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!

Electric field from a non-uniformly charged disk

  1. Nov 24, 2016 #1
    1. The problem statement, all variables and given/known data
    We are given a disk with negligible thickness, a radius of 1m, and a surface charge density of σ(x,y) = 1 + cos(π√x2+y2). The disk is centered at the origin of the xy plane. We are also given the location of a point charge in Cartesian coordinates, for example [0.5,0.5,2]. We need to find the electric field components (x,y,z) at the location of the point charge.

    2. Relevant equations
    d##\vec E## = σdS/4πε0 ⋅ ##\hat r##/r2


    3. The attempt at a solution
    My first thought was to make dS a thin ring centre origin. this would give dS=2πr'dr' where r' is the radius from the origin to the ring. I then thought the I could write r2 as r'2+z2, and r' would also be equal to √x2+y2. Plugging this and σ into the integral just to find the magnitude of ##\vec E## we get:
    ∫ (1+cos(πr'))r'/(r'2+z2) dr'
    However I have realised that this is wrong because a) the answer it gives is far to small to be reasonable, b) I think this calculation assumes a spherical field which it clearly isn't, and c) the relationship to find r in terms of r' and z only holds if the point charge is over the disk, which it isn't necessarily. I think I am meant to split the integral into x, y, and z components but am unsure of whether this is the correct approach. Now i am completely stuck, none of the notes I can find explain this, I even took out a book from the 1950s on electrostatics to try and find the way to solve this and I just cannot for the life of me find it anywhere! Any help would be very much appreciated!
     
  2. jcsd
  3. Nov 24, 2016 #2

    BvU

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    Hello mshahi, :welcome:

    Are you aware that the ##\vec r## in ##d\vec E## is a different one from the ## r ## in ##dS## ? How ? Writing ##r^2## as ##r'\,^2 + z^2 ## makes ##x## and ##y## disappear. Or are you only interested in the field on the z axis ?

    Make a drawing to oversee the situation and set up an expression for the integration.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted