View source for Potential DIfference Path Independence, claimed by Aditya Mohile



==Primary Concept==

The voltage between 2 points does not depend on the path taken to travel from one point to another.

===A Mathematical Understanding===
:<math>\Delta V_{AB}= - \int^B_A \vec{E} \cdot d\vec{l}</math>
The potential difference from A to B is found by integrating the electric field with respect to the distance between the two points.
:<math>\Delta V_{AB}=  {E} \int^B_A d\vec{l}</math>
Here, E is uniform and constant and can be isolated outside of the integral.
:<math>\Delta V_{AB} = {E}\Delta l_{AB}</math>
From this final statement, The potential difference is equivalent to the uniform electric field in the region multiplied by the change in position of the charge from A to B. As a result, it is clear that regardless of the how we get from A to B the only distance that matters is the distance between the final and initial point of the charge acted on. This indicates that the potential difference is "path independent".
===A Visual Representation===
[[File:Path_Independence.jpeg]]

==Examples==

===Example 1===

===Example 2===

===Example 3===

==References==


[[Category:Fields]]