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I am having trouble in proving the equation of the electric potential near a point charge Q. There are two different ways I can think to go about deriving the equation V=q/(4*Pi*E0*r). The first way is to calculate the change in potential energy of a test charge q0 in coming from infinite distance to a point P near the point charge Q, considering U=0 at infinity as a reference point. Then setting the change in potential energy equal to the negative of the work done by the electric field. The second way seems to me to be exactly the same mathematically. I am considering the change in potential energy in moving a test charge charge q0 from the point P to infinity. Again the change in potential energy should be equal to the opposite of the work done by the electric field along the path. Setting U=0 at infinity as a reference point, I find that the potential energy at P near the point charge Q is equal to the work done by the electric field along the path to infinity. Using the second method, I arrive at the right equation. But using the first method, I find a negative sign in the equation and I cannot get rid of it. I hope that somebody may be able to tell me what I have done wrong, or if there is something that I am not understanding correctly. I have attached a picture of my work on paper. I hope I have done a good job explaining the problem and that the picture is of decent enough quality.

Thanks so much, hope to hear a response soon.

-Alex

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# Electric Potential near a point charge.

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