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: Gauss Law and Flux for variable charge density in a sphere

  1. Jan 14, 2012 #1
    Gauss Law and Flux for variable charge density in a sphere

    1. The problem statement, all variables and given/known data

    The charge density within a sphere varies as a constant, a, times its radius, r. Find an expression for the direction and magnitude of the electric flux, D, within the sphere

    2. Relevant equations

    Gauss' Law
    sphere volume = [itex]\frac{4}{3}[/itex] [itex]\pi[/itex] r[itex]^{3}[/itex]

    3. The attempt at a solution

    I have some difficulty understanding the question, but this is what I think I should do:

    Charge Density = ar

    Charge in volume moving from r to r+δr , δQ, is: ar x volume
    =(4/3) [itex]\pi[/itex] ar [(r+δr)^3 - r^3)]
    =(4/3) [itex]\pi[/itex] ar (3 r^2 δr) (ignoring double differentials as negligible)
    =4 [itex]\pi[/itex] a r^3 δr

    integrating from 0 to r(an arbitrary distance from centre) gives charge within that volume, Q:
    Q = [itex]\pi[/itex] a r^4

    Gauss Law says flux through an area is equal to charge enclosed so;
    Magnitude of the flux ,D, = Q = [itex]\pi[/itex] a r^4
    Direction is radially outward (assuming charge is positive). (not sure on how to argue this...)

    Notes: I have no idea if this is correct, or if I'm completely of the plot!! any help greatly appreciated.
    I thought D was the flux density, though the question calls it flux, so do I need to divide by area?

    Thanks Everyone!...
  2. jcsd
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook

Can you offer guidance or do you also need help?
Draft saved Draft deleted