Electric Potential Energy
I told you I’d get around to typing this out.
Electric potential energy is a scalar (no direction). This is a simplified version of the electric field equation EF =kQ/r^2. Electric potential is written as V = kQ/r. As you can see, the electric potential energy is inversely proportional to the distance “r”. As the distance increases, the potential DECREASES. To remember this easily, it’s the opposite of gravitational potential energy where as the distance increases, so does the potential energy. Since electric potential energy is a scalar, to find the difference between two points, the displacement of “r” can be taken. The potential energy can then be viewed as the charge (q) multiplied by the change in potential. Electric PE = q(Vf - Vi).
As I stated earlier, the potential DECREASES as the distance increases. Since energy is conserved, the kinetic energy and work will equal the negative potential energy. If a positive charge increases it’s PE and moves closer to the source charge, (+)(+) = positive. Low KE. If a negative charge increases it’s PE, (-)(+) = negative PE, high KE. If a positive charge decreases it’s PE, (+)(-) = negative. A low negative PE is equal to a high KE (high velocity).
All of this can be summed up in two statements:
1. A positive charge naturally accelerates (increase in KE) when it moves towards a point of lower potential.
2. A negative charge naturally accelerates (increase in KE) when it moves towards a point of higher potential.
Simply put, if the source charge is always positive, the positive test charge will be repelled and accelerate away. A negative charge will be attracted and accelerated towards it (higher potential)
