How Do You Find the Electric Field at the Origin From a Semi-Ring of Charge?

[seang]

Homework Statement

How do I find the electric field from a semi-ring of charge at the center of the would-be circle? Does that make sense? Or another way: If the semi-circle of charge is centered at the origin, what is the electric field at the origin? I hope you know what I mean now.

the total charge of the ring is Q, the radius is R.

Oh yeah, the semi circle is in the left hand plane

Homework Equations

$$E = k\int_{}^{l}\frac{(r-r')\rho _l(r')}{|r-r'|^3} dl'<br />$$

The Attempt at a Solution

$$E = k\int_{\pi/2}^{-\pi/2}\frac{(-r')\rho _l(r')}{|-r'|^3} d\theta$$

Is converting to cylindrical coordinates the right move? Is this even the equation I should be using? What should I use as the charge density?

 

[chaoseverlasting]

Try applying Gauss's Theorem. Assume a gaussian surface enclosing the ring and $$\int E.ds=\frac{q}{\epsilon}$$

 

[Meir Achuz]

Gauss won't work here because there is not full circular symmetry
There is enough symmetry to see the direction of the E field.
Just put cos\theta into the numerator of your integral.
rho is really a linear density lambda=Q/2pi R.