Potential Difference Path Independence
The potential difference [math]\displaystyle{ \Delta V = V_B - V_A }[/math] between two locations A and B does not depend on the path taken between the locations.
Claimed alanghauser3
The Main Idea
The potential difference between two locations A and B does not depend on the path taken between the locations. A round trip potential difference is always zero.
A Mathematical Model
In a uniform electric field the potential difference is equal to
- [math]\displaystyle{ \Delta V }[/math] = -[math]\displaystyle{ \vec{E} }[/math]●[math]\displaystyle{ \Delta \vec{l} }[/math] = = -(Ex●[math]\displaystyle{ \Delta x }[/math] + Ey●[math]\displaystyle{ \Delta y }[/math] + Ez●[math]\displaystyle{ \Delta z }[/math]), units = Volts (V)
In a nonuniform electric field the potential difference is equal to [math]\displaystyle{ \textstyle\int\limits_{i}^{f}-Edl }[/math]
A Computational Model
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