Calculating Force on Charge q near Washer

[shannon]

Homework Statement

There is a washer (inner radius is a and outer radius is b) on the x-y axis with a constant surface charge density σ . What is the force felt on charge q on z-axis distance D from center of washer.

Homework Equations

The Attempt at a Solution

I don't even know where to begin...
I was thinking about drawing a triangle to a random spot on the washer from the origin to the charge q...but I don't know if that will work since it's a washer.
I don't think I can pick a gaussian surface...can I?
Please give some hints!

 

[gabbagabbahey]

Gauss's law is only useful under cylindrically symmetric cases when the cylinder extends to infinity, or it is very long and you are far from the ends; neither of these conditions are met by this problem, so that method is out.

Your idea of drawing a triangle to a random spot on the washer (x,y,0) is good. What is the separation vector \vec{r} from the point (x,y,0) to the point (0,0,D)?How much charge dq is contained in the infinitesimal area dxdy? What does that make \vec{E}? How about \vec{F}?

 

[kt7888]

Thank you very much for the help!

But I'm still a little puzzled about the problem...If I pick a random spot on the washer, then I won't know the exact distance from the origin, so I can't have a specific value for the separation vector. Right?

So, can I pick a spot on the outer radius b?

 

[gabbagabbahey]

Well, give your random spot the coordinates (x,y,0), what is the separation vector in terms of x and y? Remember, you are going to end up integrating over all possible random spots, so you can't restrict yourself to only those spots that are along the outer radius.