Path Independence: Difference between revisions

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===A Mathematical Model===
===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.
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.
 
[[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>


===A Computational Model===
===A Computational Model===

Revision as of 13:30, 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

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