# Capacitance of three-layered cylinders

• Fibo112
In summary, the conversation is discussing a system with an outer cylinder, an inner cylinder, and an ungrounded cylinder in between. The capacitance of the system is being calculated based on the charges and potential of the middle cylinder. The concept of capacitance for each conductor and for two conductors in series is also mentioned.
Fibo112
I have an outer cylinder and an inner cylinder given. They are hollow(like if you were to take a sheet of paper and tape one edge to the other), grounded, and the inner cylinder is inside the outer cylinder. Between these cylinders is an ungrounded cylinder. I am now asked to calculate the capacitance of this system. I have calculated all the charges based on the potential of the middle cylinder.

I don't quite understand what is meant by the capacitance of this system though. I know that the capacitance of one conductor is the ratio of its charge to its potential, and the capacitance of two conductors would be the ratio of charge to potential difference in the sense that they each have the same charge but with different sign.

But what is meant here?

You have two capacitors in series. You can determine the capacitance for both of them.

## 1. What is the formula for calculating the capacitance of three-layered cylinders?

The formula for calculating the capacitance of three-layered cylinders is C = 2πε/(ln(r2/r1) + ln(r3/r2)), where C is the capacitance, ε is the permittivity of the surrounding medium, and r1, r2, and r3 are the radii of the three layers of the cylinder.

## 2. What factors affect the capacitance of three-layered cylinders?

The capacitance of three-layered cylinders is affected by the permittivity of the surrounding medium, the radii of the three layers, and the length of the cylinder. It is also influenced by the material properties of the layers.

## 3. How does the capacitance of three-layered cylinders differ from that of two-layered cylinders?

The capacitance of three-layered cylinders is calculated using a different formula than that of two-layered cylinders. It also takes into account an additional layer and has a more complicated relationship with the dimensions of the cylinder.

## 4. Can the capacitance of three-layered cylinders be increased by changing the material properties of the layers?

Yes, the capacitance of three-layered cylinders can be increased by changing the material properties of the layers. Materials with higher permittivity values will result in a higher capacitance.

## 5. How is the capacitance of three-layered cylinders used in practical applications?

The capacitance of three-layered cylinders has various applications in engineering, such as in the design of capacitors, transmission lines, and sensors. It is also used in the study of biological systems, such as cell membranes and nerve fibers.

• Electromagnetism
Replies
1
Views
9K
• Electromagnetism
Replies
11
Views
1K
• Electromagnetism
Replies
3
Views
1K
• Electromagnetism
Replies
13
Views
2K
• Electromagnetism
Replies
2
Views
3K
• Electromagnetism
Replies
4
Views
1K
• Electromagnetism
Replies
11
Views
2K
• Introductory Physics Homework Help
Replies
3
Views
677
• Electromagnetism
Replies
4
Views
528
• Electromagnetism
Replies
8
Views
2K