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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![### 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.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fb052dd5d-84db-466c-a2ba-e3b39e1bdb71%2F8cfa7c2c-43c4-4601-9f09-052651c1c688%2Fmus53ci_processed.png&w=3840&q=75)
Transcribed Image Text:### 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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