1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: 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

    User Avatar
    Science Advisor
    Homework Helper

    Superposition principle.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted