Eletric Field of a Ring

  • #1
Diego Rolim Porto
1
0
  • Homework Statement

  • 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)?

Homework 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?

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.
 

Answers and Replies

  • #2
Simon Bridge
Science Advisor
Homework Helper
17,874
1,657
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).

I tried to find the dEx and dEy as a function of dθ,
... 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.

But when i calculate the integration i get 0 for both. Any ideas?
Looks like you have done the calculus wrong.
 

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