Voltage associated with a point charge

Question: What is the voltage associated with a point charge? Solution: As derived previously in a self-check, 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 r₁=∞ 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.