Motional Emf using Faraday's Law

Path Independence (Redirected from Template) by Elisa Mercando

Contents [hide] 1 Path Independence 1.1 A Mathematical Model 1.2 A Computational Model 2 Simple Example 2.1 Connectedness 2.2 History 2.3 See also 2.3.1 Further reading 2.3.2 External links 2.4 References Path Independence[edit] The potential difference between two locations does not depend on the path taken between the locations chosen.

A Mathematical Model[edit] 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.

A Computational Model[edit] How do we visualize or predict using this topic. Consider embedding some vpython code here Teach hands-on with GlowScript

Simple Example[edit] Pathindependence.png

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.

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

BC.png

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.

The potential difference between A and B is dV=VB−VA=−(Ex∗(x1−0)+0∗0+0∗0)=−Ex∗x1.

The potential difference between B and C is dV=VC−VB=−(Ex∗0+0∗(−y1−0)+0∗0)=0.

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.

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

See also[edit] 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[edit] Books, Articles or other print media on this topic

External links[edit] Internet resources on this topic

References[edit] This section contains the the references you used while writing this page

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