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Gauss law help

  1. Sep 14, 2005 #1
    ok i was flying through the homework no prob. then i hit this problem and i got an answer but i dont think its right.

    A uniformly charged sphere of radius R and volume charge density [tex] \rho_0[/tex] is adjacent to a uniformly charged infinite plane of surface charge density [tex] \sigma_0[/tex]. the charge densities are related by
    [tex] \sigma_0=\frac{\rho_0R}{2}[/tex]
    the center of the sphere is a distance d from the plane. Find two points, one inside the sphere and one outside the sphere where the electric field is oriented away from the plane at a 45 degree angle with respect to the z axis.[note these points are not on the axis] (in the figure the infinite plane lies in the xy plane )

    well i started this off by finding the electric field inside the sphere


    i then found the charge of the infinite plane via the pill box gaussian surface and came up with


    and breaking to components i got

    and by a similar approch i got

    like i said i dont think this is right, so if some one could help me out a bit that would be great

  2. jcsd
  3. Sep 15, 2005 #2


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    Mmmh. There's a problem here: you write [itex]\vec{E}= \mbox{a scalar}[/itex]. What are the directions of the E_P and E_S vectors? Write them in cartesian coordinate for a coordinate system centered on the sphere, and find the condition on E_p + E_s to be at 45°.

    Oh, and your field equations look wrong. The field inside the sphere is not uniform.
    Last edited: Sep 15, 2005
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