Capacitance between two adjacent long thin plates

[theHermes5]

Hi.

I am working on a project for the design of a capacitive sensor. In order to do that, I am required to compute capacitance using a simulation software like COMSOL. As I want to compare my simulation results with the theoretical results, I would like to know the formula to be used for the capacitance.

It is not C= epsilon0*epsilonR*A/d as the plates are long and thin like this:

------------------- --------------------
| | | |
-------------------- ---------------------

I hope this diagram makes sense. ( Consider the plates to be of large length ( in the order of 0.1mm) and very small width ( in the order of 0.005mm). I want to calculated capacitance between these two plates.

Can you help me with the formula?

Thanks for your help.

 

[marcusl]

Your drawing isn't clear. Are the "plates" supposed to be coplanar and end to end (like a ribbon that, halfway down its length, has been cut across to make two shorter ribbons)? If so, there is no analytic formula for capacitance.

 

[theHermes5]

Thanks for your reply.

The plates are like as shown in attachment.

Now, can you help me with the capacitance formula?

 

[marcusl]

I don't know of any analytic formulas for this case.

 

[sardar]

Hi there,

The formula for capacitance between two parallel plates is indeed C = ε0 * εr * A / d, where ε0 is the permittivity of free space, εr is the relative permittivity of the material between the plates, A is the area of each plate, and d is the distance between the plates.

In the case of long, thin plates, the formula can still be used as long as the distance between the plates is much smaller than the length of the plates. In this case, the capacitance can be approximated as C = ε0 * εr * (l / π) * ln(b / a), where l is the length of the plates, b is the distance between the edges of the plates, and a is the width of the plates.

I hope this helps and good luck with your project!