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 inside a cavity

  1. Oct 28, 2012 #1
    1. The problem statement, all variables and given/known data
    If I have a solid sphere of radius R and charge density [itex]+\rho \, C/m^3[/itex] and I then remove a smaller sphere of radius [itex]b[/itex] and is a distance [itex]a[/itex] from the center of the larger sphere, what is the electric field inside the cavity?
    I get an answer which I think is right. I've look at the math over and over and can't quite figure out what the teacher did.

    2. Relevant equations
    Gauss' Law:
    [tex] \oint \vec{E} \cdot d\vec{S} = \frac{q_{encl}}{\epsilon_0} [/tex]

    3. The attempt at a solution
    I know this is a classic problem using the superposition principle.
    First I apply GL to the large sphere at a distance [itex]r<R[/itex] from the center and get an electric field
    [tex] \vec{E} = \frac{ \rho }{3 \epsilon_0} \vec{r} [/tex]

    Then I do the same except with a charge density of [itex]-\rho \, C/m^3[/itex] so
    [tex] \vec{E'} = - \frac{\rho }{3 \epsilon_0} \vec{r'} = -\frac{\rho}{3 \epsilon_0} (\vec{r} - \vec{a}) [/tex]

    Now I just sum the two fields
    [tex] \begin{align}
    \vec{E} + \vec{E'} & = \frac{ \rho }{3 \epsilon_0} \vec{r} -\frac{\rho}{3 \epsilon_0} (\vec{r} - \vec{a}) \\ &= \frac{ \rho }{3 \epsilon_0} \vec{r} -\frac{\rho}{3 \epsilon_0} \vec{r} +\frac{\rho}{3 \epsilon_0} \vec{a} \\ &=\frac{\rho}{3 \epsilon_0} \vec{a} \end{align} [/tex]

    This is my solution which is supposedly wrong.
  2. jcsd
  3. Oct 28, 2012 #2


    User Avatar
    Homework Helper

    Your solution is correct. See, for example http://jkwiens.com/2007/10/24/answe...nonconducting-sphere-with-a-spherical-cavity/
    What did your teacher do?

  4. Oct 28, 2012 #3
    wrong thread :P
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook