Potential Difference Path Independence: Difference between revisions
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In a nonuniform electric field the potential difference is equal to | In a nonuniform electric field the potential difference is equal to | ||
<math> \textstyle\int\limits_{i}^{f}-Edl </math> | <math> \textstyle\int\limits_{i}^{f}-Edl </math> | ||
==Examples== | ==Examples== | ||
===Simple Example of Two Different Paths=== | |||
Calculate the potential difference going from A to C: <math>Delta V = V_C - V_A = ?<\math> | |||
===Simple=== | |||
===Middling=== | ===Middling=== | ||
===Difficult=== | ===Difficult=== | ||
Revision as of 13:29, 1 December 2015
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]
Examples
Simple Example of Two Different Paths
Calculate the potential difference going from A to C: <math>Delta V = V_C - V_A = ?<\math>
Middling
Difficult
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