**Problem 2: Analysis of a Toroidal Solenoid**A toroidal solenoid consists of \( N = 120 \) windings of wire, with each carrying a current \( I = 0.135 \, \text{A} \). The inner radius of the toroidal solenoid is \( R = 0.550 \, \text{m} \), and the diameter of each winding is \( d = 0.0120 \, \text{m} \).**Diagram Explanation:**The diagram depicts a toroidal solenoid with windings arranged in a circular pattern. The center of the toroid is marked, and a radius \( R \) extends from the center to the midpoint of the inner ring of the toroid. The small circles on the diagram denote cross-sections of the windings. Current \( I \) flows through each winding as indicated by arrows. The point \( a \) is labeled on the diagram at a radius \( r_a = 0.275 \, \text{m} \), near the center of the toroid. **Task:**a. **Objective:** Use Ampere’s Law to determine the magnitude of the magnetic field at point \( a \), located near the center of the toroid at a radius \( r_a = 0.275 \, \text{m} \). **Approach:**The task involves applying Ampere's Law, which relates the integrated magnetic field around a closed loop to the current passing through the loop. This exercise helps in understanding magnetic fields within toroidal solenoids, crucial for various electromagnetic applications.

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A toroidal solenoid consists of N = 120 windings of wire each carrying current I = 0.135 A. The inner radius of the toroidal solenoid is R = 0.550 m and the diameter of each winding is d =0.0120 m. d• R a d a. Use Ampere's Law to determine the magnitude of the magnetic field at point a near the center of the toroid at a radius r. = 0.275 m.

A toroidal solenoid consists of N = 120 windings of wire each carrying current I = 0.135 A. The inner radius of the toroidal solenoid is R = 0.550 m and the diameter of each winding is d =0.0120 m. d• R a d a. Use Ampere's Law to determine the magnitude of the magnetic field at point a near the center of the toroid at a radius r. = 0.275 m.

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

**Problem 2: Analysis of a Toroidal Solenoid**

A toroidal solenoid consists of \( N = 120 \) windings of wire, with each carrying a current \( I = 0.135 \, \text{A} \). The inner radius of the toroidal solenoid is \( R = 0.550 \, \text{m} \), and the diameter of each winding is \( d = 0.0120 \, \text{m} \).

**Diagram Explanation:**

The diagram depicts a toroidal solenoid with windings arranged in a circular pattern. The center of the toroid is marked, and a radius \( R \) extends from the center to the midpoint of the inner ring of the toroid. The small circles on the diagram denote cross-sections of the windings. Current \( I \) flows through each winding as indicated by arrows. The point \( a \) is labeled on the diagram at a radius \( r_a = 0.275 \, \text{m} \), near the center of the toroid.

**Task:**

a. **Objective:** Use Ampere’s Law to determine the magnitude of the magnetic field at point \( a \), located near the center of the toroid at a radius \( r_a = 0.275 \, \text{m} \).

**Approach:**

The task involves applying Ampere's Law, which relates the integrated magnetic field around a closed loop to the current passing through the loop. This exercise helps in understanding magnetic fields within toroidal solenoids, crucial for various electromagnetic applications.

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