- #1

Diego Rolim Porto

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## 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*m
^{2}*C^{-2}

I can add a picture later, i can't now.