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Voltage associated with a point charge
Question: What is the voltage associated with a point charge? Solution: As derived previously in a selfcheck, the field is
The difference in voltage between two points on the same radius line is
In the general discussion above, x was just a generic name for distance traveled along the line from one point to the other, so in this case x really means r.
The standard convention is to use r_{1}=∞ as a reference point, so that the voltage is
The interpretation is that if you bring a positive test charge closer to a positive charge, its potential energy is increased; if it was released, it would spring away, releasing this as kinetic energy.


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