|
|
| (77 intermediate revisions by 6 users not shown) |
| Line 1: |
Line 1: |
| by Matt Schoonover
| | The content on this page has been moved to the page [[Speed vs Velocity]]. |
|
| |
|
| ==Speed and Velocity==
| | This page should be deleted. |
| | |
| The potential difference between two locations does not depend on the path taken between the locations chosen.
| |
| | |
| ===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.
| |
| | |
| ===A Computational Model===
| |
| | |
| How do we visualize or predict using this topic. Consider embedding some vpython code here [https://trinket.io/glowscript/31d0f9ad9e Teach hands-on with GlowScript]
| |
| | |
| =Simple Example=
| |
| [[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>.
| |
| | |
| 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.
| |
| | |
| ==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.
| |
| | |
| == See also ==
| |
| | |
| Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?
| |
| | |
| ===Further reading===
| |
| | |
| Books, Articles or other print media on this topic
| |
| | |
| ===External links===
| |
| | |
| Internet resources on this topic
| |
| | |
| ==References==
| |
| | |
| This section contains the the references you used while writing this page | |
| | |
| [[Category:Which Category did you place this in?]]
| |