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Electromagnetism: charge density

  1. Nov 11, 2012 #1
    1. The problem statement, all variables and given/known data

    Given a sphere of radius R with a volumic charge distribution p find the function p.
    The electric field inside of the sphere is radial with a constant modulus E

    2. Relevant equations

    div E = p / ε

    ∫∫E.ds = 1/ε * ∫∫∫ p * dV

    3. The attempt at a solution

    I tried to solve it using those two equations. (r is the radius)

    div E = p / ε ⇔ dE/dr = p/ε ⇔ ∫dE = 1/ε ∫p dr ⇔ E = 1/ε * p * r ⇔
    ⇔ p = E*ε / r

    I don't think I can integrate p like that, since p is a function of the radius. I don't know what to do thought..

    Using the second equation and solving in a similar way I get:

    ∫∫E.ds = 1/ε * ∫∫∫ p * dV ⇔ E*4*pi*r^2 = 1/ε * p * (4/3)*pi*r^3 ⇔
    ⇔ p = 3*E*ε/r


    The correct result would have been p = 2*E*ε / r

    Any help would be appreciated!
    Thanks.
    Daniel
     
  2. jcsd
  3. Nov 11, 2012 #2
    they usually tell the function of (ρ) rho, volume charge dis... and find the totale charge... use the equation Q = ∫∫∫ρdv , dv is easy to find even they don't tell... but they not even tell the function of Q !! if they did , may be use dQ/dv=ρ.
    And the electric field to the center of the sphere is 0 , no matter of volume charge dis.. or surface charge dist... if the electric field to other point than center , it's much more complex... use the equation dE = kρdv/r^2 , k=1/4∏ε =contante
    so Ez =∫∫∫dE cosθ =0
    Ey=∫∫∫dE cosθcosα =0
    Ex=∫∫∫dE cosθsinα =0
    so E =0 to the center of sphere...
     
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