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| Path Independence
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| (Redirected from Template)
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| by Elisa Mercando
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| Contents [hide]
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| 1 Path Independence
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| 1.1 A Mathematical Model
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| 1.2 A Computational Model
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| 2 Simple Example
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| 2.1 Connectedness
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| 2.2 History
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| 2.3 See also
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| 2.3.1 Further reading
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| 2.3.2 External links
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| 2.4 References
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| Path Independence[edit]
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| The potential difference between two locations does not depend on the path taken between the locations chosen.
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| A Mathematical Model[edit]
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| In order to find the potential difference between two locations, we use this formula dV=−(Ex∗dx+Ey∗dy+Ez∗dz), 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.
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| A Computational Model[edit]
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| How do we visualize or predict using this topic. Consider embedding some vpython code here Teach hands-on with GlowScript
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| Simple Example[edit]
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| Pathindependence.png
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| In this example, the electric field is equal to E=(Ex,0,0). The initial location is A and the final location is C. In order to find the potential difference between A and C, we use dV=VC−VA.
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| Since there are no y and z components of the electric field, the potential difference is dV=−(Ex∗(x1−0)+0∗(−y1−0)+0∗0)=−Ex∗x1
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| BC.png
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| Let's say there is a location B at (x1,0,0). 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.
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| The potential difference between A and B is dV=VB−VA=−(Ex∗(x1−0)+0∗0+0∗0)=−Ex∗x1.
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| The potential difference between B and C is dV=VC−VB=−(Ex∗0+0∗(−y1−0)+0∗0)=0.
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| Therefore, the potential difference A and C is VC−VA=(VC−VB)+(VB−VA)=Ex∗x1, which is the same answer that we got when we did not use location B.
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| Connectedness[edit]
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| How is this topic connected to something that you are interested in?
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| How is it connected to your major?
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| Is there an interesting industrial application?
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| History[edit]
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| Put this idea in historical context. Give the reader the Who, What, When, Where, and Why.
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| See also[edit]
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| Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?
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| Further reading[edit]
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| Books, Articles or other print media on this topic
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| External links[edit]
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| Internet resources on this topic
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| References[edit]
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| This section contains the the references you used while writing this page
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