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| by Amira Abadir
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| ==Relativistic Energy==
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| The potential difference between two locations does not depend on the path taken between the locations chosen.
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| ===A Mathematical Model===
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| In order to find the potential difference between two locations, we use this formula <math> dV = -\left(E_x*dx + E_y*dy + E_z*dz\right) </math>, where '''E''' is the electric field with components in the x, y, and z directions. Delta x, y, and z are the components of final location minus to the components of the initial location.
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| ===A Computational Model===
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| How do we visualize or predict using this topic. Consider embedding some vpython code here [https://trinket.io/glowscript/31d0f9ad9e Teach hands-on with GlowScript]
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| =Simple Example=
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| [[File:pathindependence.png]]
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| In this example, the electric field is equal to <math> E = \left(E_x, 0, 0\right)</math>. The initial location is A and the final location is C. In order to find the potential difference between A and C, we use <math>dV = V_C - V_A </math>.
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| Since there are no y and z components of the electric field, the potential difference is <math> dV = -\left(E_x*\left(x_1 - 0\right) + 0*\left(-y_1 - 0\right) + 0*0\right) = -E_x*x_1</math>
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| [[File:BC.png]]
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| Let's say there is a location B at <math> \left(x_1, 0, 0\right) </math>. Now in order to find the potential difference between A and C, we need to find the potential difference between A and B and then between B and C.
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| The potential difference between A and B is <math>dV = V_B - V_A = -\left(E_x*\left(x_1 - 0\right) + 0*0 + 0*0\right) = -E_x*x_1</math>.
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| The potential difference between B and C is <math>dV = V_C - V_B = -\left(E_x*0 + 0*\left(-y_1 - 0\right) + 0*0\right) = 0</math>.
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| Therefore, the potential difference A and C is <math>V_C - V_A = \left(V_C - V_B\right) + \left(V_B - V_A\right) = E_x*x_1 </math>, which is the same answer that we got when we did not use location B.
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| ==Connectedness==
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| #How is this topic connected to something that you are interested in?
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| #How is it connected to your major?
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| #Is there an interesting industrial application?
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| ==History==
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| Put this idea in historical context. Give the reader the Who, What, When, Where, and Why.
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| == See also ==
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| *[[Rest Mass Energy]]
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| *[[Einstein's Theory of Special Relativity]]
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| ===Further reading===
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| Books, Articles or other print media on this topic
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| ===External links===
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| Internet resources on this topic
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| ==References==
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| #[https://en.wikibooks.org/wiki/Special_Relativity/Dynamics#Mass_and_energy Modern Physics Wiki]
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| #[http://ffden-2.phys.uaf.edu/212_fall2003.web.dir/Eddie_Trochim/Energymass.htm University of Alaska Fairbanks]
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| [[Category: Energy]]
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