Can negative electric potential be converted into kinetic energy?

Question

If we were given that the potential energy $U$ at some point in space was negative, could we calculate its kinetic energy (KE)? If potential energy were positive then we could simply use the formula $$U=KE=\frac{1}{2}mv^2.$$ From my understanding, the negative sign in electric potential simply means that the potential has an attractive nature. So wouldn't it make sense to simply treat $U$ as a magnitude giving us the scalar quantity we desire?

Answer 1

Imagine that this electric potential energy you mention happens to be stored on a capacitor as opposing charges on its plates. The equation for the energy content of that capacitor scales with the voltage squared which means there can't be negative potential energy in a capacitor, because regardless of how that voltage is expressed, its square will always be a positive number.

Now you can indeed equate that stored potential energy in the capacitor to the kinetic energy of some moving object as 1/2cV^2 = 1/2mv^2 where V is voltage and v is velocity. This assumes you have some magic means of converting all the potential energy into kinetic energy with some sort of electric motor, and in principle would allow you to set an upper limit on the speed of that object as a function of the amount of energy stored in the capacitor.

Answer 2

I think you are unclear what Potential Energy is and what/why it is negative or positive.

Potential energy is the energy stored inside the configuration of a system of 2 or more bodies that interact with each other through conservative internal forces.

Basically, there are a certain type of forces called conservative forces such that the work done in going between 2 positions only depends on the initial and final positions, and the work done in any possible closed path is always 0 (this is not true for non-conservative forces like friction). For forces like these, it is useful to define a quantity, "potential energy(U)" such that

ΔU=U(final position)-U(initial position)=-(work done in going from initial to final position.

Notice how the change in P.E, NOT P.E is defined. The reason for defining this is that it gives us a much easier, scalar method for finding initial and final velocities, as opposed to integrating vector quantities like acceleration, because it turns out

ΔU+ΔK=0 for a closed system (conservation of mechanical energy)

As you can see, P.E is used to utilize conservation of energy and as such, only the change in P.E is required. However, it is much more intuitive to define a reference point with 0 P.E, even though it is't required in any way. For example, Elastic potential energy is defined to be 0 at 0 extension, whereas gravitational/electric potential energy are defined to be 0 at infinity.

What does a positive/negative potential energy mean?

lets first answer this for the spring force. Since the elastic P.E is defined to be 0 at x=0, a positive P.E means work done by spring force in going from x=o to x=X is negative i.e it is an attractive force (U(x)-U(0)= - (Work)

Lets talk about the gravitational and Electric force now. Since both of their P.Es are defined to be 0 at infinity, if P.E is positive, it means that the work done in going from infinity (initial position) to some finite distance R is negative and thus the force is repulsive. If the P.E is negative, it means that the work done in going from infinity to a finite distance is positive and thus the force is attractive.

In conclusion, the negative/positive sign of P.E depends on where you definite it as 0, which is a completely arbitrary choice so everything about a positive P.E is equally applicable to negative P.E

Secondly, strictly speaking, it is the change in potential energy that is converted into/from K.E. If you were given the potential energy at some point in space, you cannot calculate its kinetic energy because

1. No change in P.E has occurred and thus no work has been done by the conservative force
2. the potential energy at a point in space is completely arbitrary choice

Even if you were given the potential energy at the initial and final positions, you could only calculate the CHANGE in K.e, not actual kinetic energy (in your chose frame of reference)