Week 5—Potential
Electric Potential
Defined as delta V, the electric potential between two points describes the change of the electric field due to the distance from the change. In other words, electric potential describes a field that is non-uniform with respect to distance. Using the superposition principle, we could do this by adding up the potential at incremental distances of dL away from the charge, from the initial point to the end point, but really, Isaac Newton invented integral calculus just for the purpose of making something like this easier. DeltaV is then defined as negative the integral of E times deltaL, from point A to point B. E depends on what kind of charge you are shown (i.e. a capacitor, point-charge, wire) and dL is the distance away from that charge your observation location is. Integrating with respect to this distance is usually the easier choice and sets up a nice-looking integral, which you can easily calculate.
The Difference between "Negative" and "Positive" Potential
Negative potential describes an observation location moving down the direction of the E vector. In the equation deltaU(potential energy) = q (the charge) * deltaV (potential), this is like saying you are losing potential energy and gaining kinetic energy. Positive potential describes an observation location moving UP the direction of the E vector, which is like saying you are gaining potential energy and losing kinetic energy.
But, Electric Potential is not the same as Electric Potential Energy
While it may seem easy to say "Electric Potential = Electric Potential Energy", this fact is sadly mistaken. Even though the two are proportional, the difference is that Electric Potential is a difference of potential energy between two points. Good food for thought.