===Week 9===
<div class="toccolours mw-collapsible mw-collapsed">
====Multiparticle Systems====
<div class="mw-collapsible-content">
*[[Center of Mass]]
*[[Multi-particle analysis of Momentum]]
*[[Momentum with respect to external Forces]]
*[[Potential Energy of a Multiparticle System]]
*[[Work and Energy for an Extended System]]
*[[Internal Energy]]
**[[Potential Energy of a Pair of Neutral Atoms]]
</div>
</div>

===Week 10===
<div class="toccolours mw-collapsible mw-collapsed">
====Choice of System====
<div class="mw-collapsible-content">
*[[System & Surroundings]]
</div>
</div>
<div class="toccolours mw-collapsible mw-collapsed">
====Thermal Energy, Dissipation, and Transfer of Energy====
<div class="mw-collapsible-content">
*[[Thermal Energy]]
*[[Specific Heat]]
*[[Heat Capacity]]
*[[Calorific Value(Heat of combustion)]]
*[[Specific Heat Capacity]]
*[[First Law of Thermodynamics]]
*[[Second Law of Thermodynamics and Entropy]]
*[[Temperature]]
*[[Predicting Change]]
*[[Energy Transfer due to a Temperature Difference]]
*[[Transformation of Energy]]
*[[The Maxwell-Boltzmann Distribution]]
*[[Air Resistance]]
</div>
</div>
<div class="toccolours mw-collapsible mw-collapsed">

====Rotational and Vibrational Energy====
<div class="mw-collapsible-content">
*[[Translational, Rotational and Vibrational Energy]]
</div>
</div>

===Week 11===
<div class="toccolours mw-collapsible mw-collapsed">
====Different Models of a System====
<div class="mw-collapsible-content">
*[[Point Particle Systems]]
*[[Real Systems]]
</div>
</div>
<div class="toccolours mw-collapsible mw-collapsed">
====Models of Friction====
<div class="mw-collapsible-content">
*[[Friction]]
*[[Static Friction]]
</div>
</div>

===Week 12===
<div class="toccolours mw-collapsible mw-collapsed">
====Collisions====
<div class="mw-collapsible-content">
*[[Newton's Third Law of Motion]]
*[[Collisions]]
*[[Elastic Collisions]]
*[[Inelastic Collisions]]
*[[Maximally Inelastic Collision]]
*[[Head-on Collision of Equal Masses]]
*[[Head-on Collision of Unequal Masses]]
*[[Scattering: Collisions in 2D and 3D]]
*[[Rutherford Experiment and Atomic Collisions]]
*[[Coefficient of Restitution]]
</div>
</div>

===Week 13===
<div class="toccolours mw-collapsible mw-collapsed">
====Rotations====
<div class="mw-collapsible-content">
*[[Rotation]]
*[[Angular Velocity]]
*[[Eulerian Angles]]
</div>
</div>
<div class="toccolours mw-collapsible mw-collapsed">
====Angular Momentum====
<div class="mw-collapsible-content">
*[[Total Angular Momentum]]
*[[Translational Angular Momentum]]
*[[Rotational Angular Momentum]]
*[[The Angular Momentum Principle]]
*[[Angular Momentum Compared to Linear Momentum]]
*[[Angular Impulse]]
*[[Predicting the Position of a Rotating System]]
*[[Angular Momentum of Multiparticle Systems]]
*[[The Moments of Inertia]]
*[[Moment of Inertia for a cylinder]]
*[[Right Hand Rule]]
</div>
</div>

===Week 14===
<div class="toccolours mw-collapsible mw-collapsed">
====Analyzing Motion with and without Torque====
<div class="mw-collapsible-content">
*[[Torque]]
*[[Torque 2]]
*[[Systems with Zero Torque]]
*[[Systems with Nonzero Torque]]
*[[Torque vs Work]]
*[[Gyroscopes]]
</div>
</div>

===Week 15===
<div class="toccolours mw-collapsible mw-collapsed">
====Introduction to Quantum Concepts====
<div class="mw-collapsible-content">
*[[Bohr Model]]
*[[Energy graphs and the Bohr model]]
*[[Quantized energy levels]]
*[[Quantized energy levels part II]]
*[[Entropy]]
</div>
</div>
</div>

<div style="float:left; width:30%; padding:1%;">

==Physics 2==
===Week 1===
<div class="toccolours mw-collapsible mw-collapsed">
====3D Vectors====
<div class="mw-collapsible-content">
*[[Vectors]]
*[[Right-Hand Rule]]
*[[Right Hand Rule]]
</div>
</div>

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

====Electric field====
<div class="mw-collapsible-content">
*[[Electric Field]]
*[[Electric Field and Electric Potential]]
</div>
</div>

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

====Electric force====
<div class="mw-collapsible-content">
*[[Electric Force]]
*[[Lorentz Force]]
</div>
</div>

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

====Electric field of a point particle====
<div class="mw-collapsible-content">
*[[Point Charge]]
</div>
</div>

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

====Superposition====
<div class="mw-collapsible-content">
*[[Superposition Principle]]
*[[Superposition principle]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
====Dipoles====
<div class="mw-collapsible-content">
*[[Electric Dipole]]
*[[Magnetic Dipole]]
</div>
</div>

===Week 2===
<div class="toccolours mw-collapsible mw-collapsed">
====Interactions of charged objects====
<div class="mw-collapsible-content">
*[[Electric Field]]
*[[Electric Potential]]
*[[Electric Force]]
*[[Lorentz Force]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
====Tape experiments====
<div class="mw-collapsible-content">
*[[Polarization]]
*[[Electric Polarization]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
====Polarization====
<div class="mw-collapsible-content">
*[[Polarization]]
*[[Electric Polarization]]
*[[Polarization of an Atom]]
</div>
</div>

===Week 3===
<div class="toccolours mw-collapsible mw-collapsed">
====Insulators====
<div class="mw-collapsible-content">
*[[Insulators]]
*[[Potential Difference in an Insulator]]
*[[Charged Conductor and Charged Insulator]]
*[[Charged conductor and charged insulator]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
====Conductors====
<div class="mw-collapsible-content">
*[[Conductivity]]
*[[Charge Transfer]]
*[[Resistivity]]
*[[Polarization of a conductor]]
*[[Charged Conductor and Charged Insulator]]
*[[Charged conductor and charged insulator]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
====Charging and discharging====
<div class="mw-collapsible-content">
*[[Charge Transfer]]
*[[Electrostatic Discharge]]
*[[Charged Conductor and Charged Insulator]]
*[[Charged conductor and charged insulator]]
</div>
</div>

===Week 4===
<div class="toccolours mw-collapsible mw-collapsed">
====Field of a charged rod====
<div class="mw-collapsible-content">
*[[Charged Rod]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
====Field of a charged ring/disk/capacitor====
<div class="mw-collapsible-content">
*[[Charged Ring]]
*[[Charged Disk]]
*[[Charged Capacitor]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
====Field of a charged sphere====
<div class="mw-collapsible-content">
*[[Charged Spherical Shell]]
*[[Field of a Charged Ball]]
</div>
</div>

===Week 5===
<div class="toccolours mw-collapsible mw-collapsed">
====Potential energy====
<div class="mw-collapsible-content">
*[[Potential Energy]]
</div>
</div>

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

====Electric potential====
<div class="mw-collapsible-content">
*[[Electric Potential]]
*[[Path Independence of Electric Potential]]
*[[Potential Difference Path Independence, claimed by Aditya Mohile]]
*[[Potential Difference in a Uniform Field]]
*[[Potential Difference of Point Charge in a Non-Uniform Field]]
</div>
</div>
<div class="toccolours mw-collapsible mw-collapsed">
====Sign of a potential difference====
<div class="mw-collapsible-content">
*[[Sign of a Potential Difference]]
</div>
</div>
<div class="toccolours mw-collapsible mw-collapsed">
====Potential at a single location====
<div class="mw-collapsible-content">
*[[Electric Potential]]
*[[Potential Difference at One Location]]
</div>
</div>

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

====Path independence and round trip potential====
<div class="mw-collapsible-content">
*[[Path Independence of Electric Potential]]
*[[Potential Difference Path Independence, claimed by Aditya Mohile]]
</div>
</div>

===Week 6===
<div class="toccolours mw-collapsible mw-collapsed">
====Electric field and potential in an insulator====
<div class="mw-collapsible-content">
*[[Potential Difference in an Insulator]]
*[[Electric Field in an Insulator]]
</div>
</div>
<div class="toccolours mw-collapsible mw-collapsed">
====Moving charges in a magnetic field====
<div class="mw-collapsible-content">
*[[Magnetic Field]]
*[[Magnetic Force]]
*[[Lorentz Force]]
</div>
</div>
<div class="toccolours mw-collapsible mw-collapsed">
====Biot-Savart Law====
<div class="mw-collapsible-content">
*[[Biot-Savart Law]]
*[[Biot-Savart Law for Currents]]
</div>
</div>
<div class="toccolours mw-collapsible mw-collapsed">
====Moving charges, electron current, and conventional current====
<div class="mw-collapsible-content">
*[[Moving Point Charge]]
*[[Current]]
</div>
</div>

===Week 7===
<div class="toccolours mw-collapsible mw-collapsed">
====Magnetic field of a wire====
<div class="mw-collapsible-content">
*[[Magnetic Field of a Long Straight Wire]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
====Magnetic field of a current-carrying loop====
<div class="mw-collapsible-content">
*[[Magnetic Field of a Loop]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
====Magnetic field of a Charged Disk====
<div class="mw-collapsible-content">
*[[Magnetic Field of a Disk]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
====Magnetic dipoles====
<div class="mw-collapsible-content">
*[[Magnetic Dipole Moment]]
*[[Bar Magnet]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
====Atomic structure of magnets====
<div class="mw-collapsible-content">
*[[Atomic Structure of Magnets]]
</div>
</div>

===Week 8===
<div class="toccolours mw-collapsible mw-collapsed">
====Steady state current====
<div class="mw-collapsible-content">
*[[Steady State]]
*[[Non Steady State]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
====Kirchoff's Laws====
<div class="mw-collapsible-content">
*[[Kirchoff's Laws]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
====Electric fields and energy in circuits====
<div class="mw-collapsible-content">
*[[Series circuit]]
*[[Node Rule]]
*[[Loop Rule]]
*[[Electric Potential Difference]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
====Macroscopic analysis of circuits====
<div class="mw-collapsible-content">
*[[Series Circuits]]
*[[Parallel Circuits]]
*[[Parallel Circuits vs. Series Circuits*]]
*[[Loop Rule]]
*[[Node Rule]]
*[[Fundamentals of Resistance]]
*[[Problem Solving]]
</div>
</div>

===Week 9===
<div class="toccolours mw-collapsible mw-collapsed">
====Electric field and potential in circuits with capacitors====
<div class="mw-collapsible-content">
*[[Charging and Discharging a Capacitor]]
*[[RC Circuit]]
*[[R Circuit]]
*[[AC and DC]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
====Magnetic forces on charges and currents====
<div class="mw-collapsible-content">
*[[Magnetic Force]]
*[[Lorentz Force]]
*[[Motors and Generators]]
*[[Applying Magnetic Force to Currents]]
*[[Magnetic Force in a Moving Reference Frame]]
*[[Right-Hand Rule]]
*[[Analysis of Railgun vs Coil gun technologies]]
</div>
</div>

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

====Electric and magnetic forces====
<div class="mw-collapsible-content">
*[[Electric Force]]
*[[Magnetic Force]]
*[[Lorentz Force]]
*[[VPython Modelling of Electric and Magnetic Forces]]
</div>
</div>

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

====Velocity selector====
<div class="mw-collapsible-content">
*[[Lorentz Force]]
*[[Combining Electric and Magnetic Forces]]
</div>
</div>

===Week 10===
<div class="toccolours mw-collapsible mw-collapsed">

====Hall Effect====
<div class="mw-collapsible-content">
*[[Hall Effect]]
*[[Right-Hand Rule]]
*[[Motional Emf]]
*[[Magnetic Force]]
*[[Magnetic Torque]]
</div>
</div>

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

====Motional EMF====
<div class="mw-collapsible-content">
*[[Motional Emf]]
*[[Motional Emf using Faraday's Law]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
====Magnetic force====
<div class="mw-collapsible-content">
*[[Magnetic Force]]
*[[Lorentz Force]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
====Magnetic torque====
<div class="mw-collapsible-content">
*[[Magnetic Torque]]
*[[Right-Hand Rule]]
</div>
</div>

===Week 12===

<div class="toccolours mw-collapsible mw-collapsed">
====Gauss's Law====
<div class="mw-collapsible-content">
*[[Gauss's Flux Theorem]]
*[[Gauss's Law]]
*[[Magnetic Flux]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
====Ampere's Law====
<div class="mw-collapsible-content">
*[[Ampere's Law]]
*[[Ampere-Maxwell Law]]
*[[Magnetic Field of Coaxial Cable Using Ampere's Law]]
*[[Magnetic Field of a Long Thick Wire Using Ampere's Law]]
*[[Magnetic Field of a Toroid Using Ampere's Law]]
*[[Magnetic Field of a Solenoid Using Ampere's Law]]
*[[The Differential Form of Ampere's Law]]
</div>
</div>

===Week 13===
<div class="toccolours mw-collapsible mw-collapsed">
====Semiconductors====
<div class="mw-collapsible-content">
*[[Semiconductor Devices]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
====Faraday's Law====
<div class="mw-collapsible-content">
*[[Faraday's Law]]
*[[Motional Emf using Faraday's Law]]
*[[Lenz's Law]]

</div>
</div>

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

====Maxwell's equations====
<div class="mw-collapsible-content">
*[[Gauss's Law]]
*[[Magnetic Flux]]
*[[Ampere's Law]]
*[[Faraday's Law]]
*[[Maxwell's Electromagnetic Theory]]
</div>
</div>

===Week 14===
<div class="toccolours mw-collapsible mw-collapsed">
====Circuits revisited====
<div class="mw-collapsible-content">

</div>
</div>

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

====Inductors====
<div class="mw-collapsible-content">
*[[Inductors]]
*[[Current in an LC Circuit]]
*[[Current in an RL Circuit]]
</div>
</div>

===Week 15===
<div class="toccolours mw-collapsible mw-collapsed">
==== Electromagnetic Radiation ====
<div class="mw-collapsible-content">
*[[Electromagnetic Radiation]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
====Sparks in the air====
<div class="mw-collapsible-content">
*[[Sparks in Air]]
*[[Spark Plugs]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
====Superconductors====
<div class="mw-collapsible-content">
*[[Superconducters]]
*[[Superconductors]]
*[[Meissner effect]]
</div>
</div>
</div>

<div style="float:left; width:30%; padding:1%;">

==Physics 3==

===Week 1===
<div class="toccolours mw-collapsible mw-collapsed">
====Classical Physics====
<div class="mw-collapsible-content">
</div>
</div>

===Week 2===
<div class="toccolours mw-collapsible mw-collapsed">
====Special Relativity====
<div class="mw-collapsible-content">
*[[Frame of Reference]]
*[[Einstein's Theory of Special Relativity]]
*[[Time Dilation]]
*[[Einstein's Theory of General Relativity]]
*[[Albert A. Micheleson & Edward W. Morley]]
*[[Magnetic Force in a Moving Reference Frame]]
</div>
</div>

===Week 3===
<div class="toccolours mw-collapsible mw-collapsed">
====Photons====
<div class="mw-collapsible-content">
*[[Spontaneous Photon Emission]]
*[[Light Scattering: Why is the Sky Blue]]
*[[Lasers]]
*[[Electronic Energy Levels and Photons]]
*[[Quantum Properties of Light]]
</div>
</div>

===Week 4===
<div class="toccolours mw-collapsible mw-collapsed">
====Matter Waves====
<div class="mw-collapsible-content">
*[[Wave-Particle Duality]]
</div>
</div>

===Week 5===
<div class="toccolours mw-collapsible mw-collapsed">
====Wave Mechanics====
<div class="mw-collapsible-content">
*[[Standing Waves]]
*[[Wavelength]]
*[[Wavelength and Frequency]]
*[[Mechanical Waves]]
*[[Transverse and Longitudinal Waves]]
</div>
</div>

===Week 6===
<div class="toccolours mw-collapsible mw-collapsed">
====Rutherford-Bohr Model====
<div class="mw-collapsible-content">
*[[Rutherford Experiment and Atomic Collisions]]
*[[Bohr Model]]
*[[Quantized energy levels]]
*[[Energy graphs and the Bohr model]]
</div>
</div>

===Week 7===
<div class="toccolours mw-collapsible mw-collapsed">
====The Hydrogen Atom====
<div class="mw-collapsible-content">
*[[Quantum Theory]]
*[[Atomic Theory]]
</div>
</div>

===Week 8===
<div class="toccolours mw-collapsible mw-collapsed">
====Many-Electron Atoms====
<div class="mw-collapsible-content">
*[[Quantum Theory]]
*[[Atomic Theory]]
*[[Pauli exclusion principle]]
</div>
</div>

===Week 9===
<div class="toccolours mw-collapsible mw-collapsed">
====Molecules====
<div class="mw-collapsible-content">
</div>
</div>

===Week 10===
<div class="toccolours mw-collapsible mw-collapsed">
====Statistical Physics====
<div class="mw-collapsible-content">
</div>
</div>

===Week 11===
<div class="toccolours mw-collapsible mw-collapsed">
====Condensed Matter Physics====
<div class="mw-collapsible-content">
</div>
</div>

===Week 12===
<div class="toccolours mw-collapsible mw-collapsed">
====The Nucleus====
<div class="mw-collapsible-content">
*[[Nucleus]]
</div>
</div>

===Week 13===
<div class="toccolours mw-collapsible mw-collapsed">
====Nuclear Physics====
<div class="mw-collapsible-content">
*[[Nuclear Fission]]
*[[Nuclear Energy from Fission and Fusion]]
</div>
</div>

===Week 14===
<div class="toccolours mw-collapsible mw-collapsed">
====Particle Physics====
<div class="mw-collapsible-content">
*[[Elementary Particles and Particle Physics Theory]]
*[[String Theory]]
</div>
</div>
</div>