### Diagram 6: Toroid Structure and Cross-SectionThe diagram presents a toroid, which is a three-dimensional geometric shape resembling a doughnut. In this image, the toroid is shown with a green and gray coloration.#### Toroid Description:- **Inner Radius (r1):** The radius from the center of the toroid to the inner edge.- **Outer Radius (r2):** The radius from the center of the toroid to the outer edge.- **Height (a):** The vertical distance through the toroid's cross-section.#### Cross-Section of the Toroid:The right side of the diagram features a cross-sectional view of the toroid, highlighted by a purple rectangular section:- **Height (a):** Consistent with the vertical distance mentioned.- **Width (r2 - r1):** The distance between the outer and inner radius of the toroid's cross-section.This depiction helps visualize the structure and dimensions of a toroid as well as its geometric properties when sliced to examine its internal characteristics. ### Explanation of the Toroid Flux CalculationA tightly wrapped toroid with the following specifications is to be analyzed:- **Inside Radius (\( r_1 \))**: 8.14 cm- **Outside Radius (\( r_2 \))**: 54.4 cm- **Height (\( a \))**: 59.6 cm- **Number of Turns**: 9,656- **Current**: 858 AThe cross-section of this toroid is rectangular, meaning if you slice it at any point, it appears as a rectangle. This rectangle has the dimensions \( a \) and \( r_2 - r_1 \).To visualize, imagine drawing an imaginary rectangle inside the toroid in such a way that it is perpendicular to the radii and spans the entire cross-section.**Objective**: Calculate the magnetic flux passing through this rectangle in Tesla-square meters (T·m²).**Note**: This is an opportunity to apply integration for the calculation.This concept combines understanding of the toroidal geometry with electromagnetic principles to calculate magnetic flux through a defined pathway. ### Diagrams and GraphsWhile the image refers to "diagram 6," no diagrams or graphs are provided in the text. For a detailed explanation on an educational platform, it is helpful to create or provide a visual representation of the toroid. This would include:- A cross-sectional view showing the rectangular area described.- Labels indicating \( r_1 \), \( r_2 \), and \( a \).This representation aids in comprehending the flow of magnetic field lines and the spatial layout required for calculations.

Given: Inner radius of toroid r1=8.14 cm. Outer radius of toroid r2=54.4 cm. Height of toroid a=59.6…

Refer to diagram 6. A tightly wrapped toroid has inside radius r1 = 8.14 cm and outside radius r2 = 54.4 cm, height a = 59.6 cm, 9,656 turns and carries current 858 A. This toroid has a rectangular cross-section- if you cut it at any point, you would see a rectangle, Suppose you have an imaginary rectangle across the inside of the toroid (perpendicular to the radii and across the entire cross-section: sides a and r2 - r1). Calculate the flux, in T-m², that passes through this rectangle.

Refer to diagram 6. A tightly wrapped toroid has inside radius r1 = 8.14 cm and outside radius r2 = 54.4 cm, height a = 59.6 cm, 9,656 turns and carries current 858 A. This toroid has a rectangular cross-section- if you cut it at any point, you would see a rectangle, Suppose you have an imaginary rectangle across the inside of the toroid (perpendicular to the radii and across the entire cross-section: sides a and r2 - r1). Calculate the flux, in T-m², that passes through this rectangle.

Introductory Circuit Analysis (13th Edition)

13th Edition

ISBN:9780133923605

Author:Robert L. Boylestad

Publisher:Robert L. Boylestad

Chapter1: Introduction

Section: Chapter Questions

Problem 1P: Visit your local library (at school or home) and describe the extent to which it provides literature...

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Concept explainers

Solenoids

A solenoid is a common term for a telephone coil used as an electromagnet. It also refers to any device that uses a solenoid to convert electrical energy into mechanical energy. The device generates a magnetic field from an electric field and uses the magnetic field to produce precise motion. Solenoid valves are often used to change power, such as in-car transmitters or valves, such as in the fuel system.

Question

### Diagram 6: Toroid Structure and Cross-Section

The diagram presents a toroid, which is a three-dimensional geometric shape resembling a doughnut. In this image, the toroid is shown with a green and gray coloration.

#### Toroid Description:
- **Inner Radius (r1):** The radius from the center of the toroid to the inner edge.
- **Outer Radius (r2):** The radius from the center of the toroid to the outer edge.
- **Height (a):** The vertical distance through the toroid's cross-section.

#### Cross-Section of the Toroid:
The right side of the diagram features a cross-sectional view of the toroid, highlighted by a purple rectangular section:
- **Height (a):** Consistent with the vertical distance mentioned.
- **Width (r2 - r1):** The distance between the outer and inner radius of the toroid's cross-section.

This depiction helps visualize the structure and dimensions of a toroid as well as its geometric properties when sliced to examine its internal characteristics.

### Explanation of the Toroid Flux Calculation

A tightly wrapped toroid with the following specifications is to be analyzed:

- **Inside Radius (\( r_1 \))**: 8.14 cm
- **Outside Radius (\( r_2 \))**: 54.4 cm
- **Height (\( a \))**: 59.6 cm
- **Number of Turns**: 9,656
- **Current**: 858 A

The cross-section of this toroid is rectangular, meaning if you slice it at any point, it appears as a rectangle. This rectangle has the dimensions \( a \) and \( r_2 - r_1 \).

To visualize, imagine drawing an imaginary rectangle inside the toroid in such a way that it is perpendicular to the radii and spans the entire cross-section.

**Objective**: Calculate the magnetic flux passing through this rectangle in Tesla-square meters (T·m²).

**Note**: This is an opportunity to apply integration for the calculation.

This concept combines understanding of the toroidal geometry with electromagnetic principles to calculate magnetic flux through a defined pathway.

### Diagrams and Graphs

While the image refers to "diagram 6," no diagrams or graphs are provided in the text. For a detailed explanation on an educational platform, it is helpful to create or provide a visual representation of the toroid. This would include:

- A cross-sectional view showing the rectangular area described.
- Labels indicating \( r_1 \), \( r_2 \), and \( a \).

This representation aids in comprehending the flow of magnetic field lines and the spatial layout required for calculations.

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