### Problem Statement1. A closed circuit consists of two semicircles of radii 2R and R that are connected by straight segments. A current I flows around this circuit as shown below. Find the magnetic field at point P if R = 40 cm and I = 14 A. Take the positive direction of the field INTO the page.### Choices:A. \( 1.5 \, \mu T \) B. \( -5.5 \, \mu T \) C. \( -5.5 \, \mu T \) D. \( -12 \, \mu T \) E. \( 12 \, \mu T \) ### Diagram ExplanationThe diagram accompanying the question shows a closed circuit with a current \( I \) flowing through it. The circuit is composed of two semicircular arcs, one with radius \( 2R \) and another with radius \( R \), connected by straight segments. There is a point \( P \) at the center where the magnetic field is to be determined. - The larger semicircle has a radius of \( 2R \).- The smaller semicircle has a radius of \( R \).- The direction of current flow is indicated by an arrow along the semicircle.This setup is connected in a way that forms two opposing semicircular arcs. The point \( P \) is located at the center of the structure.### Solution DetailsTo find the magnetic field at point \( P \) created by the current flowing in the given geometry, we consider the contributions from each segment:- **For the larger semicircle (radius \( 2R \))**: The magnetic field at the center due to a current-carrying loop can be given by Ampère’s circuital law and the Biot-Savart law, specific for a semicircular loop.- **For the smaller semicircle (radius \( R \))**: Similarly, use Ampère’s circuital law and the Biot-Savart law.The contributions from the two segments are to be summed vectorially considering their directions. The positive direction of the magnetic field is stated to be INTO the page.### Applications and ConceptsThis problem demonstrates principle applications like:- Magnetic fields due to current-carrying wires.- Use of Biot-Savart Law and Ampère's Law in different geometrical configurations.Exercises like this one are important

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1. A closed circuit consists of two semicircles of radii 2R and R that are connected by straight segments. A current I flows around this circuit as shown below. Find the magnetic field at point P if R = 40 cm and I = 14 A. Take the positive direction of the field INTO the page. A. 1.5 µT B.-5.5 µT C.-5.5 µT D. -12 µT E. 12 µT

1. A closed circuit consists of two semicircles of radii 2R and R that are connected by straight segments. A current I flows around this circuit as shown below. Find the magnetic field at point P if R = 40 cm and I = 14 A. Take the positive direction of the field INTO the page. A. 1.5 µT B.-5.5 µT C.-5.5 µT D. -12 µT E. 12 µT

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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Question

### Problem Statement

1. A closed circuit consists of two semicircles of radii 2R and R that are connected by straight segments. A current I flows around this circuit as shown below. Find the magnetic field at point P if R = 40 cm and I = 14 A. Take the positive direction of the field INTO the page.

### Choices:
A. \( 1.5 \, \mu T \)
B. \( -5.5 \, \mu T \)
C. \( -5.5 \, \mu T \)
D. \( -12 \, \mu T \)
E. \( 12 \, \mu T \)

### Diagram Explanation

The diagram accompanying the question shows a closed circuit with a current \( I \) flowing through it. The circuit is composed of two semicircular arcs, one with radius \( 2R \) and another with radius \( R \), connected by straight segments. There is a point \( P \) at the center where the magnetic field is to be determined.

- The larger semicircle has a radius of \( 2R \).
- The smaller semicircle has a radius of \( R \).
- The direction of current flow is indicated by an arrow along the semicircle.

This setup is connected in a way that forms two opposing semicircular arcs. The point \( P \) is located at the center of the structure.

### Solution Details

To find the magnetic field at point \( P \) created by the current flowing in the given geometry, we consider the contributions from each segment:

- **For the larger semicircle (radius \( 2R \))**: The magnetic field at the center due to a current-carrying loop can be given by Ampère’s circuital law and the Biot-Savart law, specific for a semicircular loop.
- **For the smaller semicircle (radius \( R \))**: Similarly, use Ampère’s circuital law and the Biot-Savart law.

The contributions from the two segments are to be summed vectorially considering their directions. The positive direction of the magnetic field is stated to be INTO the page.

### Applications and Concepts

This problem demonstrates principle applications like:
- Magnetic fields due to current-carrying wires.
- Use of Biot-Savart Law and Ampère's Law in different geometrical configurations.

Exercises like this one are important

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