Potential vs Potential EnergyWatch
Potential tells you something about a point in a field. We talk of potential at a point in a field.
In an electric field it tells you how much energy a charge would have if placed there.
In a gravitational field it tells you how much energy a mass would have if placed there.
So the units of potential in an electric field would be energy per unit charge (JC-1), and
the units of potential in a gravitational field would be energy per unit mass.(Jkg-1)
To find out how much energy (in Joule) a mass or charge has in its gravitational or electric field, you multiply the mass or charge by the potential at that point.
How does one differentiate and make sure the right equation is used without rearranging the units everytime (and what are the units of potential? is it just an arbitrary unit?)
I would like to add to what Stonebridge had already mentioned.
Potential energy is a description of interaction between 2 or more particles based on a scalar property while the potential is a description of the effect of a point in space due to a property of a source.
Note that potential energy is always associated with a system of two or more interacting particles and potential can be associated with the property of source.
Both potential energy and potential are intimately connected.
This may sound abstract. I illustrate with an example.
The space around a source charge Q is altered.
This source charge creates electric field EQ and electric potential VQ.
Electric potential, like the electric field, is a property of the source charge Q – electric potential and electric field are not two distinct entities but, instead, two different perspectives or two different mathematical representations of how source charges alter the space around them.
An electric field is a region where an electric charge q experiences a force
Electric force exerting on q = qEQ
while electric potential tells us what is the electric potential energy U associated with source charge Q and electric charge q places at a point in space around the source charge.
USource Q and q = qVDue to source Q
Electric field is mathematical related with electric potential and electric potential energy respectively as shown below:
Lastly, I would like to “re-write” the opening description based on electric potential and electric potential energy:
The electric potential is characteristic of the electric field only, independent of a charge q that may be placed in the electric field.
Electric potential energy is characteristic of the charge-electric field system due to an interaction between the field and a charge q placed in the electric field.
Hope it makes sense to you.