# Magnetic Field of a rotating Cylinder

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In summary, the conversation discusses a problem involving an infinitely long charged metal cylinder rotating at an angular velocity ##\omega## with a charge density per unit length of ##\rho##. The task is to find the magnetic field within the cylinder using Ampere's law. The person asking for help is struggling to make progress and is asking for hints. The template and guidelines provided by PF are highlighted to emphasize the importance of showing effort and following the guidelines when seeking help.
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## Homework Statement

.[/B]
Given an infinitely long charged metal cylinder that is rotating with an angular velocity ##\omega## The charge density per unit length is ##\rho##. Find the magnetic field within the cylinder.

I'm trying to solve this problem by using Ampere's Law. But couldn't reach anywhere, if anyone could give me some hints, that would be great.
Thanks.

Hello AA, welcome to PF !

Well, you have a relevant equation then: Ampere's law. How does it read ?
Fill that in under 2. in the template and show us how far you can get under 3.: attempt at solution.

PF requires an effort and the template is mandatory. For good reasons. read the guidelines to find out why.

ECooper

## 1. What is the concept of a magnetic field of a rotating cylinder?

The magnetic field of a rotating cylinder is a phenomenon that occurs when a cylindrical object is rotated at a constant speed. As the cylinder rotates, electric charges on the surface of the cylinder are set in motion, creating a circular flow of electric current. This current, in turn, creates a magnetic field around the cylinder.

## 2. How is the strength of the magnetic field of a rotating cylinder determined?

The strength of the magnetic field of a rotating cylinder is determined by several factors, including the speed of rotation, the size and shape of the cylinder, and the material it is made of. Additionally, the strength of the magnetic field is directly proportional to the current flowing through the cylinder and the distance from the surface of the cylinder.

## 3. What is the direction of the magnetic field of a rotating cylinder?

The direction of the magnetic field of a rotating cylinder is always perpendicular to the surface of the cylinder and follows the right-hand rule. This means that if you curl your fingers in the direction of the rotation, your thumb will point in the direction of the magnetic field.

## 4. What are some practical applications of the magnetic field of a rotating cylinder?

The magnetic field of a rotating cylinder has many practical applications in various industries. It is commonly used in electric motors and generators, where the rotating cylinder is used to convert mechanical energy into electrical energy. It is also used in MRI machines, where a strong rotating magnetic field is used to produce detailed images of the body.

## 5. How can the magnetic field of a rotating cylinder be manipulated or controlled?

The strength and direction of the magnetic field of a rotating cylinder can be manipulated by changing the speed of rotation, the current flowing through the cylinder, and the distance from the surface of the cylinder. Additionally, the use of ferromagnetic materials can enhance the magnetic field, while non-magnetic materials can weaken it.

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