Speed and Velocity
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Speed and Velocity
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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.
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