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How To Find Potential ?

  1. Sep 22, 2009 #1
    How To Find Potential ??

    1. The problem statement, all variables and given/known data

    Consider the uniformly charged sphere with
    radius R = 4.65461 m,
    Q = 6.66731 μC is the
    total charge
    inside the
    sphere.

    a) Find the total flux passing through the
    Gaussian surface (a spherical shell) with ra-
    dius 2.08762 m.

    b) Find the electric field at radius r =
    2.08762 m.

    c) Find the value of the electrostatic potential
    at the same radius r = 2.08762 m.


    2. Relevant equations

    E=kq/r^2
    v=kq/r

    3. The attempt at a solution

    I have answered Parts A & B , I got for part A : Total Flux = (Q/Epsilon)*(r/R)^3
    & for part B : E = kQr/R^3 , But part C have stopped me so any hint or clue will be gratefull and thx in advance.
     
  2. jcsd
  3. Sep 22, 2009 #2

    tiny-tim

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    Welcome to PF!

    Hi Fazza3_uae! Welcome to PF! :smile:

    (try using the X2 tag just above the Reply box :wink:)
    [STRIKE](But isn't the total flux independent of radius?)
    [/STRIKE]
    What definition do you know for electric potential?
     
    Last edited: Sep 23, 2009
  4. Sep 23, 2009 #3
    Re: Welcome to PF!

    Hi Tiny-Tim! Thx 4 Welcoming ^^




    Please check my steps of solving this part & tell me if i made a mistake :


    [tex]\phi=\int\vec{E}.d\vec{A}[/tex]

    = Int(EdACos[theta]) = Int(EdA) = EA


    E : Electric Field inside a uniform sphere of charge = KQr/R3

    A : Area of the spherical Shell of radius r = 4*Pi*r2

    Inserting these Values we get :

    [tex]\phi=[/tex] (Q/epsilon)(r/R)3


    As far as i knew from the lectures the electric potential is the potential energy divided by the charge of a point in space.I also do know that Difference in potential is the same as Flux.

    If i understood it wrongly please correct it for me & let me know & it will be appreciated. ^^
     
  5. Sep 23, 2009 #4

    tiny-tim

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    Hi Fazza3_uae! :smile:

    (have a pi: π and an epsilon: ε :wink:)
    oops! ignore that … I misread the numbers. :redface:

    No …

    i] when we say "potential", we always mean the difference in potential anyway (and the same for "potential energy")

    ii] Flux is the integral of a vector across a surface.

    (In particular, there is no such thing as flux "at a point".)

    So electric flux is the integral of the electric field (E) across a surface.

    (Read http://en.wikipedia.org/wiki/Flux#Flux_definition_and_theorems_2" :smile:)

    So the way you answer a) (the flux) is simply by measuring the charge inside the surface, and dividing by ε0

    then you answer b) (the field) by using your formula flux = EA.
    It would be more accurate to say that electric potential = potential energy per charge.

    But for c) you need an equation for the potential (or for the potential energy) … what equation do you know? :smile:
     
    Last edited by a moderator: Apr 24, 2017
  6. Sep 23, 2009 #5
    Re: How To Find Potential ??

    Hi again sir ^.*

    Thx a lot for the information and corection that U've posted & I appreciate your help to me Sir.

    Part C ) MmmMmmm.... I actually know an equation for potential which is V=kq/r but I tried it and got wrong answer. I've tried for r once and for R once & still got wrong answer.

    I doubt if there is another formula of potential that is related to the Formula I got in part B. I mean it could be like this : V=kqr/R

    I know that My doubt is Maybe 1% correct but still a try. I can't check if this new equation is right or not because I have tried to put an answer twice in the website & still one chance to insert my last answer otherwise i'll get Zero in this part.

    Thank you again sir. ^^

    ( Please Excuse Me If My English Is So Bad, I will Try To Improve It )
     
  7. Sep 23, 2009 #6

    tiny-tim

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    oh i see … you used v for the potential.

    Yes, if E = kq/r2, then E = -gradU, so U (or v) = -kq/r. :smile:
     
  8. Sep 23, 2009 #7
    Re: How To Find Potential ??

    You said if E=kq/r², then E=-gradU , What do u mean by (gradU) & why it is minus ?

    and here we have E=kqr/R³, so what V must equal now??
     
  9. Sep 23, 2009 #8

    tiny-tim

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    If you haven't done grad, then just read it as (d/dr) … so E = -dV/dr.

    And it's minus because that's how the potential is defined.

    (For example, the field outside the sphere is K/r2, and the potential is -K/r, so that the potential is 0 at r = ∞ :wink:)
    oh, I forgot that E=kqr/R³ … ok, then dV/dr = -kqr/R³, so V = … ? :smile:
     
  10. Sep 23, 2009 #9
    Re: How To Find Potential ??

    Yup , Finally I got right answer Thx a lot Sir.

    & thx also for the clarification about grad ^^ Appreciate it.

    May God Bless You Sir.
     
  11. Sep 23, 2009 #10

    tiny-tim

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    thanks …

    but no need to call me Sir …

    i'm only a little goldfish! :smile:
     
  12. Sep 23, 2009 #11
    Re: How To Find Potential ??

    Alright Tiny Miny Little GoldFish U got it ^^
     
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