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!

Gauss' Law and integration

  1. Oct 22, 2013 #1
    1. The problem statement, all variables and given/known data
    A hollow sphere of outer radius R2 and inner radius of R1 carries a uniform charge 2Q. The sphere is then cut in half to create a hemispherical shell of charge Q. Calculate E at the center point (origin) P.


    2. Relevant equations
    equation of a hollow sphere = 2/3π(r2-r1)
    Gauss' Law ∫E dot dA
    surface area hemisphere = 2πr^2


    3. The attempt at a solution
    Well, I know this is an integration problem and that I am better off integrating with polar coordinates and that I will be integrating from 0-->π as my lower and upper integral bounds.
    But in all honesty I haven't had much fortune setting the integral up. The set up is the help I am asking for.
     
  2. jcsd
  3. Oct 23, 2013 #2
    If I am not mistaken, you need to find the E field due to a HEMISPHERICAL shell

    That involves some somewhat-complicated multiple integrals and E form Coulumb's law. Gauss's law will not work due to lack of symmetry
     
  4. Oct 23, 2013 #3
    Assuming that that is your problem, here is my hint:

    Use spherical coordinates. find the charge density. consider an infinitesimal piece of the shell and the Coulomb force on a test charge at the origin. Then choose appropriate limits for r, theta, and phi and integrate
     
  5. Oct 23, 2013 #4
    Yes that is the problem. spherical coordinates make more sense. I will try that and post tomorrow what I have come up with. I don't have my calculus book nearby to refresh my memory of spherical coord. integration. This is one of those problems that has me intrigued and eager to "beat". It isn't worth a lot of points but it is due Thursday.
    Thank you for the hint!!
     
  6. Oct 23, 2013 #5
    no problem!

    I might add: depending on how comfortable you are with multivariable, you don't have to use a triple integral; just find the field of a ring, sum into a washer, sum the washers into a shell. The spherical coordinates are just a way of thinking, no need to get formal about it
     
  7. Oct 23, 2013 #6
    I follow you up until you state sum the washers into a shell. Please provide a hint as to that specific.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted



Similar Discussions: Gauss' Law and integration
  1. Gauss Law (Replies: 5)

  2. Gauss' law (Replies: 2)

Loading...