This is an extra credit homework problem for my physics class. Two square plates, 5cm on a side, are set at an angle of thirty degrees. The leading edges of the plates begin at a radius of 1cm from the center of the angle. What is the capacitance?

I believe I will have to integrate along the length such that dx becomes the width of plates for individual little capacitors. Thus, I have the integration of (.05dx/(2xsin15)) from .01 to .06 times ε. Does this sound like the right approach? I get approximately 153pF.

 

Well, for anyone interested...when I finished my calculations, I actually came up with 1.53pF...we turned it in today and the prof gave us the solution...turns out I was close. I needed to take the arc length instead of the straight line distance. The answer ended up being 1.51pF. I am happy that I was able to apply integration in a practical situation though, as I am still not completely comfortable with calculus.

 

I am curious...... Can you post the calculations...

 

This is what it looked like. The way it was explained was that not only were we integrating along the radius (what I was calling x), but we also had to take θ down to where the tiny plates were approximately parallel, hence the arc length as opposed to the straight line.

 

...and my (incorrect) solution: