# Derivation for capacitance of cylindrical capacitor

• ChiralSuperfields
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ChiralSuperfields
Homework Statement
Relevant Equations
I don't understand how they got from the previous step to the next step of the derivation circled in red:

Many thanks!

They replaced ##E_r## with the expression for the radial electric field for a very long rod in the region outside the rod. See equation 23.8 in the textbook that they quote.

ChiralSuperfields
kuruman said:
They replaced ##E_r## with the expression for the radial electric field for a very long rod in the region outside the rod. See equation 23.8 in the textbook that they quote.
Thank you @kuruman !

## 1. What is the formula for calculating the capacitance of a cylindrical capacitor?

The formula for calculating the capacitance of a cylindrical capacitor is C = 2πε0εrl / ln(b/a), where C is the capacitance, ε0 is the permittivity of free space, εr is the relative permittivity of the dielectric material between the cylinders, l is the length of the cylinders, and a and b are the radii of the inner and outer cylinders, respectively.

## 2. How is the capacitance of a cylindrical capacitor affected by the distance between the cylinders?

The capacitance of a cylindrical capacitor is inversely proportional to the distance between the cylinders. This means that as the distance between the cylinders increases, the capacitance decreases. This is because the electric field between the cylinders weakens as the distance increases, resulting in a lower capacitance.

## 3. What is the dielectric material used in a cylindrical capacitor?

The dielectric material used in a cylindrical capacitor can vary, but commonly used materials include air, paper, mica, and ceramic. The choice of dielectric material depends on factors such as the required capacitance, voltage rating, and operating temperature of the capacitor.

## 4. How does the length of the cylinders affect the capacitance of a cylindrical capacitor?

The length of the cylinders has a direct effect on the capacitance of a cylindrical capacitor. As the length increases, the capacitance also increases. This is because a longer length allows for more surface area between the cylinders, resulting in a larger capacitance.

## 5. Can the capacitance of a cylindrical capacitor be increased by increasing the radii of the cylinders?

Yes, the capacitance of a cylindrical capacitor can be increased by increasing the radii of the cylinders. This is because a larger radius results in a larger surface area between the cylinders, which in turn increases the capacitance. However, the distance between the cylinders must also be taken into consideration, as a larger radius alone does not guarantee an increase in capacitance.

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