- #1

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[tex]V_A = \frac{PE_A}{q}= \frac{Q}{4πε_0r}[/tex] (where A is the position configuration of a point charge q in an electric field)

My derivation is as follows -

If a graph of force of electric attraction (y axis) and distance r (x axis) from the the center of a point charge Q to a test charge q is plotted, then the area between the x axis and the curve must represent the potential energy. Since the standard definition of the potential energy at a point in an electric field is the work done in bringing a unit positive charge from

*infinity*to that point, it follows that the area between the limits r

_{A}and ∞ represents the potential energy at point A. From the definition of an asymptote, F=0 when r=∞ .

So, [tex]\frac{PE_A}{q} = \frac{1}{q}\int_r^∞ F dr = \frac{1}{q} \int_r^∞ \frac{Qq}{4πε_0r^2} \, dr = 0-(-\frac{Q}{4πε_0r})[/tex]

Have I made any incorrect assumptions or used faulty reasoning? Could a better approach to this derivation be adopted?