**Transcription for Educational Website:****Title: Magnetic Field of a Rotating Charged Cylinder**A long, uniform cylinder of charge density \( \rho \) (coul/m\(^3\)) and radius \( R \) rotates at the angular rate \( \omega \). Use Ampère’s law to find an expression for the magnetic field strength in the regions \( 0 \leq r \leq R \) and \( r > R \).**Diagram Explanation:**The diagram illustrates a long cylindrical object with a uniform charge density \( \rho \). The cylinder has a radius \( R \) and is shown rotating around its central axis with an angular velocity \( \omega \). An arrow curved in the clockwise direction represents the angular velocity. The charge distribution is indicated along the length of the cylinder.**Key Concepts:**- **Charge Density \( \rho \)**: Represents the amount of electric charge per unit volume in the cylinder. - **Angular Velocity \( \omega \)**: The rate of rotation of the cylinder around its axis.- **Ampère’s Law**: A fundamental law used to determine the magnetic field generated by a current distribution.**Objective:**To derive expressions for the magnetic field in two regions:1. Inside the cylinder (\( 0 \leq r \leq R \))2. Outside the cylinder (\( r > R \)) Using Ampère’s law and considering the rotational movement of the charged cylinder.

Expression for magnetic field strength in the region 0≤r≤R and r>R: Ampere's circuital law: It…

A long, uniform cylinder of charge density p (coul/m³) and radius R rotates at the angular rate w. Use Ampère's law to find an expression for the magnetic field strength in the regions 0 R. charge density p

A long, uniform cylinder of charge density p (coul/m³) and radius R rotates at the angular rate w. Use Ampère's law to find an expression for the magnetic field strength in the regions 0 R. charge density p

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

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Concept explainers

Magnetic Field Of Coaxial Cable

The word coaxial means same axis. So for a long straight cable to be coaxial, it must have concentric cylindrical shaped conductor around it. Coaxial cable (popularly called ‘coax’) has various applications ranging from current conductors to radiofrequency signal transmitters. This cable has lower emission losses and provides protection from electromagnetic interference which allows signals with less power to transmit over longer distances.For example, currents produced in the pickup of a stereo turntable generally travel to the amplifier through a coaxial cable.The self-inductance of a coaxial cable is another important characteristic, because it influences the propagation of electrical signals in the cable.

Question

**Transcription for Educational Website:**

**Title: Magnetic Field of a Rotating Charged Cylinder**

A long, uniform cylinder of charge density \( \rho \) (coul/m\(^3\)) and radius \( R \) rotates at the angular rate \( \omega \). Use Ampère’s law to find an expression for the magnetic field strength in the regions \( 0 \leq r \leq R \) and \( r > R \).

**Diagram Explanation:**

The diagram illustrates a long cylindrical object with a uniform charge density \( \rho \). The cylinder has a radius \( R \) and is shown rotating around its central axis with an angular velocity \( \omega \). An arrow curved in the clockwise direction represents the angular velocity. The charge distribution is indicated along the length of the cylinder.

**Key Concepts:**

- **Charge Density \( \rho \)**: Represents the amount of electric charge per unit volume in the cylinder.

- **Angular Velocity \( \omega \)**: The rate of rotation of the cylinder around its axis.

- **Ampère’s Law**: A fundamental law used to determine the magnetic field generated by a current distribution.

**Objective:**

To derive expressions for the magnetic field in two regions:

1. Inside the cylinder (\( 0 \leq r \leq R \))
2. Outside the cylinder (\( r > R \))

Using Ampère’s law and considering the rotational movement of the charged cylinder.

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