# I Voltage derivation for charged particles

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1. Feb 12, 2017

### Logical Dog

I have a very weak understanding of the particle modelling of electrical phenomena.

1:$$Electric field =\frac{Force}{Magnitude of charge}$$
1 is The definition of electric field on a particle (?)

2:$$Force = \frac{Q1*Q2*K}{R^2}\\$$
2 is Coulombs law, to find force between two particles.

3:$${\frac{(Q1*Q2*K)}{R^2}} / (Q2) = \frac{Q1*k}{R^2}$$
3 is the substitution of 2 onto 1s numerator, Force

4:$$\frac{Q1*k}{R^2} * D = Work done$$
4 is the formula for work done. D here meaning distance, or should one use S for displacement?

5:$$[\frac{Q1*k}{R^2} * D] /Q2 = Voltage$$
5 is work done divided by magnitude of charge, which is voltage.

My question is, since, in 5, this:
$$[\frac{Q1*k}{R^2}]$$

Is the electric field on a particle,
it fair to say, that the voltage is the electric field on a charge * distance moved as a result of fields force divided by the magnitude of that charge?

2. Feb 12, 2017

### cnh1995

You can't use diplacement directly as S. You have to consider infinitesimal displacement ds because force is not constant. Work done in an electric field is given by integrating F⋅ds along a certain path. It is a line integral where F may be variable.

For what system are you using these equations? Two charges Q1 and Q2, out of which Q2 is fixed and Q1 is moved?

3. Feb 13, 2017

### Logical Dog

Yes.

4. Feb 13, 2017

### sophiecentaur

It doesn't matter; the Potential is the same if one, the other or both are moved in an inertial frame.

5. Feb 13, 2017

### Logical Dog

Os the derivation correct?

6. Feb 13, 2017

### sophiecentaur

The Potential Energy at separation x is the work done to change the separation between the two from Infinity to x. The "derivation" is wrong as it fails to calculate the work done. It assumes that the field doesn't change as the separation changes.
It amazes me that people don't find this sort of information themselves, rather than trying to work it out from scratch. There are hundreds of sources for this information. Why not try this Hyperphysics Page? or this Wiki Link? Q and A is just not the way to learn Science. Getting from A to B by Brownian motion takes an awful long time.

7. Feb 13, 2017

### Khashishi

In equation 4 you have multiple errors. You introduced D for distance, but R in the denominator is also the distance. The force and the field depend on the distance, so you need to integrate over R.
Also, you left off Q2 in the work done. Work is calculated from the force, which has both Q1 and Q2. The voltage is the work divided by Q2, so the Q2 will cancel out from the equation.

8. Feb 13, 2017

### Logical Dog

thanks, I will re read everything. I thought I understood but it was clear I had no idea. I read books but sometimes I am always confused, no deriving things from scratch. I think I will take questions elsewhere :)

Last edited: Feb 13, 2017
9. Feb 13, 2017

### sophiecentaur

You can try but there's no guarantee that you will be asking the right questions in the right order to give you better understanding. I suggest that you come to terms with reading text books and get an appropriate path through this stuff. Perhaps the text books you have tried are too advanced for you at present? Good luck.

10. Feb 14, 2017

### jim hardy

by changing from the complicated field that exists between two charges

http://www.pstcc.edu/nbs/WebPhysics/Chapters 25 and 26.htm

to a simpler uniform electric field such as exists between two large parallel plates.
same link, http://www.pstcc.edu/nbs/WebPhysics/Chapters 25 and 26.htm

Think "Millikan Oil Drop Experiment " for a minute ......
It should be intuitive that in the bottom diagram,
if the field is E volts per meter
a single electron will acquire or give up E electron volts for each meter in moves along a field line.
Electron volts to Joules is straightforward enough. Hmm, it looks mighty close to ~1/6.2E18 , a familiar enough number....

Approach: Make your math work for a simple model, then hone it for the more general case.

Any help ?

old jim

11. Feb 14, 2017

### Logical Dog

thanks sir, may I take some time and reply later? I am re reading the fundamentals and doing questions of schaums college physics..

Last edited: Feb 14, 2017
12. Feb 19, 2017

### Logical Dog

Ok, I think I understood a lot.
So, I understood that I can't really derive voltage in the electric field between two point particles or one charge and one point particle, as the maths background and understanding needed is beyond my capabilities, furthermore the electric field isn't constant, hence the integral. I got the formula for potential and voltage though, but only for point particles and an electric charge distribution of a “sheet” (?).

I can derive the voltage in a constant electric field like the one between the capacitors (that is fairly easy and stems from the definition of the electric field between two parallel plate capacitors)...easy electric field there.

What I do not understand yet is the electric field inside a circuit, though I have looked for it and am reading some other stuff on it, I feel it can help me if I read more on it…even if it’s an approximation. I also get confused due to circuit analysis conventions like negative and positive voltages etc. Yes I really struggle with this stuff for some reason :-(. I see no alternative but to keep learning more electromagnetism on my own (to the minimum level of maxwells equations) . Unfortunately its not offered for my degree. Thanks for the help.

today I will read this thouroughly: http://science.uniserve.edu.au/school/curric/stage6/phys/stw2002/sefton.pdf
http://www.abc.net.au/science/articles/2014/02/05/3937083.htm

Last edited: Feb 19, 2017
13. Feb 19, 2017

### sophiecentaur

That would be the ideal approach but, if you are like me, you can work through the simple case and that can often allow you to 'believe' that it would work for a more difficult case.
Haha - do as I do - not necessarily as I say. It just depends on where you need to take this, of course.
That's only a problem if you insist on including ELECTRONS in the argument. They are totally unnecessary for nearly all circuit analysis. Charges (i.e. Positive Charges) flow 'downhill' from + to - unless they are 'pumped uphill' by a generator / emf / battery etc. That is actually NOT confusing, surely, any more than balls roll down a slope unless you actually carry them uphill.

14. Feb 19, 2017

### jim hardy

When i hit "real world" I soon learned that the textbook problems given in 'university' were carefully designed to be solvable.
When we go to work in industry we find out Mother Nature is seldom so accommodating,
and i appreciated why EE's in my school took Fluid Mechanics over in Civil Engineering department - for the graphical approach to working out pressure and flow profiles around irregular shapes.

Here's an example that relates to OP's plight.... (Oh No , another Boring Anecdote !)

There exists around reactors a need for a gamma ray radiation detector that has electrically adjustable sensitivity.
Those WW2 geniuses figured out how to do it.

They create an electric field between two plates, but one of the plates has exaggerated "corrugations". Those two plates form the walls of a gamma ray detector that's filled with ionizable gas.
Voltage is impressed between the plates.Gamma rays ionize the gas and charges migrate to the respective plates.
Somebody had to calculate the field inside those corrugations but i had to settle for drawing the field as if it were a hydraulic flow problem.
In the narrow parts of the chamber E field is simple, constant Volts/meter just like between two parallel plates.
Within the deep corrugations however it's not so simple

here's a better drawing from the patent but it's rotated 90 degrees
http://pdfpiw.uspto.gov/.piw?PageNum=0&docid=02852694&IDKey=AF8EA366EA31 &HomeUrl=http://patft.uspto.gov/netacgi/nph-Parser?Sect1=PTO1%26Sect2=HITOFF%26d=PALL%26p=1%26u=%252Fnetahtml%252FPTO%252Fsrchnum.htm%26r=1%26f=G%26l=50%26s1=2852694.PN.%26OS=PN/2852694%26RS=PN/2852694

Equipotential lines, always perpendicular to Efield lines (just as in fluid flow problems) distort over(up in good drawing ) into the corrugations.
As field inside the corrugation weakens it becomes too feeble to collect ions and they recombine instead of moving toward a plate.
By adjusting the applied voltage one controls how far into the corrugation that happens, which effectively adjusts the volume(hence sensitivity) of the detector.
That's the heart of our reactor wide range power meter. It works over eight decades of power , from just above startup to 100%.

Here's a description of the detector and ts use

Anyhow my point is,
we must simplify to the point we can grasp what's going on
then use whatever math ability the Lord saw fit to grant us to describe the phenomenon.
Some will use vector calculus with its dels grads and curls;
'Children of the Lesser Gods' like myself will resort to simpler means .

I want OP to have some intuitive "feel" for fields. My old fluid mechanics course has saved my butt more than once in that regard.
If he masters Vector Calculus, and he probably will, he's a better man than me .

old jim

Last edited: Feb 19, 2017
15. Feb 19, 2017

### sophiecentaur

@Jim. You may have scared the OP off this topic for life.
@BD. You won't come across anything like that until you have a lot more experience of this stuff. In any case, there are computers available these days for providing some pretty good solutions to such problems.

16. Feb 19, 2017

### Logical Dog

Its not a problem, I think when I read from the experts I get very happy, especially when they talk about the limitations and challenges they faced...when I was studying economics I read the economics anti textbook and was very happy..in particular its good to know the limitations of models or formulas I guess.

thanks again for your time..I think I studied too much today and am tired. I know one day ill get closer to a better understanding, and not have to use water analogies.

17. Feb 19, 2017

### cnh1995

I liked the link in your post #12. The 'surface charges and poynting vector' approach is indeed the correct approach to teach circuits instead of the water analogies. But I am not sure if high school students can grasp those concepts since they are not introduced to the concept of field (at least not in my country).
I remember how confused I used to be about this whole circuits stuff in high school and the best explanation my teacher would come up with after I asked queries was either the water analogy or the traffic analogy.
If you are interested in studying it in depth for a satisfactory (not complete!) understanding, I think you'd enjoy D.J.Griffiths' Introduction to Electrodyamics and 'Matter and Interactions' by Chabay and Sherwood. (Both are available in pdf format I guess)..

Last edited: Feb 19, 2017
18. Feb 19, 2017

### sophiecentaur

What level were you proposing to teach 'circuits' with Poynting vectors? It's strange to include that in the same sentence as 'Water Analogies'. One is for twelve year olds (if you really must) and the other is for University Undergraduates. (I would have thought).
You seem to be missing out the normal circuit equations and Kirchoff on the way.

19. Feb 19, 2017

### sophiecentaur

The water analogy really brings me out in spots. The problem is that people do not actually make the right connections between the so called analogous components in the water analogy and it tends to push understanding further away (judging from the way that people come back with 'wrong' conclusions, when they use it). I feel very strongly that the desire to 'understand' circuits without having to go through the process of V=IR, the Potential Divider, Kirchoff etc etc. is just self indulgence. The only reasonable analogy for circuits is the MATHS model. Non mathematical EE is only half a job.

20. Feb 19, 2017

### jim hardy

I hope not !
Electronics is a lot of fun..... i still remember my elation when it dawned on me how that compensated ion chamber works.

@Bipolar Demon Work your basics in your head until you've resolved the seeming conflicts. When a mental model leads intuitively to the formula by a couple different thought paths you've built another powerful mental tool. Keep them sharp , like fine chisels.