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Gauss' Law Question

  1. Jul 9, 2006 #1
    How would you solve this:

    A small charge of 443 C is at the center of a 7.97 cm radius ball. How much flux passes through the ball's surface?

    The answer is 4.922 E-8 N.m2/C

    I don't know how to get this answer. Please explain. Thank you!!!
     
  2. jcsd
  3. Jul 9, 2006 #2

    siddharth

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    You wrote the title as "Gauss Law Question". Do you know what Gauss' law says? Can you apply it here?
     
  4. Jul 9, 2006 #3
    I know it is Gauss' Law because that is what the website I got it from said. I have looked everywhere and applied the Gauss' Law how I thought I should apply it but I keep getting the wrong answer and have no idea how they got that answer. So that is why I need someone to explain it for me if they know.
     
  5. Jul 9, 2006 #4

    Hootenanny

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    Perhaps if you showed your working we could point out where you have gone wrong...
     
  6. Jul 9, 2006 #5
    Well, I am confused as to what Gauss Equation to use... I have tried q=Eo*flux and then I tried flux=q/4pi*k and then I tried flux=k*q/r^2... none of them turn out correct.

    What is the equation to use for a point charge in a sphere?
     
  7. Jul 9, 2006 #6
    I keep finding that flux= q/Eo and so I put 443 in for q and 8.85*10^-12 for Eo and get 5.006*10^13.
     
  8. Jul 9, 2006 #7
    Assuming that you are familiar with calculus, you can have a look at http://en.wikipedia.org/wiki/Gauss_law. The flux is indeed [itex]q/\epsilon_{0}[/itex] in your case :smile: Do you have a doubt about the flux being independent of [itex]R[/itex]? If so, the wiki article/a reading from any standard textbook should clear it.
     
    Last edited: Jul 9, 2006
  9. Jul 9, 2006 #8

    siddharth

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    443 C, is an awful lot of charge. Are you sure you got the numbers right from the question?

    You calculated the flux as q_enc/Eo, and that should work.
     
  10. Jul 9, 2006 #9
    I copied and pasted it so I know that is right. And I keep getting the wrong answer for ALL of the examples... which are all similar to that one.
     
  11. Jul 9, 2006 #10
    Another example on the webpage is:

    A small charge is at the center of a 9.77 cm radius ball. If 8.322 E-8 N.m2/C passes through the ball's surface, how much charge is at the center?

    and the answer is 749C.

    I don't get this one either. I am assuming the use the same equation.
     
  12. Jul 9, 2006 #11
  13. Jul 9, 2006 #12

    siddharth

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    Ok, Gauss' law is

    [tex] \int \vec{E}.d\vec{a} = \frac{q_{enc}}{\epsilon_0} [/tex]

    That's the equation you're going to use for these problems.
    Now, note that
    (i) The value of [itex]\int \vec{E}.d\vec{a}[/itex] is the flux passing through the surface.
    (ii) Using Gauss' law, it follows from the previous step that [itex]\frac{q_{enc}}{\epsilon_0}[/itex] is also the flux passing through the surface.
    So, you've got 2 ways to calculate the flux.

    Why have they given the radius? Because you can calculate the area of the ball. Notice that, when a charge is at the center of a sphere, the integral [itex]\int \vec{E}.d\vec{a}[/itex] can be simply reduced to E times A. Can you figure out why, and solve the problems from here?
     
  14. Jul 9, 2006 #13
    no i have no idea what to do... i need step by step. and everything i read said you dont need the radius.
     
  15. Jul 9, 2006 #14

    Mute

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    I think the problem is that whoever calculated the answers on that site is incorrectly using the Coloumb force constant {1/(4*Pi*epsilon_0)} instead of the permittivity of free space (epsilon_0) in their calculations. For instance, they ask this question:

    "A small charge of 45 C is at the center of a ball. If 5 E-9 N.m2/C passes through the ball's surface, what is the radius of the ball (if it matters)? "

    Now, obviously for that question the answer is that the radius doesn't matter, but if you use their values for charge and the flux, and plug into Flux = charge/k, solving for k you get 9x10^9, which is 1/(4*Pi*epsilon_0), not epsilon_0.

    Also, if in the original question you asked, if you say Flux = 443/(9x10^9), you'll find you get their answer.

    So, you were doing everything correctly; it's the website that is wrong.
     
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