# Guass Law involving conducting cylinders

In summary, two coaxial cylindrical conductors with radii a = 2.0 cm and b = 6.0 cm, lengths L = 10.0 m, and charges Qinner = +8.0 nC and Qouter = -16.0 nC are shown. The question asks for the x-component of the electric field at point P (located at r = 4.0 cm from the origin and making an angle of 30.0o with the x-axis). Using Gauss's law and assuming cylindrical symmetry, the charge enclosed can be thought of as λL, where λ is the linear charge density. However, the length L drops out of the final answer, so it does not matter which

## Homework Statement

Two coaxial cylindrical conductors are shown in perspective and cross-section above. The inner cylinder has radius a = 2.0 cm, length L = 10.0 m and carries a total charge of Qinner = + 8.0 nC (1 nC = 10-9 C). The outer cylinder has an inner radius b = 6.0 cm, outer radius c = 7.0 cm, length L = 10.0 m and carries a total charge of Qouter = - 16.0 nC (1 nC = 10-9 C). What is Ex, the x-component of the electric field at point P which is located at the midpoint of the length of the cylinders at a distance r = 4.0 cm from the origin and makes an angle of 30.0o with the x-axis?

https://www.smartphysics.com/Content/Media/Images/EM/IE/cylinderx/coaxial.gif

## Homework Equations

E A= q(enclosed)/$\epsilon$

## The Attempt at a Solution

I simply treated the enclosed charge as +8nC, but I've seen ppl using linear charge density and yet they still got the answer. Is just just fluke luck that i got the answer? This is an online hmwk grading system btw.

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I simply treated the enclosed charge as +8nC, but I've seen ppl using linear charge density and yet they still got the answer. Is just just fluke luck that i got the answer?
No, it's not a fluke. You are to assume that this section of length L is just a piece out of a much longer cable (or you are looking only at the field near the center of the piece). The field is cylindrically symmetric, so the length you choose to analyze doesn't matter.

Regardless of how you choose to solve it, if you use Gauss's law you'll need the charge enclosed in whatever Gaussian surface you use. That charge can be thought of as λL, where λ is the linear charge density. Note that L drops out of your final answer.

## 1. What is Guass Law and how does it relate to conducting cylinders?

Guass Law is a fundamental law in physics that helps us understand the electric field around a charged object. It states that the electric flux through a closed surface is directly proportional to the enclosed electric charge. This law is applicable to conducting cylinders because they have a uniform charge distribution on their surface, making it easier to calculate the electric field using the law.

## 2. How do you calculate the electric field using Guass Law for conducting cylinders?

To calculate the electric field, you first need to determine the enclosed charge by finding the total charge on the surface of the cylinder. Then, choose a closed surface that intersects the cylinder and use the formula E = Q/ε0A, where Q is the enclosed charge, ε0 is the permittivity of free space, and A is the area of the chosen surface. This will give you the electric field at any point outside the cylinder.

## 3. Can Guass Law be used for conducting cylinders with non-uniform charge distributions?

No, Guass Law is only applicable for conducting cylinders with a uniform charge distribution on their surface. For cylinders with non-uniform charge distributions, other methods such as Coulomb's Law or integration techniques must be used to calculate the electric field.

## 4. How does the electric field of a conducting cylinder vary with distance from its center?

The electric field of a conducting cylinder varies inversely with the distance from its center. This means that as the distance from the center increases, the electric field decreases. This relationship is known as the inverse-square law and is a direct consequence of Guass Law.

## 5. What are some real-world applications of Guass Law involving conducting cylinders?

One common application is in the design of capacitors, which use conducting cylinders to store electric charge. Another application is in the design of electronic circuits, where conducting cylinders are used to shape and direct the flow of electric current. Additionally, Guass Law and conducting cylinders are used in the study of electromagnetic fields, such as those produced by power lines or in medical imaging.

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