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Date Posted: 5/16/2008 10:07:59 AM  Status: Closed
Gauss's law
Course Textbook Chapter Problem
Calculus Based Physics Fundamentals of Physics Extended (6th) by Halliday, Resnick, Walker 24 37E
Question Details:
In a 1911 paper, Ernest Rutherford said "In prder to form some idea of the forces required to deflect an α particle through a large angle, consider an atom [as] containing a point positive charge Ze at its centre and surrounded by a distribution of negative electricity -Ze within a sphere of radius R. The electric field at a distance r from the center for a point inside the atom is
\         E=Ze/4πε(1/r2 -r/R3)

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Date Posted: 5/28/2008 2:12:26 AM  Status: Live
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Response:
given
let us consider a point P at a distance r from the center of the atom & construct a spherical Gaussian surface around the point P.
so from  Gauss's law we have
    = qenclosed / ε0
  or cos00 = qenclosed/ε0
here qenclosed = Ze -(Ze/4/3*πR3)*4/3*πr3
                       = Ze(1-r3/R3)
      so E = Ze(1-r3/R3) / ε0
   or E.4πr2 = Ze(1-r3/R3) / ε0
     or E = Ze/4πε0 *[1/r2 - r/R3]
 
 
  

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Date Posted: 5/28/2008 3:02:39 AM  Status: Live
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