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Eletric Field of a Ring

  1. Sep 25, 2016 #1
    • 1. The problem statement, all variables and given/known data
    • A Ring with center in (0,0) and R radius.
    • The charge distribution from the ring is: ψ(θ) = ψo*Sin(θ), where θ is the angle from the x axis (counterclowise).
      Negative values of the sine determine negative charge, and 0 no charge at all.
    • What is the field (E) created from this distribution (only x and y components)?
    2. Relevant equations
    • If there we introduce a constant eletric field, F, in the positive direction of the y axis. How can i find the
      equipotentials lines from the sum of the fields?
    3. The attempt at a solution
    I tried to find the dEx and dEx as a function of dθ, so i could integrate from 0 to 2*π and get the field vector as function of x and y.
    I found:
    • dEx = K*ψ(θ)*[x-R*Cos(θ)]*dθ/[ (y-R*Sin(θ))2+(x-R*Cos(θ))2 ]3/2
    • dEy = K*ψ(θ)*[y-R*Sin(θ)]*dθ/[ (y-R*Sin(θ))2+(x-R*Cos(θ))2 ]3/2
    • where K = 1/(4*π*εo) or about 9*10^9 N*m2*C-2
    But when i calculate the integration i get 0 for both. Any ideas?
    I can add a picture later, i can't now.
     
  2. jcsd
  3. Sep 26, 2016 #2

    Simon Bridge

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    There is too much missing from the problem statement to complete the assignment.
    ie.
    What is the orientation of the ring? Is it in the x-y plane?
    Where are we supposed to find the ##\vec E## field? only in the x-y plane? (we are only asked for x,y components).

    ... you mean you tried to find ##dE_x## and ##dE_y## in terms of ##\theta##
    The reasoning usually goes like this: The electric field element ##d\vec E## due to the charge element ##dq## on the ring between ##\theta## and ##\theta +d\theta## is given by ... etc.

    Looks like you have done the calculus wrong.
     
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