# Potential ##V## and potential energy ##E_{pot}##?

Hi,
I know that in an elecric field the potential energy ##E_{pot}## is equal to the potential ##V## times the charge ##E_{pot}=q V##.

Here my problem:
I know that the potential energy of a spring is ##E_{pot}= \frac{1}{2}kx^2##.
In my theoretical physics book i read also that the potential is ##V=\frac{1}{2}kx^2## for a spring.

Is the potential and potential enrgy for a spring exactly the same?
And why?

PeroK
Homework Helper
Gold Member
2020 Award
Hi,
I know that in an elecric field the potential energy ##E_{pot}## is equal to the potential ##V## times the charge ##E_{pot}=q V##.

Here my problem:
I know that the potential energy of a spring is ##E_{pot}= \frac{1}{2}kx^2##.
In my theoretical physics book i read also that the potential is ##V=\frac{1}{2}kx^2## for a spring.

Is the potential and potential enrgy for a spring exactly the same?
And why?

The main difference between these two scenarios is that the spring has an inherent potential energy, but the electric field has an inherenet potential energy per unit charge: which gives the potential energy of a particle depending on its charge.

ZapperZ
Staff Emeritus
I know that the potential energy of a spring is ##E_{pot}= \frac{1}{2}kx^2##.
In my theoretical physics book i read also that the potential is ##V=\frac{1}{2}kx^2## for a spring.

Is the potential and potential enrgy for a spring exactly the same?
And why?

In this case, yes, it is the same thing.

The terms "potential" and "potential energy" are often intermixed, especially when the non-energy form of "potential" is not relevant or not used often enough, as in the case of gravitational field. This is different from the electric field case where we do use electric potential and electric potential energy more frequently. So often times, in gravity case, book authors often tend to go sloppy.

You will encounter many times where the terminology may change and vary from book to book, person to person, situation to situation. It is why it is extremely important not to get too attached to a particular symbol or label being given to something. It is more important that you look at the mathematical form or definition of that thing, because THAT is the only description that matters, not the name we give to it.

Zz.

Last edited:
• nasu and PeroK