Calculating the capacitance of a system of two plates tilted at a small angle

  • #1

Homework Statement


A capacitor is made up of a pair of square plates, each of side length L, that are very nearly parallel (such that θ is very small) and seperated by a distance D. The plates make an angle, θ, with one another. The capacitor may be thought of as being comprised of many infitesimally think strips of width, dx, and length L, which are effectively in parallel with one another. Recall that sinθ≈θ for θ<<1rad. Calculate the capacitance of the system of two plates. Capacitor.jpg attached is a picture of the problem.

Homework Equations


C=Kε0A/d, K=1(vacum)

The Attempt at a Solution


C=Kε0A/d=ε0L2/d=ε0L2∫1/(Lsinθ+D)dL (integral lower limit 0 upper limit L)
C=ε0(LN(Lsinθ+D)-LN(0))
I believe this is right just wanted confirmation on my method...
 

Attachments

Last edited by a moderator:

Answers and Replies

  • #2
gleem
Science Advisor
Education Advisor
1,775
1,124
A quick look at your answer and I see a problem ln(0) = ∞ .
 
  • Like
Likes cookiemnstr510510
  • #3
gleem
Science Advisor
Education Advisor
1,775
1,124
You start out ok but you assumed that the charge on each elemental capacitor is constant and that is not correct.

After you solve a problem check your answer. In this case if the angle approaches 0 then the capacitance should be that of a L x L plates separated a distance D.
 
  • Like
Likes cookiemnstr510510

Related Threads on Calculating the capacitance of a system of two plates tilted at a small angle

Replies
17
Views
313
  • Last Post
Replies
4
Views
3K
Replies
1
Views
2K
  • Last Post
Replies
9
Views
237
Replies
7
Views
2K
  • Last Post
Replies
13
Views
2K
  • Last Post
Replies
2
Views
631
Top