Understanding Potential Difference: Work Done per Unit Charge?

[Studiot]

Why would you claim that any reconciliation is needed? Coulombs law discusses the Potential due to the existence of two charges. It doesn't say that is the only way to treat Fields. You can rearrange Coulomb's law and substitute some of the terms with E without any conflicts. The integral of E over distance will tell you the Potential in all circumstances

This is not mainstream.
It is the express aim of Physics Forums to lead students such as physics kiddy along mainstream paths.
I have been waiting for someone to do this in this thread and it has not happened, so I am not suprised pk is still confused.

Physics at this level is constructed to provide a logical development of ideas, based on real physical observations, that hang together as a coherent whole. These days we follow the 'MKS' system for this purpose.

So we introduce fundamental properties of matter and space such as length, mass and time and derive subsidiary mechanical quantities such as force, energy, work, power and so on from them.

One particular mechanical relation is Newton's law which states that there exists a force of attraction between any two masses, proportional to the masses and inversely proportional to the square of the distance between them.

[tex]F \propto \frac{{{m_1}{m_2}}}{{{d^2}}}[/tex]

We can directly observe and measure this force and confirm the relation.

Note also that if either m₁ or m₂ are zero (ie there is only one mass) the force is zero.

When we start electricity we learn that for some matter we observe an additional force, over and above this relation.
We attribute this extra force to a property we label electric charge and, as Coulomb discovered, it obeys a similar relationship to that of Newton.

[tex]F \propto \frac{{{q_1}{q_2}}}{{{d^2}}}[/tex]

This provides a direct link or introduction from mechanics to electrics.

Further it allows us to directly calculate the work done in moving a charge against this force.

The concept of electric potential follows from this work calculation as the potential energy added to the charged matter in moving it. A mechanical concept already well established.

Two things to note.

Firstly I have not mentioned fields and there is no need for them. Fields are a convenient mathematical and visualisation technique, not a fundamental necessity of the system.

Secondly, as with Newton's Law, if either q₁ or q₂ are zero (ie do not exist) and there is only one charge then the force is zero and no work is done in moving the other charge.

It is absolutely necessary to involve fields (/potential) in those cases, which don't relate in any way to other charges.

As to the question of electric fields in free space or conductors, I am sure you know the rules for field lines. They must either go on to infinity or start/end on a charge. So somewhere in the universe there must be a charge or charges terminating these lines.

 

[sophiecentaur]

Where does physics kiddy first come across fields and potential?? Answer: Gravity

What is the first bit about gravity that they learn?? Answer: g (a uniform) gravitational field and the weight of a mass in a g field on Earth.
So I should imagine that the concept of a field, at that level, is not too taxing for someone who has started off with this and has reached the stage of formulating a question on PF. The parallel between g field with gpe and electric field and Potential shouldn't be beyond PK and others like him. (Perhaps we could have some feedback, PK?)

There really isn't any need to spell out the parallel between the gravitational and electrical laws of attraction. I'd bet that PK is happy enough with them. The inverse square law is not hard to grasp.

But I could point out that energy transfer in a uniform field is a lot easier to grasp because you don't need to understand what happens when you integrate an inverse square relationship. We start off in School with mgh, don't we? Some of us then progress to Gm1m2/d.

The bottom line is that there are two possible approaches to this and each is more appropriate in its own context. The situation in a conductor, an electrical circuit or, in fact, most places where there are a lot of charges involved is going to be more straightforward to treat in terms of Fields relating to Potential - just look at textbooks on Electricity.

Your 'rules' for field lines are a bit difficult to apply to a radiating dipole. How would you draw them for the far field? The 'charges' have long gone from where the field lines started their life.

BTW, the "MKS" system died some while ago. It's called SI, nowadays. Let's not confuse the current student body.

 

[Studiot]

I don't always see eye to eye with academicians but in this case they have constructed a sensible and self consistent edifice of Physics at this level.

I do not have any american textbooks at this level but a look at the UK syllabus and resulting texts shows:

Work is introduced as force times distance and as a form of energy at GCSE level.

At 'A' Level:

Gravity and Newton's Law is introduced as I have given but in equation form with suitable constants added.
Fields are nowhere mentioned. In fact they are specifically avoided and the phrase ' the pull of gravity' is employed in precursor material.

Electric theory also follows the same pattern as I have given, with suitable constants to turn it into an equation, called Coulomb's Law, also described as the fundamental law of electric action.

Fields are introduced as a consequence of this ( I don't deny they are useful).

You would obtain full marks if asked to state either Newton's or Coulomb's Law and responded with as I have done.
You might be marked incorrect if you responded with an equation or statement about fields.

All this is natural preparation for further study of say the Rutherford-Bohr atom and all that leads to.

Incidentally, the integration you refer to is not difficult and used to be included in the syllabus.
Concomitantly to deal with fields properly we are talking about the solution of Laplace's or Poisson's equations. Is that easier?

 

[jtbell]

It takes two to tango.

You need at least two charges in the system for there to be any electric potential.

You need two charges in order for there to be any electric potential energy. You need only one in order for there to be electric potential.

Look at e.g. Griffiths, which defines the electric potential as the line integral of the electric field, and then brings in the idea of electric potential energy associated with it.

With one dancer you have a "potential tango" which becomes actual "tango energy" when a partner shows up.

 

[sophiecentaur]

At 'A' Level:

Gravity and Newton's Law is introduced as I have given but in equation form with suitable constants added.
Fields are nowhere mentioned. In fact they are specifically avoided and the phrase ' the pull of gravity' is employed in precursor material.

Electric theory also follows the same pattern as I have given, with suitable constants to turn it into an equation, called Coulomb's Law, also described as the fundamental law of electric action.

Fields are introduced as a consequence of this ( I don't deny they are useful).

You would obtain full marks if asked to state either Newton's or Coulomb's Law and responded with as I have done.
You might be marked incorrect if you responded with an equation or statement about fields.

All this is natural preparation for further study of say the Rutherford-Bohr atom and all that leads to.

Incidentally, the integration you refer to is not difficult and used to be included in the syllabus.
Concomitantly to deal with fields properly we are talking about the solution of Laplace's or Poisson's equations. Is that easier?

I have the AQA Physics A level Coursebook (Nelson Thornes 2008) on my lap and the word 'Field' occurs throughout the section which is titled "fields and further mechanics". This is in the context of both Gravitational and Electric forces. The book says Electric field is due to the presence of charges (fair enough at this level) but it clearly states that the force is proportional to Field. Non-radial fields are considered, and rightly so imo.

I have a feeling that you have a personal preference and that you are assuming that this implies that everyone should approach things in the same way. I am saying that situations dictate the best approach and that even beginners are assumed to be able to cope with either.

You quote Coulomb's Law almost as if it is an 'Law of God' and not just a way of describing and predicting - which is all that any 'Law of Science' can be expected to be. I can't think of any such 'Laws' that have been produced, and named as "Laws' since Modern Science came along. The reason for this is obvious to me.

 

[Studiot]

I have the AQA Physics A level Coursebook (Nelson Thornes 2008) on my lap and the word 'Field' occurs throughout the section which is titled "fields and further mechanics". This is in the context of both Gravitational and Electric forces.

Interesting your source should state that.

Extract from the AQA A level Physics Specification and Syllabus Document

A2 Module 4 : Waves, Fields and Nuclear Energy

Section 13.3.3 : Gravity, Newton's Law, The gravitational constant G

Recall and use of

[tex]F = - \frac{{G{m_1}{m_2}}}{{{r^2}}}[/tex]

gravitational field strength is included in A2, but comes in a later section and does not require recall.

Section 13.3.7 : Coulombs's law, permittivity and free space.

Recall and use of

[tex]F = \frac{1}{{4\pi {\varepsilon _0}}}\frac{{{Q_1}{Q_2}}}{{{r^2}}}[/tex]

Again field strength and potential are introduced in later sections of A2 and do not require recall.

I rest my case M'Lud.

 

[sophiecentaur]

Did I suggest that no one should know those formulae?
I think you are failing to understand my point, which is that 'action at a distance' is appropriate sometimes and that 'force due to a field' is appropriate at others. You seem to want to EXCLUDE f = Eq and I cannot think why. I can take solace from the fact that there are more enlightened people choosing what to tell A level students.

But let's not go down the road of the level of competence of those who are responsible for building Specifications, these days. AQA, in their wisdom, start the AS Physics course - and the students who choose this course may well not have had a 'qualified' Physics teacher for their GCSE Science - contains the topic of Fundamental Particles. This includes Feynman diagrams, Quarks, leptons, Bosons etc and is presented to kids who have no idea how an electron behaves or what is meant by One Electron Volt. There is a term 'scaffolding' which has been bandied about in 'education' for some while. It involves letting students advance from what they already know with some guidance from the teacher. Apart from reading the word 'Hadron', to do with something going on in Geneva, what sort of prior knowledge can help 16 year olds get familiar (let's not suggest actual knowledge) with Modern Physics?

"Do not require recall"?? I frequently read the clause but fail to see what it has to do with Education. Many questions give students 'the Formula' and still expect them to use it. That sort of question involves just a tad of familiarity and understanding.If you were in a closed room, on a planet, and you had a know mass and a Force Meter with you, would you have any chance of knowing the mass of that Planet (unless, possibly, the room were several km high)? But you could easily find the Gravitational Field.

 

[Studiot]

Thank you JT Bell for reminding us all to be more precise in our wording.

You are, of course, exactly right it takes only one charge for electric potential, measured in volts but two charges or more to achieve electric potential energy as measured in energy units.

In my defence mitigation I have looked again at the offending post you have extracted from.
I was replying to a query about electric potential energy and indeed did state this in my first line. It is unfortunatethat I missed the vital word from my last line.

I note that this distinction error continued through many subsequent posts by all concerned.

1: Potential : The electric potential energy at a point is equal to the electric potential energy of a charged particle at that location divided by charge of the particle.


And how does a charged particle come by this electric potential energy?

It takes two to tango.

You need at least two charges in the system for there to be any electric potential.