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: Energy of Spherical Distribution

  1. Feb 20, 2008 #1
    1. The problem statement, all variables and given/known data

    Determine the energy required to generate a spherical charge distribution
    of radius R and uniform density ρ0 . In class, we went over two different
    methods. For this assignment, you need to work out the following two
    integrals over a volume (and surface) of a concentric sphere of radius a,
    where a > R.

    U = [tex]\epsilon//2[/tex] [ [tex]\int[/tex]E^2 +[tex]\oint[/tex] VE ]
    here the first integral is a volume integral over the sphere and the second integral is a surface integral over the surface of the sphere.
    this is equation 2.44 in Griffiths

    2. Relevant equations
    I started with the equation for electric field inside a sphere of uniform distribution

    which is E = kQr/R^3 in radially outward, where k is the 1/4 pi epsilon constant and r is some some distance from the center less than R

    Then I use the equation for Potential inside the sphere as V= (kQ/2R)(3-r^2/R) again where r is less than R

    3. The attempt at a solution

    I am just stuck with the integration I guess. The first integral uses the square of E which is easily found by just squaring the equation above, so that now E^2 is not a vector but just the scalar square of the equation above. then dTau for the volume of the sphere is just the volume element for spherical coordinates? (r^2)sin(phi)drd(phi)d(theta)

    The second integral uses the V equation, multiplied by the E equation and integrates over the surface where the da = area element for area of surface of sphere = (r^2)sin(phi)d(phi)d(theta)

    I apologize if this is hard to read, I am terrrrrrible at using the latex stuff, it ever seems to work out

    Edit: I don't yet have a complete solution but I just realized my confusion was coming form mistranslation in the coordinate systems. I always forget what theta and phi correspond to as i have had teachers switch them up before. I saw the sin(phi) thinking the integrals were going to integrate sin (phi) from 0---2Pi which would yield zero
    Last edited: Feb 20, 2008
  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