# Wording clarification about the concept of electric potential

So I am struggling with trying to understand what electric potential is and I wondering if this statement is correct based on my readings:

## "Electric potential is the electric potential energy a charge would have if you were to place a charge at that point."

Is that correct? Because if we have two plates where one is positive and one negative with a space between them, the electrical potentials of the positive and negative plates combine, so we know that near the negative plate and far from the positive plate, the electrical potential is very low, but far from the negative plate and near the positive plate that electrical potential is very high (Khan Academy).

Thoughts?

• Electric potential is kind of like gravity. The potential energy of an electron in an electric field is kind of like the potential energy of a golf ball being held some distance off the ground. – Hot Licks Feb 1 '19 at 2:38

That’s not quite right. You can’t say “Electric potential is the electric potential energy...” because these two things don’t even have the same units.

What you can say is “Electric potential tells you the electric potential energy any charge would have if you were to place a charge at that point; just multiply the potential by the charge to get the potential energy.”

Here is another description: “The gradient of the potential gives you the field, just like the gradient of the potential energy gives you the force.”

• Awesome, thank you for rewording my statement. The concept of electric potential makes sense to me now. Thanks! – Kyle Feb 1 '19 at 4:03

The electrical potential difference, voltage $$V$$ in volts (Joules per Coulomb), between two points is the work (energy) per unit charge required to move the charge between the two points. For two parallel plates where one is positive and one negative with a space $$d$$ in meters between them, the electrical potential difference, $$V$$, between the plates is

$$V=Ed$$

Where $$E$$ is the strength of the electric field in volts per meter between the plates directed from the positive plate to the negative plate. If you assign the negatively charged plate as being at zero potential, then the work done (electrical potential energy gained by the charge) in moving positive charge $$Q$$ from the negative plate to the positive plate will be

$$PE_{elec}=QV=QEd$$

This is somewhat analogous to the gravitational potential energy gained when doing work on a mass to elevate it a height $$h$$ in the earth's gravitational field above the surface of the earth.

$$PE_{grav}=mgh$$

Hope this helps.

• Great, thank you for that useful example, it did help me quite a bit. – Kyle Feb 1 '19 at 4:04