# Voltage - measured in a field or in a conductor ?

#### RipClaw

Joined Oct 9, 2008
3
I find different definitions/understandings of voltage.

Part1 :
One is analogous to gravitational potential energy .
[where we have the all present gravitational field on the Earth's surface.
And I try to pick a 1 KG dumbbell 10 cms vertically high from the ground, so its potential energy increases by mgh, 1* 9.8 * 0.1 = 0.98 ≈ 1 Joule
It also means that I wasted 1 Joule of energy or 0.239 calories.]

Now let us move to a space which is filled with electric field.
Let the field be produced by the theoretical +ve charge(s).
Let us place our test ball which is an aggregate of 1 coulomb of -ve charges near to it as shown in the diagram

(+ve)----(-ve)

Now, I keep on pushing the -ve ball towards the right.

(+ve)----====----====----(-ve)

I stop when I had spent exactly 1 Joule of energy.
Naturally I will see that the charge has moved a distance
====----====----

Let us give names to both ends of the line
A====----====----B

Now, I say that the potential difference between two points A&B is 1 Volt
Is my understanding correct ??

Part2:
Another definition I see is the one without fields.

"The volt is defined as the potential difference across a conductor when a current of one ampere dissipates one watt of power"

Here we see that 'time' comes into the equation the 3rd time in the form of watts, though it gets canceled with amperes. The other two comes from Force, which is composed of acceleration, which in turn is composed of inverse square of time.

Why do we need all this confusion ??
The 2nd definition suits current flow through conductors. Will it suit static electricity ? For eg. though current is not flowing, we could say that the voltage difference between Earth and clouds is 10000V.

Kindly correct me, I am new to this stuff #### triggernum5

Joined May 4, 2008
216
Its a matter of convenience, depending on the material properties in question..
displacement_current_vector = epsilon*E
D can be though of as the elastic response to E.. Its related to the charge density, while E is related to the forces.. Essentially a medium with a low elastic response is a good conductor.. Conductivity can be derived from the field concept.. Ohm's law simply saves you a whole lot of nitty gritty physics to solve common problems..
Its analogous to the e^x thread that just popped up.. e^x is a simplified way of expessing the series that defines it, and just like Ohm's law, alot of ppl know how to use it, but don't understand the fundamentals of its existance..

#### RipClaw

Joined Oct 9, 2008
3
I am looking for a single reference point for the idea expressed.
Like ... when we say that a rock is 8 Kilograms, it means that the rock behaves like an amalgamation of 8 one kilogram Platinum-Iridium alloy blocks kept in the International Bureau of Weights and Measure in France.

Of course!, we can express mass in other terms. But the one mentioned is so intuitive! & its accuracy is ok for a physics student #### mik3

Joined Feb 4, 2008
4,843
Voltage is defined as the energy an amount of charge needs to move between two points which are the points where we measure the voltage across.

If we measure the voltage between two points to be Vab=1V and we release a 1C positive charge from point a it will move to point b and will require 1J of energy to make this movement.

In other words, if you have a 1C charge and it requires a 1J of energy to move between to points a and b, then the voltage across these points is 1V.

#### triggernum5

Joined May 4, 2008
216
Ohm's law can be expressed in terms of electric fields though.. I think your reference point should be the permitivity, and the difference between the displacement field, and the electric field.. Follow that through and you can derive current density, conductance, resistance etc.. Its just easier to refer to charts for precalculated values than to crunch the complex algebra each time..