# Determining the capacitance of the two conductors

• franktherabbit
In summary, the electric field from the conducting cylinder to the mirror image is twice the electric field from the original object.
franktherabbit

## Homework Statement

For a given system, a conducting cylinder with radius ##r=a## with a linear charge density ##Q'## and a conducting surface at a distance ##z=h## from the cylinder, calculate the linear capacitance of the cylinder.Take that ##h>>a##
##C'=\frac{Q'}{U}##

## Homework Equations

3. The Attempt at a Solution [/B]
This is my first thread on physicsforums so you tell me if i break any rules ok :D?
As shown in the image above, i took a mirror image of an object and charged it with a negative sign of the given charge. All i need to find is the potential from the cylinder to the image cylinder right?
The total electric field along the line i am integrating the potential (##\int_{r1}^{r2} Edl=U##) is equal to the sum of the two electric fields now present which is just two times the first one. That would give us the electric field of a cylinder ##E=\frac{Q'}{2\pi\epsilon_0r}## but times ##2## and my limits of my integration should be ##\int_{a}^{2h}##. When i integrate i get ##U=\frac{Q'}{\pi \epsilon_o}ln{\frac{2h}{a}}##. This is where my result disagrees with the result i have been given by the professor. He states ##U=\frac{Q'}{2\pi \epsilon_o}ln{\frac{2h}{a}}##. Where am i wrong?

franktherabbit said:
The total electric field along the line i am integrating the potential (##\int_{r1}^{r2} Edl=U##) is equal to the sum of the two electric fields now present which is just two times the first one.
For an arbitrary point between the conductors, the field from one conductor does not equal the field from the other conductor. So, it is not a matter of just multiplying by 2.
my limits of my integration should be ##\int_{a}^{2h}##.
These limits don't seem right. How are you defining the variable of integration? How are r1 and r2 expressed in terms of your variable of integration? It will be helpful if you show the complete setup of the integral, including the integrand.

## 1. What is capacitance?

Capacitance is the ability of a conductor to store electrical charge. It is measured in farads (F) and is determined by the size, shape, and material of the conductors.

## 2. How do you determine the capacitance of two conductors?

The capacitance of two conductors can be determined by dividing the charge stored on one of the conductors by the potential difference between the two conductors. This is known as the capacitance formula: C = Q/V.

## 3. What factors affect the capacitance of two conductors?

The capacitance of two conductors is affected by the distance between the conductors, the size and shape of the conductors, and the type of material they are made of. It also increases with the surface area of the conductors and decreases with the distance between them.

## 4. How does the dielectric material between the two conductors affect capacitance?

The dielectric material between the two conductors can increase the capacitance by reducing the electric field between the conductors. This allows more charge to be stored on the conductors, resulting in a higher capacitance. The dielectric constant of the material also plays a role in determining the capacitance.

## 5. What is the use of determining the capacitance of two conductors?

Determining the capacitance of two conductors is useful in various applications, such as designing electronic circuits, measuring the charge of a capacitor, and calculating the energy stored in a conductor. It is also important in understanding the behavior of electrical systems and devices.

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