Path Independence: Difference between revisions

Revision as of 19:12, 30 November 2015

PLEASE DO NOT EDIT THIS PAGE. COPY THIS TEMPLATE AND PASTE IT INTO A NEW PAGE FOR YOUR TOPIC.

Short Description of Topic

The Main Idea

State, in your own words, the main idea for this topic Electric Field of Capacitor

A Mathematical Model

What are the mathematical equations that allow us to model this topic. For example [math]\displaystyle{ {\frac{d\vec{p}}{dt}}_{system} = \vec{F}_{net} }[/math] where p is the momentum of the system and F is the net force from the surroundings.

A Computational Model

How do we visualize or predict using this topic. Consider embedding some vpython code here Teach hands-on with GlowScript

Examples

Be sure to show all steps in your solution and include diagrams whenever possible

Simple

Middling

Difficult

Connectedness

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

History

Put this idea in historical context. Give the reader the Who, What, When, Where, and Why.

@@ Line 1: / Line 1: @@
-by Elisa Mercando
+PLEASE DO NOT EDIT THIS PAGE. COPY THIS TEMPLATE AND PASTE IT INTO A NEW PAGE FOR YOUR TOPIC.
-==Path Independence==
+Short Description of Topic
-The potential difference between two locations does not depend on the path taken between the locations chosen.
+==The Main Idea==
+State, in your own words, the main idea for this topic
+Electric Field of Capacitor
 ===A Mathematical Model===
-In order to find the potential difference between two locations, we use this formula <math> dV = -\left(E_x*dx + E_y*dy + E_z*dz\right) </math>,  where '''E''' is the electric field with components in the x, y, and z directions. Delta x, y, and z are the components of final location minus to the components of the initial location.
+What are the mathematical equations that allow us to model this topic.  For example <math>{\frac{d\vec{p}}{dt}}_{system} = \vec{F}_{net}</math> where '''p''' is the momentum of the system and '''F''' is the net force from the surroundings.
 ===A Computational Model===
@@ Line 13: / Line 16: @@
 How do we visualize or predict using this topic. Consider embedding some vpython code here [https://trinket.io/glowscript/31d0f9ad9e Teach hands-on with GlowScript]
-=Simple Example=
+==Examples==
-[[File:pathindependence.png]]
-In this example, the electric field is equal to <math> E = \left(E_x, 0, 0\right)</math>. The initial location is A and the final location is C. In order to find the potential difference between A and C, we use <math>dV = V_C - V_A </math>.
-Since there are no y and z components of the electric field, the potential difference is <math> dV = -\left(E_x*\left(x_1 - 0\right) + 0*\left(-y_1 - 0\right) + 0*0\right)  = -E_x*x_1</math>
-[[File:BC.png]]
-Let's say there is a location B at <math> \left(x_1, 0, 0\right) </math>. Now in order to find the potential difference between A and C, we need to find the potential difference between A and B and then between B and C.
-The potential difference between A and B is <math>dV = V_B - V_A = -\left(E_x*\left(x_1 - 0\right) + 0*0 + 0*0\right) = -E_x*x_1</math>.
-The potential difference between B and C is <math>dV = V_C - V_B = -\left(E_x*0 + 0*\left(-y_1 - 0\right) + 0*0\right) = 0</math>.
+Be sure to show all steps in your solution and include diagrams whenever possible
-Therefore, the potential difference A and C is <math>V_C - V_A = \left(V_C - V_B\right) + \left(V_B - V_A\right) = E_x*x_1 </math>, which is the same answer that we got when we did not use location B.
+===Simple===
+===Middling===
+===Difficult===
 ==Connectedness==

Path Independence: Difference between revisions

Revision as of 19:12, 30 November 2015

Contents

The Main Idea

A Mathematical Model

A Computational Model

Examples

Simple

Middling

Difficult

Connectedness

History

See also

Further reading

External links

References

Navigation menu