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Why when two conductors connected by a conducting wire gain the same potential . ?

  1. May 8, 2012 #1
    Why when two charged conductors connected by a conducting wire gain the same potential .
    Lets say we have two spheres of different charges why when we connect them by a single copper wire they gain the same potential
    Thanks in advance
     
  2. jcsd
  3. May 8, 2012 #2

    tiny-tim

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    hi nishantve1! :wink:

    tell us what you think, and then we'll comment! :smile:
     
  4. May 8, 2012 #3
    Re: Why when two conductors connected by a conducting wire gain the same potential .

    I am new to Electrostatics , first of all I have no idea but still what I am able to figure out is maybe the charges on both become equal but I see thats not much to do with the potential or is it am I right ?
     
  5. May 8, 2012 #4

    tiny-tim

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    ok, well, always start with the definitions, then write out all the equations you know, and see if any of them help …

    (btw, that is why the pf homework template requires you to write out the equations first, and please post in the homework sub-forum in future)

    DEFINITION:

    what is electric potential?

    what does it do?​

    EQUATIONS:

    what equations do you know for electric potential?​
     
  6. May 8, 2012 #5
    Re: Why when two conductors connected by a conducting wire gain the same potential .

    Sorry , next time I will definitely post in homework sub forum

    Electric potential I know is Work done per charge in bringing it from infinity to a point .
    Electric potential is Like gravitational potential it The closer a test charge is to a electric field source more potential energy it has and thus more Electric potential .
    Electrons flow from higher to lower potential thats what makes electricity flow


    V(a) - V(b) = integral from a to b E.dl

    E = -dV/dr

    V = E.d

    Due to a point charge at a distance R the electric potential is Q/4 pi Epsilno0 R
     
  7. May 8, 2012 #6

    tiny-tim

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    mmm … that's only if the potential defined to be zero at infinity (in electric circuits, it usually isn't :wink:)

    better is to talk about potential difference

    electric potential difference

    = potential energy difference per charge

    = minus work done, per charge, by the electric field :wink:
    i always get confused about this :redface:, but isn't that for positive charge? :confused:
    ok :smile:, now call the potentials V and W, and apply the above to how an individual charge will move, and how that will affect the potential difference
     
  8. May 8, 2012 #7
    Re: Why when two conductors connected by a conducting wire gain the same potential .

    oh yeah electrons flow form lower to higher potential .if both the bodies have charge of same polarity say Positive then electrons from one with lower potential say W will flow to one with higher potential V . now what ? the electrons will go and neutralize the positive charge on the other one . And if there polarities were to be different then electrons will flow the same way as above . I am seriously not able to figure out please Help me !
     
  9. May 8, 2012 #8

    tiny-tim

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    you're more or less there :smile:

    the information you haven't yet used is that there's only a fixed amount of total charge

    (i assume the spheres are isolated, ie not connected to any voltage source)

    so if the total charge is fixed, what's going to happen? :wink:
     
  10. May 8, 2012 #9
    Re: Why when two conductors connected by a conducting wire gain the same potential .

    Ok so lets name the spheres there is Sphere A with four Positive charges (just keeping things simple) and is at a higher Potential and the another sphere B has one Positive charge and is at a lower potential .
    {That means the work done per charge on Bringing a test charge from a Point where we assume U to be 0 will be higher in case of A }


    Now we connect them by a conducting wire , so the electrons from A will want to flow to B . and since the charge is conserved we have only 5 positive charges in the system .
    Now what the charges on A and B could be like
    5 0
    6 -1
    7 -2
    8 -3

    and similarly many keeping the charge +5 constant What happens then
     
  11. May 8, 2012 #10
    Re: Why when two conductors connected by a conducting wire gain the same potential .

    Hi. Say two charged conductors of charge +Q, -Q form condenser of electrostatic capacity C. So, potential difference is V=Q/C.
    WHY: By current in connecting wire Q decrease so V also decrease.
    WHEN: When Q=0, V=0 same potential.
    Regards.
     
  12. May 8, 2012 #11
    Re: Why when two conductors connected by a conducting wire gain the same potential .

    I have also learnt that if there are two bodies(with similar characteristics) with charges Q1 and Q2 if they are brought in contact the charges gets distributed like (Q1 + Q2)/2 . Is that the case here
     
  13. May 8, 2012 #12
    Re: Why when two conductors connected by a conducting wire gain the same potential .

    I get what you are trying to say . but how does charge Q becomes 0 ?
     
  14. May 8, 2012 #13

    tiny-tim

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    that's right! :smile:

    so it'll go (it's easier with an even number :wink:)
    6 0
    5 1
    4 2
    3 3 ​

    sooo … when the charges are equal, what is the potential difference (and why?)
     
  15. May 8, 2012 #14
    Re: Why when two conductors connected by a conducting wire gain the same potential .

    When the charges are equal this means that they are at the same potential . So the potential Difference will be zero . Its very easy to understand that Equal charges are at the same potential . Is it like the Potential Energy required in bringing that charge from infinity to a point in space is same for the other charge since they are equal in magnitude . Is there any Mathematical Equation that proves it I mean I tried using

    V(a) - V(b) = Integral from A to B E.dr

    which should be zero but how ?
     
  16. May 8, 2012 #15

    tiny-tim

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    ooops! :redface:

    i thought these were identical spheres, but looking back, they're not

    so … correction … the charges won't equalise, although the potentials will equalise

    so the question should be, why will the electrons keep moving while the potential difference is non-zero, and stop moving when the potential difference is zero? :wink:
     
  17. May 8, 2012 #16
    Re: Why when two conductors connected by a conducting wire gain the same potential .

    Hi.
    You say Why Ohm's law V=RI.
    Regards.
     
  18. May 8, 2012 #17
    Re: Why when two conductors connected by a conducting wire gain the same potential .

    Hi.
    Cancel of Q in positive charge plate and -Q in negative charge plate. Total discharge of battery.
    Regards.
     
  19. May 8, 2012 #18
    Re: Why when two conductors connected by a conducting wire gain the same potential .

    I am still in Capacitance so No idea about Ohm's law . Also its almost time I have to go to school . If someone please please explain it I will be very thankful . Also if potential difference is zero why will electrons move ? If I am still not Familiar with current Electricity is this question out of the scope ?

    @sweet springs I got that but what if both charges were of same polarity and different magnitude ?
     
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