### Problem Statement**12.** A wire consists of a half circle whose ends extend perpendicularly to the circle as shown. If current \( I \) flows downward through the wire, what is the magnitude of the magnetic field at the center of the circle? Does it point into or out of the page?### Diagram ExplanationThe diagram shows a wire bent into a half-circle with radius \( R \). The current \( I \) is directed downward along the wire. The circular section curves to the right. ### Handwritten Solution**Direction of Magnetic Field:**The solution notes that the magnetic field at the center of the circle points "Out of the page," indicated with a large arrow and annotation.**Calculation for the Magnetic Field:**The formula used for calculating the magnitude of the magnetic field \( B \) at the center of the circle is given by:\[ B = \frac{\mu_0 I}{4\pi} \int \frac{d\vec{s} \times \hat{r}}{r^2} \]A check mark indicates that the setup and direction are correct.### ExplanationFor a circular wire, Ampère's law is used to find the magnetic field at the center. The right-hand rule is applied to determine the direction of the magnetic field due to the current flow.

Answered: Image /qna-images/answer/8cfa7c2c-43c4-4601-9f09-052651c1c688.jpg

12. A wire consists of a half circle whose ends extend perpendicularly to the circle as shown. It current I flows downward through the wire, what is the magnitude of the magnetic field at the center of the circle? Does it point into or out of the page?

12. A wire consists of a half circle whose ends extend perpendicularly to the circle as shown. It current I flows downward through the wire, what is the magnitude of the magnetic field at the center of the circle? Does it point into or out of the page?

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 Statement

**12.** A wire consists of a half circle whose ends extend perpendicularly to the circle as shown. If current \( I \) flows downward through the wire, what is the magnitude of the magnetic field at the center of the circle? Does it point into or out of the page?

### Diagram Explanation

The diagram shows a wire bent into a half-circle with radius \( R \). The current \( I \) is directed downward along the wire. The circular section curves to the right.

### Handwritten Solution

**Direction of Magnetic Field:**

The solution notes that the magnetic field at the center of the circle points "Out of the page," indicated with a large arrow and annotation.

**Calculation for the Magnetic Field:**

The formula used for calculating the magnitude of the magnetic field \( B \) at the center of the circle is given by:

\[ B = \frac{\mu_0 I}{4\pi} \int \frac{d\vec{s} \times \hat{r}}{r^2} \]

A check mark indicates that the setup and direction are correct.

### Explanation

For a circular wire, Ampère's law is used to find the magnetic field at the center. The right-hand rule is applied to determine the direction of the magnetic field due to the current flow.

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