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!

Calculating E-field and potential of a charged ring

  1. Aug 13, 2013 #1
    Hello folks!

    I've been trying to calculate the E-field of a charged ring. It seems well documented for a symetric point(a line from the center etc.) but what I'm interested in is say if I'm slightly of the center of the ring, how can I make a more general equation?

    I've tried calculating the potential and the field from there but I get a dominating 0 somewhere so that must be wrong ( V = ∫(λ(x')*dl'(1/(|x-x'|))) and E = -∇V , substituting dl' and λ(x') I get the product of those vectors to (-ρcos(θ')*ρsin(θ') + ρcos(θ')*ρsin(θ'))λdθ' = 0 ??).

    Anybody knows where I'm wrong and what to do?
     
  2. jcsd
  3. Aug 13, 2013 #2

    Simon Bridge

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member
    2016 Award

    Welcome to PF;
    The reason everyone does the field along the axis is because the symmetry is easy.
    Off that axis, things get trickier.

    Specify cylindrical polar coords, and specify a vector ##\vec{r}## to an arbitrary point.
    The resulting field should look a lot like that in a plane from two like charges - then rotated about the z axis.

    It may be easier to solve Poisson's equation or follow the differential form.

    Anyway - you could also search for "off axis electric field of a ring of charge"
    http://www.mare.ee/indrek/ephi/efield_ring_of_charge.pdf
    http://electron.physics.buffalo.edu/sen/documents/field_by_charged_ring.pdf
     
  4. Aug 14, 2013 #3
    Thank you for the welcome. And thanks, I will check it out, although I found something out that I did miss. Apparently I've treated λ and dl' as vectors when they probably should not have been. Now I went straight to the general integralform of the E-field equation and solved it as λ being a constant over the integration and dl' = ρ*dθ'. For x,y = 0 I get the same equation as for the symetric equations as expected. I'm going to use it in electron path simulation so I solved the integral numericaly, probably going to do it proper later though.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook