**Magnetic Field in a Hollow Cylindrical Conductor**The problem presents a cross-section of a long, hollow, cylindrical conductor with an inner radius \( r_1 = 2.5 \, \text{cm} \) and an outer radius \( r_2 = 7 \, \text{cm} \). A uniform current of 52 A flows into the page through this conductor. The task is to calculate the magnetic field at three specific radial distances: \( r = 0 \, \text{cm} \), \( r = 3.5 \, \text{cm} \), and \( r = 8 \, \text{cm} \).**Diagrams and Explanation:**- The diagram shows a hollow cylindrical shell, with two concentric circles representing the inner and outer boundaries at \( r_1 \) and \( r_2 \) respectively.**Magnetic Field Calculations:**- **(a)** Magnetic field at \( r = 0 \, \text{cm} \) is calculated within the hollow area (center of the cylinder).- **(b)** Magnetic field at \( r = 3.5 \, \text{cm} \) is calculated within the material of the cylindrical shell.- **(c)** Magnetic field at \( r = 8 \, \text{cm} \) is calculated outside the cylindrical conductor.**Hints:**- Additional help is provided for each part of the calculation: - *Additional hint for (a)* - *Additional hint for (b)* - *Additional hint for (c)***Scientific Notation:**- Answers should be entered using "E" notation. For instance, \( 3.14 \times 10^{-12} \) should be entered as "3.14E-12".This exercise illustrates the calculation of magnetic fields in different regions around a cylindrical conductor as per Ampère's Law and the Biot-Savart Law principles.

Answered: Image /qna-images/answer/1f31598b-3c86-48ea-9b2f-8ac6f8394165.jpg

The accompanying figure shows a cross-section of a long, hollow, cylindrical conductor of inner radius ri = 2.5 cm and outer radius r2 = 7 cm. A 52-A current distributed uniformly over the cross-section flows into the page. Calculate the magnetic field at r = 0 cm, r = 3.5 cm, and r = 8 cm. Hints a. Magnetic field at r = 0 cm is T. Additional hint for (a). b. Magnetic field at r = 3.5 cm is T. Additional hint for (b). c. Magnetic field at r = 8 cm is T. Additional hint for (c). -12 Use the "E" notation to enter your answer in scientific notation. For example, to enter 3.14 × 10 enter "3.14E-12".

The accompanying figure shows a cross-section of a long, hollow, cylindrical conductor of inner radius ri = 2.5 cm and outer radius r2 = 7 cm. A 52-A current distributed uniformly over the cross-section flows into the page. Calculate the magnetic field at r = 0 cm, r = 3.5 cm, and r = 8 cm. Hints a. Magnetic field at r = 0 cm is T. Additional hint for (a). b. Magnetic field at r = 3.5 cm is T. Additional hint for (b). c. Magnetic field at r = 8 cm is T. Additional hint for (c). -12 Use the "E" notation to enter your answer in scientific notation. For example, to enter 3.14 × 10 enter "3.14E-12".

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

**Magnetic Field in a Hollow Cylindrical Conductor**

The problem presents a cross-section of a long, hollow, cylindrical conductor with an inner radius \( r_1 = 2.5 \, \text{cm} \) and an outer radius \( r_2 = 7 \, \text{cm} \). A uniform current of 52 A flows into the page through this conductor. The task is to calculate the magnetic field at three specific radial distances: \( r = 0 \, \text{cm} \), \( r = 3.5 \, \text{cm} \), and \( r = 8 \, \text{cm} \).

**Diagrams and Explanation:**

- The diagram shows a hollow cylindrical shell, with two concentric circles representing the inner and outer boundaries at \( r_1 \) and \( r_2 \) respectively.

**Magnetic Field Calculations:**

- **(a)** Magnetic field at \( r = 0 \, \text{cm} \) is calculated within the hollow area (center of the cylinder).

- **(b)** Magnetic field at \( r = 3.5 \, \text{cm} \) is calculated within the material of the cylindrical shell.

- **(c)** Magnetic field at \( r = 8 \, \text{cm} \) is calculated outside the cylindrical conductor.

**Hints:**

- Additional help is provided for each part of the calculation:
- *Additional hint for (a)*
- *Additional hint for (b)*
- *Additional hint for (c)*

**Scientific Notation:**

- Answers should be entered using "E" notation. For instance, \( 3.14 \times 10^{-12} \) should be entered as "3.14E-12".

This exercise illustrates the calculation of magnetic fields in different regions around a cylindrical conductor as per Ampère's Law and the Biot-Savart Law principles.

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