|Mar14-06, 12:20 AM||#1|
Electric field of a charged rod
just looking for some help on an electric field question involving a rod of charge. heres 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.
|Mar14-06, 05:52 AM||#2|
Blog Entries: 9
Did you make an appropriate drawing...? Consider a small element of the chargel circular contour of length [itex] dl [/itex]. 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...?
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