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Derivation of Electric Field with Gauss's Law

  1. Nov 14, 2015 #1
    I did everything I could to solve the following problem:
    A solid ball of radius rb has a uniform charge density ρ.

    What is the magnitude of the electric field E(r) at a distance r>rb from the center of the ball?
    E(r) =

    My third attempt went like this: qencl=[ρ(4/3)(π)rb3]


    And ah, well, a little simple division and cancelling leads to:

    However, the book answer is 1/3 my answer. Could someone please tell me where this constant develops?
  2. jcsd
  3. Nov 14, 2015 #2


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    Try Gauss's law. Start by writing the equation for Gauss's law.
  4. Nov 14, 2015 #3


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    The righthand side is okay. Check the details on the lefthand side of this equation.
  5. Nov 14, 2015 #4
    Why did you multiply the electric field with the volume?
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