Electric Potential: Difference between revisions

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::::<math>\mathbf{E}</math> is the source charge's electric field
::::<math>\mathbf{E}</math> is the source charge's electric field
::::<math>d\mathbf{L}</math> is a differential length along the path from point b to point a
::::<math>d\mathbf{L}</math> is a differential length along the path from point b to point a
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<div style="font-weight:bold;line-height:1.6;">Solution</div>
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[[File:ElectricPotentialPaths.png|400px|right|thumb|Some sets of electrically equivalent paths for a charge.]]
[[File:ElectricPotentialPaths.png|400px|right|thumb|Some sets of electrically equivalent paths for a charge.]]

Revision as of 16:38, 24 March 2020

The Main Idea

Electric Potential Energy, like all forms of potential energy, is the potential for work to be done, in this case by the electric force. The Electric Potential (frequently referred to as voltage, from its SI unit, the Volt) is the Electric Potential Energy associated with the test charge (1 Coulomb), such that it depends only on the source, just as the electric field is related to the electric force, but depends only on the source. One may similarly remember the parallel concept of the gravitational potential, which was gravitational potential energy divided by mass.

A Mathematical Model

Electric Potential Energy is defined with respect to the Electric Force & Electric Field:

[math]\displaystyle{ U_{ab} = - q \int_{b}^{a} \mathbf{E} \cdot d\mathbf{L} }[/math], where
[math]\displaystyle{ U_{ab} }[/math] is the Electric Potential Energy from point b to point a
[math]\displaystyle{ q }[/math] is the charge in the electric field
[math]\displaystyle{ \mathbf{E} }[/math] is the source charge's electric field
[math]\displaystyle{ d\mathbf{L} }[/math] is a differential length along the path from point b to point a
Solution