# Capacitance of a cylinder containing an infinite number of cylinders

• IanS
In summary, the question pertains to the capacitance of a cylinder containing an infinite number of infinitely thin cylinders, with unclear specifications regarding the outer cylinder and its relationship to the inner ones. This may result in a potentially infinite capacitance.
IanS
I am a struggling physiology PhD student and would very much appreciate some help...

I need an expression for the capacitance of a cylinder (of finite radius and length) containing an infinite number of infinitely thin cylinders.

Any help would be greatly appreciated!

Many thanks,
-Ian

Your question is poorly posed. Capacitance is defined as the ratio of the charges on two conductors (+Q on one and -Q on the other) to the voltage (V) between them,
so C=Q/V. With an infinite number, what do you mean by capacitance?
Is the outer cylinder of finite length open or closed at the ends?

Is the outside cylinder fully closed (that is, closed off at both ends)? If it is, then it does not matter what is inside it (I'm 90% sure of that, but someone correct me please).
Is there any separation between the outside cylinder and the inner ones? If not, then it would be identical to a solid cylinder, which would be identical (in capacitance) to a cylindrical shell.

Otherwise, the problem implies an infinitessimal distance between layers of a capacitor, which implies a capacitance that approaches infinity.

## 1. What is the definition of capacitance for a cylinder containing an infinite number of cylinders?

The capacitance of a cylinder containing an infinite number of cylinders is the ability of the system to store electrical charge. It is defined as the ratio of the electric charge on one of the cylinders to the potential difference between the cylinders.

## 2. How is the capacitance of a cylinder containing an infinite number of cylinders calculated?

The capacitance can be calculated using the formula C = 2πε0h/ln(b/a), where ε0 is the permittivity of free space, h is the height of the cylinder, and a and b are the inner and outer radii of the cylinders, respectively.

## 3. What factors affect the capacitance of a cylinder containing an infinite number of cylinders?

The capacitance is affected by the size and shape of the cylinders, the distance between them, and the dielectric material between the cylinders. It also depends on the permittivity of the material between the cylinders and the surrounding medium.

## 4. How does the capacitance change as the number of cylinders increases?

As the number of cylinders increases, the capacitance also increases. This is because the electric field between the cylinders becomes stronger, leading to a higher ability to store charge.

## 5. What is the significance of studying the capacitance of a cylinder containing an infinite number of cylinders?

Studying the capacitance of this system can help us understand how capacitors work and how they can be optimized for various applications. It also has practical applications in the design of electronic circuits and energy storage devices.

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