# Homework Help: Electric field at the center of an arc

1. Dec 2, 2009

### tag16

1. The problem statement, all variables and given/known data
A charge Q is arranged evenly on a wire bent into an arc or radius R as shown in the
Figure. What is the electric field at the center of the arc as a function of the opening
angle theta? Sketch a graph of the electric field as a function of theta for 0<theta<180 degrees.

2. Relevant equations

E= KQ/R^2 cos theta

3. The attempt at a solution

Is the above equation correct? If not, I'm not really sure what to do, also I'm not sure how the graph should look.

2. Dec 2, 2009

### ApexOfDE

where is the figure?

3. Dec 2, 2009

### MaxL

Where'd you get that equation?

Also, if you're worried about how the graph should look, start by figuring it out for some easy points. What's the E field going to be at the center if theta is zero (so all the charge is concentrated in a single point)? How bout if Theta is 360 degrees (so a full circle)? It's a bit harder to figure out for 180 degrees, or 90 or 270 degrees, but you should be able to make a very rough estimate. That will give you some insight into the shape of the graph.

4. Dec 3, 2009

### tag16

sorry this is the best I can do: http://i848.photobucket.com/albums/ab41/tag16/problem1.jpg?t=1259862072 [Broken]

The equation I found in my physics book except the cos theta part, I was just guessing there. Though it would probably be integral cos theta or sin theta, if it's suppose to be in there at all.

Last edited by a moderator: May 4, 2017
5. Dec 4, 2009

### tag16

$$\lambda$$=Q/$$\pi$$R

dE= kdQ/R^2
dE= (kdQ/R^2) cos$$\theta$$

dQ=$$\lambda$$dl
dl= Rd$$\theta$$
dQ=$$\lambda$$Rd$$\theta$$

dE=(k[$$\lambda$$Rd$$\theta$$]/R^2)cos$$\theta$$

E=$$\int$$(k$$\lambda$$Rcos$$\theta$$/R^2)d$$\theta$$(from $$\pi$$/2 to -$$\pi$$/2)
E=k$$\lambda$$/R$$\int$$ cos$$\theta$$d$$\theta$$
E=k$$\lambda$$/R$$\int$$sin$$\theta$$
E=k$$\lambda$$/R[sin($$\pi$$/2)-sin(-$$\pi$$/2)]
E=k$$\lambda$$/2R
E=k(Q/$$\pi$$R)/2R=2kQ/$$\pi$$R^2
E= 2kq/$$\pi$$R^2

Is this right?