Capacitance of Wire Loops: Formula for Equal Radii R

In summary, the capacitance of wire loops can be calculated using the formula C = (2πεr)/ln(b/a), where C is the capacitance, ε is the permittivity of free space, r is the radius of the loop, b is the distance between the two loops, and a is the radius of the wire. This formula assumes that the loops have equal radii and are situated parallel to each other. It can be used to determine the capacitance of various wire loop configurations, which is an important factor in designing electrical circuits and systems.
  • #1
csopi
82
2
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!
 
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  • #2
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/.
 
  • #3
Can you assume the radius R is >> d ?? In which case isn't this just the same as two parallel wires?
 
  • #4
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.
 
  • #5


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.
 

1. What is the formula for calculating the capacitance of wire loops with equal radii?

The formula for calculating the capacitance of wire loops with equal radii is C = (πε0h/ln(b/a)), where C is the capacitance, ε0 is the permittivity of free space, h is the height of the loop, b is the outer radius, and a is the inner radius.

2. How is the capacitance of wire loops affected by the radius of the loop?

The capacitance of wire loops is directly proportional to the radius of the loop. This means that as the radius increases, the capacitance also increases, and vice versa.

3. Can the capacitance of wire loops be increased by changing the shape of the loop?

Yes, the capacitance of wire loops can be increased by changing the shape of the loop. For example, increasing the number of turns in the loop or changing the shape from circular to rectangular can increase the capacitance.

4. How does the distance between wire loops affect the capacitance?

The capacitance of wire loops is inversely proportional to the distance between the loops. This means that as the distance between the loops increases, the capacitance decreases, and vice versa.

5. What is the significance of the capacitance of wire loops?

The capacitance of wire loops is an important factor in determining the amount of charge that can be stored in the loop. It is also used in various electronic applications, such as inductors and transformers, where the wire loops are used to store and transfer energy.

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