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Homework Help: Electric field, potential

  1. Oct 11, 2008 #1
    1. The problem statement, all variables and given/known data
    A spherical charge distribution is given by

    [tex]\rho[/tex] = [tex]\rho_0[/tex][tex]\left([/tex]1-(r^2/a^2)) , (r<= a)
    [tex]\rho[/tex] = 0, (r> a)

    a) calculate the total charge Q
    b) find the electric field intensity E and the potential V outside the charge distribution
    c) find E and V inside
    d) show that the maximum value of E is at (r/a) = 0.745
    e) the above charge distribution applies roughly to light nuclei. Draw graphs showing [tex]\rho[/tex], E, and V as functions of r/a for calcium (atomic number 20), assuming that [tex]\rho_0[/tex][tex] = 5.0 x 10^25 C/m^2 and a = 4.5 femtometers

    2. Relevant equations

    [\tex]\oint E.da = Q/\epsilon_0[\tex]

    3. The attempt at a solution
    \ Guass'a law and other general equations for E and V were used. I do not think I am close to the correct answer.
  2. jcsd
  3. Oct 11, 2008 #2
    (a) follows from the definition of charge *density*; there is no need to use Gauss's law

    (b) and (c) do follow from Gauss' law: choose the right surface and volume, and find E as a function of r. From that, obtain V(r).
  4. Oct 11, 2008 #3
    Thanks borwal, yeah that's what i've done. I am not quite sure about d and e, those are my real problems. Listed all the questions just let the entire problem be clearer. thanks for replying :)
  5. Oct 11, 2008 #4
    If you have E as a function of r, it should be rather easy to find its maximum!
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