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Homework Help: Understanding Electrical Potential

  1. Mar 11, 2006 #1

    This is probably a dumb question, but I am really having problems understanding just what electrical potential energy/voltage really is. I can apply the formulas in numerical questions, but I just dont understand the concept at all. I totally understand the concept of gravatational potential energy though. Can someone please help me here, possibly with some analogies?

    Thanks a lot!
  2. jcsd
  3. Mar 11, 2006 #2
    Ok well if you understand gravitational potential energy then you know that the gravitational potential energy of a mass near somewhat near to the surface of earth is given by U = mgh where h is it's height above whatever reference point. Well if you understand the concepts of force and field then potential and potential enrgy can be broken up similarly. Electric potential enrgy is given by U = Vq, well V is in a way like g in teh equation for gravitational potential energy, it is the contributin to potential energy by the electric field of your test charge. Most of teh concepts dealing with electric forces fields, potential and potential energy have analogies in gravatation. Does this make any sense?
  4. Mar 12, 2006 #3
    I think Im understanding the concept more. But just one more question. When reading about parallel plate capacitors, it says there is a potential difference between the two plates. Can you explain what exactly is by "potential difference between the two plates"

    Thanks so much!!
  5. Mar 12, 2006 #4
    Ok well sticking with the same gravity analogy, with gravitational potential energy the difference in potential energy between 2 places is determined mainly by the height difference, its the same with electric potential if a charge is at one plate it has some potential relative to another plate which is determined by the field produced by the other plate and its distance from it. Does that help?
  6. Mar 12, 2006 #5


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    gravitational Potential difference is "g Delta h" ; h is measured opposite of g.
    Electric Potential Difference is "- E dot Delta s" , or -E Delta x if x is along E.

    Potential is the "environment half" of the PE, the "topographic map" half.
    The object that is put in this environment has object property m, making mgh
    or has q , making qV. The Potential Difference "g Delta h" or "Delta V"
    is what shows up as Delta PE/m or Delta PE/q .
  7. Mar 13, 2006 #6


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    If we assume that the initial PE is zero than the PE is just the Work (force tomes distance) needed to move a mass/charge against the resistance of a certain enviorment. If we are in a gravitational field, we need to do mgh joules of work to move a mass m a distance of h against the gravitational field aith accel. g.
    The same for EPE and "potential difference between the two plates", it is the work needed to move against the electrical field or from one plate to the other.
  8. Mar 13, 2006 #7


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    It's better to work by analogy with gravity. The electric potential energy of a charge is the analogue to the gravitational potential energy of a mass.
    What is the analogue to the electric potential? It can be taken as being the height in a gravitational field (actually, g times h is the best analogy but it might just make things sound more complicated).

    the key point is that you can talk about the difference of height between two points without having any mass placed at either point. Likewise, you can talk about the difference of electric potential between two points without having charges there. There is something creating the potential difference (the plates) as there is something creating the gravitational potential (Earth) but there is no need to have a mass placed at a point to define the height there. Likewise, there is no need to have an electric charge at a point in order to have an electric potential defined there.

    The fact that there is a potential difference between two points is like saying that (in he analogy with gravity) two points are not at the same height. Then a mass released from rest at the point of larger height will move toward the point of lower height (assuming they are one above the other). A positive charge behaves in the same way as a mass, in our analogy. If it is released from rest at the point of higher electric potential, it will move ("fall") toward the point of lower potential. If it is "thrown" from the point of lower potential toward the point of higher potential, it will slow down, etc.

    One striking difference is that there are negative charge which act like "negative masses" would act under gravity. If released from rest, they move toward a higher potential, etc.

    Hope this helps.

    Last edited: Mar 13, 2006
  9. Mar 14, 2006 #8
    not a dumb question at all! but the other answers might make your head hurt...

    try this: electrical potential energy, especially easy to see in the model of a parallel-plate capacitor, means there are more electrons on one plate than the other. very simple. the more the difference in the number of electrons, the higher the voltage potential between the plates.

    if an electron is released (imagine it to be miraculously injected into the space between the plates) near one plate, say the Negative plate, all those electrons there will repel that new one inbetween the plates, and it will be accelerated towards the other plate.

    the higher the potential between the plates, the faster the electron will be accelerated across the space between the plates. the change in energy of the electron as it's accelerated from one plate to the other is proportional to the difference in electrical "potential" between the plates, or the "voltage."

    hope that might help a little. also, nrqued's version is very good, too.
  10. Jan 24, 2007 #9
    This is an old thread but I found it and just wanted to say this post helped me very much in understanding electric potential. Thanks nrqed!
  11. Jan 24, 2007 #10


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    You are very welcome! :biggrin:
    Just a few additional comments:

    1) as I mentioned very briefly at the beginning of my post, the real analogy should be made between gh and the electric potential. This shows clearly that the source of the gravitational potential is the Earth (through "g').

    2) The electric potential and gravitational potential "gh" are really analogue in the case when the two plates creating the electric field (and hence the electric potential) are two infinite plates with the positive plate above the negative plate (so that positive charges, if released from rest, will move down, like masses do under gravity). Of course, you can have much more fancy electric potentials (produced by some complicated distribution of charges other than infinite uniformly charged plates) in which case a positive charge released from rest may move in some crazy three-dimensional pattern

    3) Th eforce of gravity is not exactly given by mg. This is an approximation valid for points close to the surface of the Earth (in the sense that the height is very small compared to the radius of the Earth). For the same reason, the gravitational potential is about gh only close to the surface. When you look at points much farther, you must use Newton's universal law of gravitation [itex] \frac{G m_{object} M_{Earth} }{r^2} [/itex] in which case the gravitational potential is actually [itex] - \frac{G M_{Earth}}{r} [/itex] and then the analogy with the electric potentia of a point charge is even more obvious!

    Thanks for your post. It is very nice to know that som epeople benefit from one's posts.

    Best regards

  12. Jan 24, 2007 #11
    We are studying this right now, and I was also having trouble understanding this until now. Thanks for posting this nrqed! (and also, thanks for digging it up from the archives mace2).
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