Sign of Potential Difference: Difference between revisions
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Potential difference is the product of the electric field <math>\vec{E}</math> and the relative path <math>\Delta x</math>: | Potential difference is the product of the electric field <math>\vec{E}</math> and the relative path <math>\Delta x</math>: | ||
:<math>\Delta V</math> = <math>\vec{ | :<math>\Delta V</math> = -<math>\vec{E}</math>●<math>\Delta \vec{x}</math> | ||
Sign of <math>\Delta V</math> | Sign of <math>\Delta V</math> | ||
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===Simple=== | ===Simple=== | ||
If <math>x_i</math> = <3,0,0> m, <math>x_f</math> = <5,0,0> m, and <math>\vec{E}</math> = <100,0,0> | If <math>x_i</math> = <3,0,0> m, <math>x_f</math> = <5,0,0> m, and <math>\vec{E}</math> = <100,0,0> V/m: | ||
:<math>\Delta \vec{x}</math> = <math>x_f</math> - <math>x_i</math> = <5,0,0> - <3,0,0> = <2,0,0> m | :<math>\Delta \vec{x}</math> = <math>x_f</math> - <math>x_i</math> = <5,0,0> - <3,0,0> = <2,0,0> m | ||
:<math>\Delta V</math> = <math>\vec{ | :<math>\Delta V</math> = -<math>\vec{E}</math>●<math>\Delta \vec{x}</math> = -<100,0,0>●<2,0,0> = -200 V | ||
===Middling=== | ===Middling=== | ||
Revision as of 23:16, 21 November 2015
Claimed by Wendy Sheu
This page provides an explanation to determine the sign of potential difference in which the sign shows whether energy is lost or gained by a moving charged particle.
The Main Idea
By determining the direction of path relative to the direction of electric field, the sign of potential difference can then be determined. The sign of potential difference then shows if there is an increase or a decrease in potential energy, as well as kinetic energy.
A Mathematical Model
Potential difference is the product of the electric field [math]\displaystyle{ \vec{E} }[/math] and the relative path [math]\displaystyle{ \Delta x }[/math]:
- [math]\displaystyle{ \Delta V }[/math] = -[math]\displaystyle{ \vec{E} }[/math]●[math]\displaystyle{ \Delta \vec{x} }[/math]
Sign of [math]\displaystyle{ \Delta V }[/math]
- [math]\displaystyle{ \Delta x }[/math] in the direction of [math]\displaystyle{ \vec{E} }[/math]: negative
- [math]\displaystyle{ \Delta x }[/math] in the opposite direction of [math]\displaystyle{ \vec{E} }[/math]: positvie
- [math]\displaystyle{ \Delta x }[/math] is perpendicular to the direction of [math]\displaystyle{ \vec{E} }[/math]: [math]\displaystyle{ \Delta V }[/math]=0
A Computational Model
How do we visualize or predict using this topic. Consider embedding some vpython code here Teach hands-on with GlowScript
Examples
Simple
If [math]\displaystyle{ x_i }[/math] = <3,0,0> m, [math]\displaystyle{ x_f }[/math] = <5,0,0> m, and [math]\displaystyle{ \vec{E} }[/math] = <100,0,0> V/m:
- [math]\displaystyle{ \Delta \vec{x} }[/math] = [math]\displaystyle{ x_f }[/math] - [math]\displaystyle{ x_i }[/math] = <5,0,0> - <3,0,0> = <2,0,0> m
- [math]\displaystyle{ \Delta V }[/math] = -[math]\displaystyle{ \vec{E} }[/math]●[math]\displaystyle{ \Delta \vec{x} }[/math] = -<100,0,0>●<2,0,0> = -200 V
Middling
Difficult
Connectedness
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- Is there an interesting industrial application?
History
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See also
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Further reading
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External links
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References
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