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Homework Help: Energy and potential charge

  1. Dec 12, 2013 #1
    When a negative charge moves from a point of higher potential to a lower potential will it gain or lose PE? How do you figure that out?
    Also what is the correlation between kinetic energy and potential energy?
    Is it that as one gains the other loses and so forth?
  2. jcsd
  3. Dec 12, 2013 #2

    Simon Bridge

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    You figure it out by looking at the definition of potential for the situation. There is also a standard one to use when a definition is not provided. It is usually defined for sa positive charge - so a negative charge does the opposite.

    They are usually complimentary quantities - total energy is conserved.

    If all the potential energy lost goes into moving the particle, then yes. But there are other ways that potential energy can get spent as there are other forms (or manifestations) of energy. In general you are usually exchanging some form of potential energy for some form of kinetic energy.
  4. Dec 12, 2013 #3
    So a negative charge will gain PE when it moves from higher to lower?? Can you explain that more please
  5. Dec 12, 2013 #4

    Simon Bridge

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    If a positive charge will naturally go one way - the negative charge will naturally go the other way.
    What is the definition of "potential"?

    We used to say that "electrons roll uphill" - referring to the electron current in a circuit going from - to +, from low potential to high potential.
  6. Dec 13, 2013 #5
    So moving from high to low potential means that it loses PE
  7. Dec 13, 2013 #6
    Likewise if it was a positive going from high to low potential it would also lose potential
  8. Dec 13, 2013 #7
    I know that if you go with nature you lose potential energy . If you go against you gain potential energy . So if a negative charge moves from high to low that means you lose PE since you are going with nature?
  9. Dec 13, 2013 #8

    Simon Bridge

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    I cannot help you if you do not answer questions.
    They are not there for decoration - I need to see how you answer them so I know how to reply.

    What is the definition of potential?
  10. Dec 13, 2013 #9
    potenital energy is the energy of storage.
  11. Dec 13, 2013 #10

    Simon Bridge

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    But moving objects store kinetic energy don't they? So the "energy of storage" for a moving object would be kinetic.

    You didn't answer the question though:
    You told me about potential energy - not potential, which is what I asked for.
    You gave me a description instead of a definition.

    I think you are getting confused because you do not know what "potential" or "potential energy" is.
    You should review your class notes on this topic - I can only go briefly here.

    Potential Energy of an object at a position is the amount of work needed to get the object to that position from some agreed-upon reference position (usually an infinite distance away).

    Thus, if we know ##\vec F(\vec r)##: how force varies with position, the work to move a small distance ##\text{d}\vec r## is ##dW=\vec F(\vec r)\cdot\text{d}\vec r##. Which needs vector calculus - which is why, when you start out, we just tell you the result.

    Gravitational Potential Energy of a mass at a position is the amount of work done to get that mass to that position from an infinite distance away.

    Potential is the potential energy per unit <something> - where the <something> is the property of the object that is important to the potential energy.

    the important property for gravity is mass so -
    Gravitational Potential is the gravitational potential energy divided by the mass.

    For gravity - the force on mass m a distance r from mass M is $$\vec F(r)=-\frac{GMm}{r^2}\hat{r}$$

    The potential energy of mass m at that distance is the work needed to get it there from infinitely far away.##\renewcommand{\dr}{\;\text{d}r}##
    The work needed to bring the mass m to distance r is given by: $$U(r)=-\int_\infty^r F(r^\prime)\dr^\prime = -\frac{GMm}{r}$$The gravitational potential associated with distance r is U/m: $$\phi = \frac{GM}{r}$$.In electrostatics - we have to deal with having two charges ... so the general definition for potential energy is changed a bit.

    Charges get a bit more ticklish because there are two kinds, but we can follow the definition:
    Electrostatic Potential Energy of a charge q distance r from another charge Q is: $$U=\frac{kQq}{r}$$ ... if they are both positive charges or both negative charges, the U is positive (because the force is repulsive, you have to do work on the charge q to get it there).

    Electrostatic Potential for distance r due to charge Q is U/q: $$\phi=\frac{kQ}{r}$$

    A chage in potential would involve a change in position (final - initial) like this: $$\Delta\phi = kQ\left(\frac{1}{r_2}-\frac{1}{r_1}\right)$$ and the change in potential energy is related as follows: $$\Delta U = q\Delta\phi$$ ... so the answer to your question (back in post #1)
    ...You put the numbers into the equation.

    If the change in potential is negative, and the charge is negative, then the charge has gained PE.
    If the change in potential is positive, and the charge is negative, then the charge has lost PE.

    If the charge has moved from a high potential to a low potential ... then ##\phi(r_2)>\phi(r_1)\implies \Delta\phi < 0## ... the change in potential is negative. Then the charge has gained potential energy.

    If the charge q were moving freely (no other forces), then it slowed down - losing kinetic energy.
    Last edited: Dec 13, 2013
  12. Dec 14, 2013 #11


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    Assume the electron is between two fixed point charges, one is positive and the other is negative.

    The potential is positive near the positive charge and negative near the negative charge with respect to infinity.

    Which charge - the positive or the negative will attract and which one will repel an electron? If you release the electron from rest, in which direction will it move "by nature" ? towards the negative or towards the positive charge?

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