Infinitely Long Cylindrical Surface Problem

In summary, the conversation is about using Gauss' law to find the electric field at a specific point on the surface of a charged infinitely long cylinder. The formula used for an infinitely long line of charge, lamda/2pi(E0)r, is mentioned, but it is suggested to use Gauss' law instead. The charge density and radius of the cylinder are given, and it is mentioned that the length of the cylinder can be treated as infinite when solving the problem. The solution is found by setting up and solving an integral using the given information.
  • #1
jordanjj
4
0

Homework Statement


Here is my problem. I don't fully understand Gauss' law so any assistance there would be greatly appreciated
Charge is distributed uniformly throughout the volume of an infinitely long cylinder of radius R = 4.00×10-2 m. The charge density is 1.00×10-2 C/ m3. What is the electric field at r = 2.00×10-2 m?
(in N/C)


Homework Equations





The Attempt at a Solution


I understand that gauss' law is the integral EdA and that the E for a cylinder is lamda/2pi(E0)r , but I don't understand it for an infinite cylinder
 
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  • #2
nevermind figured it out
 
  • #3
You mention Gauss' law, so maybe you are supposed to use it to find the answer rather than that formula. You must imagine a cylinder that has the point you are interested in on its surface. Just the given charged cylinder will do nicely in this case. You figure out how much charge is inside - maybe use L for the length and let it tend to infinity in your final answer (most likely it will cancel out before then). Looks like E will be the same at all points around the cylinder so that integral is very easy. Solve for E. I would expect the answer to be just that formula lamda/2pi(E0)r which is for an infinitely long line of charge.

Of course you will put the numbers into find a numerical answer.
 

1. What is the "Infinitely Long Cylindrical Surface Problem"?

The "Infinitely Long Cylindrical Surface Problem" is a theoretical problem in physics and mathematics that involves calculating the electric potential and electric field surrounding a long, straight, and infinitely thin cylindrical surface. This problem is often used as a simplified model for real-life scenarios, such as the electric field surrounding a long wire.

2. What is the importance of studying the "Infinitely Long Cylindrical Surface Problem"?

The "Infinitely Long Cylindrical Surface Problem" is important because it allows us to understand and make predictions about the electric field in real-life situations. It also serves as a building block for more complex problems in electromagnetism, making it an essential concept for students and researchers in the field.

3. How is the "Infinitely Long Cylindrical Surface Problem" solved?

The "Infinitely Long Cylindrical Surface Problem" is solved using mathematical techniques, such as integration and vector calculus. By applying Gauss's law, which states that the electric flux through a closed surface is equal to the charge enclosed by that surface divided by the permittivity of free space, we can derive the electric field and potential at any point surrounding the cylindrical surface.

4. What are some real-life applications of the "Infinitely Long Cylindrical Surface Problem"?

One of the most common applications of the "Infinitely Long Cylindrical Surface Problem" is in the design and analysis of electrical systems, such as power lines and electrical circuits. It is also used in the study of materials with cylindrical symmetry, such as cylindrical capacitors and coaxial cables.

5. Are there any limitations to the "Infinitely Long Cylindrical Surface Problem"?

While the "Infinitely Long Cylindrical Surface Problem" is a useful and widely applicable concept, it does have some limitations. It assumes that the cylindrical surface is infinitely long and infinitely thin, which is not always the case in real-life situations. It also ignores any effects of the material surrounding the surface and assumes a uniform charge distribution along the surface.

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