Capacitance of Wire Loops: Formula for Equal Radii R

[csopi]

Hi,

Does anybody know a nice formula for the capacitance of two metallic wire loops with equal radius R?

(The center of the loops are above each other, their distance is d. The whole system is in vacuum)

Thank you!

 

[the_emi_guy]

There will not be a nice formula for that.

If you just need the capacitance value of a specific geometry you can use the free field solver at http://www.fastfieldsolvers.com/.

 

[CWatters]

Can you assume the radius R is >> d ?? In which case isn't this just the same as two parallel wires?

 

[csopi]

CWatters: yes, in that case it would be just two parallel wires. However I was looking for a general formula, that works when R ~ d as well. Actually, I'm trying to estimate the capacitance of a coil, because when you have a coil made of thick wire and you have just a few turns, it cannot be negected in general.

the_emi_guy: thank you very much for the software. It seems rather professional. It'll take some time to learn how to use it though.

 

[sardar]

Hello,

Yes, there is a formula for the capacitance of two metallic wire loops with equal radius R. It is given by C = 2πε0R/d, where C is the capacitance, ε0 is the permittivity of vacuum, R is the radius of the loops, and d is the distance between the loops. This formula assumes that the loops are perfectly circular and are aligned with each other. If the loops are not perfectly circular, the formula may need to be adjusted.

This formula is derived from the general formula for the capacitance of two parallel plate capacitors, which is C = ε0A/d, where A is the area of the plates. In the case of two wire loops, the area of the plates is replaced by the circumference of the loops, which is 2πR. The factor of 2 accounts for the fact that there are two loops in the system.

I hope this helps! Let me know if you have any other questions.