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Electric field of a point charge inside a sphere

  1. May 5, 2014 #1
    1. The problem statement, all variables and given/known data

    (a)Consider a charged sphere of radius R centred at the origin with the spherically symmetric charge density ρ(r) = ρ0(r4/R4) where ρ0 is a constant and r is the radial coordinate.
    Find the charge dQ0 contained in a spherical shell of radius r0 < R and infinitesimal thickness dr0.
    Hence find the charge Q(r) contained inside the sphere as a function of
    r < R.
    Using Gauss’s law in integral form, determine the magnitude of the radial electric field Er(r) inside the sphere as a function of r < R.
    Using the fact that [itex]\underline{∇}[/itex][itex]\cdot[/itex]E(r) = [itex]\frac{1}{r^2}[/itex][itex]\frac{∂}{∂r}[/itex](r2Er(r)) in this case, verify Gauss’s law in
    differential form at a general point inside the sphere.

    (b) A positive point charge Q is added to a point P0 with position vector R0 with components (1, 1, 1) inside a sphere with the same charge density as in part
    (a) apart from the charge Q. Calculate the vector electric field E(r) at a point
    P with position vector r with components (1, 2, 1) inside the sphere in terms
    of the unit vectors [itex]\widehat{x}[/itex], [itex]\widehat{y}[/itex], [itex]\widehat{z}[/itex] and Q and Er (considered in part (a)).

    2. Relevant equations



    3. The attempt at a solution
    i have done part b of the question already. i am just not quite sure how to deal with a point charge inside a sphere with charge density. Do i just add up the two field?
     
  2. jcsd
  3. May 5, 2014 #2

    Simon Bridge

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    Superposition principle.
     
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