## Intuitive Definition of Electric Potential

Hello all,

For a few months, I've been (off and on) trying to come up with a more intuitive definition for Electric Potential (or Voltage, if you prefer), as all I can seem to find are mathematical equations. I believe I have finally come up with a satisfactory result, and I merely wanted to verify it with those that may be more knowledgeable on this matter than I.

Here's my intuitive definition:

"Analogous to the electric field, which is essentially the force vector that would occur were a test charge present in the field, the electric potential (being the integral of the electric potential energy divided by a test charge) is the change in electric potential energy between two points that would occur were a test charge present in the displacement from one point to the other."

This has, for me, significantly helped my intuitive understanding of it. Nevertheless, if someone finds fault with this definition in any way, please let me know, as I would hate to misinterpret the facts, especially as a undergraduate physics major! And, of course, as anyone who's taken at least a semester of physics knows, the devil's in the details.

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Hello Skoth!
 Quote by Skoth "Analogous to the electric field, which is essentially the force vector that would occur were a test charge present in the field, the electric potential (being the integral of the electric potential energy divided by a test charge) is the change in electric potential energy between two points that would occur were a test charge present in the displacement from one point to the other."
Yes, that looks ok (assuming the electric field is conservative).

Potential energy is defined as minus the work done by a conservative force, = change in energy (by the work-energy theorem ).

And electric potential energy = potential energy per charge.

(an easier analogy would be to gravitational potential, which is gravitational potential energy per mass )

 which is essentially the force vector that would occur were a test charge present in the field
It should be noted that there are two vectors associated with an electric field.

The electric field intensity, E which is considered alwys present, whether a test charge is introduced or not.
The direction of E is away from a positive charge and towards a negative one.

The electric force vector, F which is the field vector multiplied by the test charge.

The potential is a scalar quantity.

## Intuitive Definition of Electric Potential

 Quote by Studiot It should be noted that there are two vectors associated with an electric field. The electric field intensity, E which is considered alwys present, whether a test charge is introduced or not. The direction of E is away from a positive charge and towards a negative one. The electric force vector, F which is the field vector multiplied by the test charge. The potential is a scalar quantity.
Yes, I figured that bit would be scrutinized, which is why I put "essentially" before it. I guess it's not the greatest analogy--especially since the one's a scalar and the other's a vector (which thankfully I am aware of). But besides that, I felt them to be analogous because they both go off a sort of if-then basis of 'if a test charge is present, then....' Of course, it's the 'then' part that defines the two differently from one another.
 No you don't need a test charge for the electric field to be present.
 Yes, I know, but if a test charge were present in an electric field, then the charge would be accelerated by the field vector. The same is also true of an electric potential difference: that is, that a test charge does not need to be present for one to exist.
 Yes that's all correct. Incidentally you said you didn't want to go mathematical, then mentioned integrals?
 Ha ha ha, good point! Well I guess all I can say to that is that the mind works in mysterious ways and mine is no different. To quote one eminent philosopher of our generation: "The inner machinations of my mind are an enigma." --Patrick Star And thanks for the verification, guys!