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How the distance from centre decides type of charge motion?

  1. Sep 24, 2015 #1
    If charge -Q of mass m is kept on y axis at large distance from the center,then it will execute oscillatory and periodic motion but if it is released very close to the origin then it will execute SHM .I want to know why?I mean how the distance from centre decides type of motion oscillatory or SHM?
     
  2. jcsd
  3. Sep 24, 2015 #2

    jbriggs444

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    What is at the origin to cause this? What, in your opinion distinguishes "oscillatory and periodic" motion from simple harmonic motion?

    Edit: at a guess, we have a diffuse, spherically symmetric cloud with a uniform positive charge density centered on the origin. A charge far away sees an inverse square force law (-1/r^2) and a charge located within the cloud sees a force law that is directly proportional to distance (-r).
     
  4. Sep 24, 2015 #3
    Both are periodic. The basic difference between the two is that in shm acceleration is directly proportional to displacement which is not there in case of oscillation.
     
  5. Sep 24, 2015 #4
    This is coulomb's force,I know.
    But I don't know which force are you talking about here?
     
  6. Sep 25, 2015 #5

    jbriggs444

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    The Coulomb force.

    According to the spherical shell theorem, the portion of the charge cloud farther from the origin than the -Q test charge cancels out to a net of zero. So only the portion of the cloud nearer the origin than the test charge matters. That portion of the cloud has volume proportional to r3 and inverse square attraction proportional to 1/r2. That means that the net attraction is proportional to r.
     
  7. Sep 25, 2015 #6
    but it is for gravitation.
     
  8. Sep 25, 2015 #7

    jbriggs444

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    That is for any force that follows an inverse square law.
     
  9. Sep 25, 2015 #8
    Ok.Please don't go anywhere.I have to some queries.
     
  10. Sep 25, 2015 #9
    could you please elaborate this part?
     
  11. Sep 25, 2015 #10
    That means overall(total) charge can be treated as/assumed to be concentrated at a point at its centre.
     
  12. Sep 25, 2015 #11
    You meant centre of the sphere.
     
  13. Sep 25, 2015 #12

    jbriggs444

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    Right.

    Uniform charge density. Sphere with volume that goes as r3. So total enclosed charge proportional to r3. Field equivalent to that charge at origin. Inverse square force law. So net field strength at radius r scales as r3/r2.
     
  14. Sep 25, 2015 #13

    jbriggs444

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    Yes, as in post #2, I am guessing that you are discussing a situation with a cloud of charge of uniform density centered at the origin. The center of a sphere of radius r centered at the origin is at the origin (by definition).
     
  15. Sep 25, 2015 #14
    If we take distance of -Q from centre of sphere i.e origin as "a" & the portion of the charge cloud to be q and radius of sphere to be r
    let b be any value less than r .If r>b or r>a
    that's what it means?
     
  16. Sep 25, 2015 #15

    jbriggs444

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    That is nonsense. You stated that -Q is a quantity of charge. It cannot also be a distance.
     
  17. Sep 25, 2015 #16
    Where i said -Q is distance?
     
  18. Sep 25, 2015 #17

    jbriggs444

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    Edit: I apologize. You mean the distance from the origin to the charge whose value is -Q. And you want to denote that as a. I am not sure what you want q and r and b to denote.
     
  19. Sep 25, 2015 #18
    yes
     
  20. Sep 25, 2015 #19
    please make it more clear.It's my humble request
     
  21. Sep 25, 2015 #20

    jbriggs444

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    What is it that you would like clarified?
     
  22. Sep 25, 2015 #21
    Uniform charge density. Sphere with volume that goes as r3. So total enclosed charge proportional to r3
    Till here I understood.
     
  23. Sep 25, 2015 #22
    Field equivalent to that charge at origin. Inverse square force law. So net field strength at radius r scales as r3/r2.
    I am unable to link
     
  24. Sep 25, 2015 #23

    jbriggs444

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    So you agree that if we have a uniform cloud of charge centered on the origin and a test charge at distance r from the origin that the total charge closer to the origin than the test charge is proportional to r3

    Do you agree that if this cloud of charge is spherical then the portion which is farther than r from the origin produces no net electrical field on the test charge? The spherical shell theorem should tell you this.

    Do you agree that the field from the portion of the could which is nearer than r from the origin produces an electrical field on the test charge identical to that which would be produced if its entire charge were concentrated at the origin? The spherical shell theorem should also tell you this.
     
  25. Sep 25, 2015 #24
    yes.
    yes
    I am so sorry ;did not get you.
     
  26. Sep 25, 2015 #25
    Should I think of coordinate system.
     
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