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!

Potential inside sphere with empty cavity

  1. Oct 15, 2013 #1
    1. The problem statement, all variables and given/known data
    An insulating sphere of radius R , centered at point A, has uniform chagre density ρ. A spherical cavity of radius R / 2 , centered at point C, is then cut out and left empty, see Fig.

    (a) Find magnitude and direction of the electric field at points A and B.

    (b) Find the potential at points A and B. Set V(r → ∞) = 0.

    (c) Write down an algebraic solution (no integrals!) for E(r) and V (r) for the space outside the larger sphere, r > R. Choose r = 0 at point A, and the radius vector of point C as r = RC .

    (question1) in the uploaded file


    3. The attempt at a solution
    (a)First I want to figure out the volume charge distribution, which I wanted to do by finding the the volume of the whole sphere minus the volume of the cavity.
    [tex] \int_V \rho \cdot dVolume = \frac{4}{3}\pi \rho (R^3-\frac{R^3}{8})=\frac{7}{6}\pi R^3 \rho [/tex]

    Then to get [itex] E_B [/itex] I wanted to use Gauss' law, but Im not sure how i would set that up because the E field isnt isotropic, so instead Im trying to use the equation for E-field of a volume charge distribution:
    [tex] E(r)=k\int \frac{dq \hat{s}}{s^2} [/tex]
    Where i just calculated dq. [itex] s^2=R [/itex], but im not sure what [itex] \hat{s} [/itex] is
     

    Attached Files:

  2. jcsd
  3. Oct 15, 2013 #2
    thinking about it though, im pretty sure that what i got for dq is wrong, because i dont think what i did takes into account that the cavity isn't centered at the origin
     
  4. Oct 16, 2013 #3

    haruspex

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member
    2016 Award

    Treat it as one sphere minus another. Find the fields and potentials for each sphere and take the difference.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted