Electrical Potential - Difference, Field

[Hunt4Higgs]

Yet another quick one I bet one of you will be able to explain in twenty seconds.

Going over Electric on my own and I've come across the basics of Potential Difference, when looking at it between points (not in a field) it is defined as electric potentials being different at two points creates a potential difference which allows the flow from one point to the other. Potential difference is represented by "V" in both of my textbooks (I know it is U in other places).

Now skipping ahead slightly and I meet Electric Potential in a field. Also denoted by "V". Is this due to a relation between the two?
Is it as simple as Potential Difference is a change in Electrical Potential between the two points (a difference of V between the two points?), so you "could" say it as V₂ - V₁? Hence why they are both called V?

As a similar point, are the equations for the types of P.d different due to looking at different "systems", i.e. when the equation V=IR is used, this is because you are looking at a conductor which will have a voltage drop associated with it?
Whereas when you are looking at an electrical field, the equation V=Q/4∏εr is used because...?

Cheers guys/girls. :)

 

[DennisN]

Hi Higgs, what are you doing here? You should be at CERN right now . You said:

Is it as simple as Potential Difference is a change in Electrical Potential between the two points (a difference of V between the two points?), so you "could" say it as V2 - V1? Hence why they are both called V?

You are correct/on the right path. The sometimes sloppy use of variable names add to the confusion.

U = ΔV = Voltage = Potential Difference
V = Electrical Potential

Both are measured in Volts. In electrical engineering the voltage U is usually understood as the potential difference between let's say the potential V₁ and a defined ground (let's say V₂=0 Volt). If so, U = V₁, since U = V₁ - V₂ = V₁ - 0 = V₁. Thus, obviously U≠V₁ if the ground V₂≠0.

You can make a pretty similar comparison with distance and position. U (voltage) is similar to distance, and V (potential) is similar to position. To measure a distance, you need two positions.

Considering the equation V=IR, I prefer U=IR as U means voltage here. ΔV = IR is fine too.