Speed and Velocity: Difference between revisions
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by Elisa Mercando | |||
==Path Independence== | |||
== | |||
The potential difference between two locations does not depend on the path taken between the locations chosen. | |||
A | ===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]] | |||
Therefore, the potential difference A and C is | 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. | Put this idea in historical context. Give the reader the Who, What, When, Where, and Why. | ||
See also | == 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? | |||
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 | Books, Articles or other print media on this topic | ||
External links | ===External links=== | ||
Internet resources on this topic | Internet resources on this topic | ||
References | ==References== | ||
This section contains the the references you used while writing this page | This section contains the the references you used while writing this page | ||
[[Category:Which Category did you place this in?]] | |||
Revision as of 12:58, 30 November 2015
by Elisa Mercando
Path Independence
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]\displaystyle{ 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 Teach hands-on with GlowScript
Simple Example
In this example, the electric field is equal to [math]\displaystyle{ 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]\displaystyle{ dV = V_C - V_A }[/math].
Since there are no y and z components of the electric field, the potential difference is [math]\displaystyle{ dV = -\left(E_x*\left(x_1 - 0\right) + 0*\left(-y_1 - 0\right) + 0*0\right) = -E_x*x_1 }[/math]
Let's say there is a location B at [math]\displaystyle{ \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]\displaystyle{ 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]\displaystyle{ 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]\displaystyle{ 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