Electric field of a charged rod

[twiztidmxcn]

hey

just looking for some help on an electric field question involving a rod of charge. here's the problem:

You have a charge, Q, uniformly distributed along a thin, flexible rod with length L. The rod is then bent into a semi-circle.

a) Find expression for electric field at center of semicircle
b) Evaluate field strength if L = 10cm, Q = 30nC.

The rod starts out straight and is then bent into a half circle.

We are also given the hint that: A small piece of arc length delta-s spans a small angle delta-theta = delta-s / R , where R is the radius.

Now, I realize that this problem has lots of symmetry, mostly where the x and y components of the electric field are concerned. I know that all the y components will cancel due to this symmetry and all that we're left with are the x components.

I'm attempting to use the equation of a rod of charge to derive something for the circle, but I am a bit stuck. Basically, I'm stuck at E = kq/r, r hat.

I believe that I can just use that equation, find r in terms of x and y (using triangles, pythagorean theorem) and then integrate in terms of x. I'm not quite sure about this though...

Any sort of help in the right direction would be much appreciated.

thanks
twiztidmxcn

 

[dextercioby]

Did you make an appropriate drawing...? Consider a small element of the chargel circular contour of length dl. What electric charge does it have...? Can you compute the electric field it creates using the formula of Coulomb and the particular (axially symmetric) geometry of the picture...?

Daniel.