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As shown in the figure below, four wires have current flowing perpendicular to the plane of the page. The wires go through the corners of a square, and their current magnitudes are identical. 2 3 If l and I2 have current I flowing into the page, and I3 and l4 have current I flowing out of the page, what is the direction of the magnetic field at the center of the square?

As shown in the figure below, four wires have current flowing perpendicular to the plane of the page. The wires go through the corners of a square, and their current magnitudes are identical. 2 3 If l and I2 have current I flowing into the page, and I3 and l4 have current I flowing out of the page, what is the direction of the magnetic field at the center of the square?

College Physics
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 As shown in the figure below, four wires have current flowing perpendicular to the plane of the page. The wires go through the corners of a square, and their current magnitudes are identical. ![Diagram of a square with four corners, labeled 1, 2, 3, and 4 counterclockwise] Current configuration: - \( I_1 \) at corner 1 and \( I_2 \) at corner 2 have current \( I \) flowing into the page. - \( I_3 \) at corner 3 and \( I_4 \) at corner 4 have current \( I \) flowing out of the page. **Question:** What is the direction of the magnetic field at the center of the square? #### Answer Options: - [ ] \( +y \) - [ ] \( -z \) - [ ] \( +x \) - [ ] \( -x \) - [ ] \( -y \) - [ ] \( +z \) - [ ] there is not enough information to determine - [x] none of these ### Explanation of the Diagram The diagram illustrates a square with four wires placed at its corners. The wires are labeled as follows: - Corner 1 at the top-left. - Corner 2 at the top-right. - Corner 3 at the bottom-right. - Corner 4 at the bottom-left. The current directions are noted as follows: - \( I_1 \) and \( I_2 \) (top-left and top-right) have currents flowing into the page. - \( I_3 \) and \( I_4 \) (bottom-right and bottom-left) have currents flowing out of the page. ### Answer Key The correct answer is marked as "none of these".
Transcribed Image Text:### Problem Statement As shown in the figure below, four wires have current flowing perpendicular to the plane of the page. The wires go through the corners of a square, and their current magnitudes are identical. ![Diagram of a square with four corners, labeled 1, 2, 3, and 4 counterclockwise] Current configuration: - \( I_1 \) at corner 1 and \( I_2 \) at corner 2 have current \( I \) flowing into the page. - \( I_3 \) at corner 3 and \( I_4 \) at corner 4 have current \( I \) flowing out of the page. **Question:** What is the direction of the magnetic field at the center of the square? #### Answer Options: - [ ] \( +y \) - [ ] \( -z \) - [ ] \( +x \) - [ ] \( -x \) - [ ] \( -y \) - [ ] \( +z \) - [ ] there is not enough information to determine - [x] none of these ### Explanation of the Diagram The diagram illustrates a square with four wires placed at its corners. The wires are labeled as follows: - Corner 1 at the top-left. - Corner 2 at the top-right. - Corner 3 at the bottom-right. - Corner 4 at the bottom-left. The current directions are noted as follows: - \( I_1 \) and \( I_2 \) (top-left and top-right) have currents flowing into the page. - \( I_3 \) and \( I_4 \) (bottom-right and bottom-left) have currents flowing out of the page. ### Answer Key The correct answer is marked as "none of these".
**Understanding the Magnetic Field at the Center of a Square with Four Currents** **Question:** As shown in the figure below, four wires have current flowing perpendicular to the plane of the page. The wires go through the corners of a square, and their current magnitudes are identical. **Diagram:** There is a square diagram with vertices labeled 1, 2, 3, and 4 in a clockwise order starting from the top left corner. The axes are labeled: - The horizontal axis is the x-axis. - The vertical axis is the y-axis. - **Wire at Vertex 1:** \(I_1\) - **Wire at Vertex 2:** \(I_2\) - **Wire at Vertex 3:** \(I_3\) - **Wire at Vertex 4:** \(I_4\) **Given condition:** If \(I_1\) and \(I_4\) have current \(I\) flowing out of the page, and \(I_2\) and \(I_3\) have current \(I\) flowing into the page, what is the direction of the magnetic field at the center of the square? **Answer Choices:** - \( \, \, - \, y \) - \( \, \, + \, x \) - \( \, \, + \, z \) - \( \, \, - \, z \) - \( \, \, - \, x \) - \( \, \, \text{none of these} \) - \( \, \, + \, y \) Please select the correct direction for the magnetic field at the center which results from the given current configuration.
Transcribed Image Text:**Understanding the Magnetic Field at the Center of a Square with Four Currents** **Question:** As shown in the figure below, four wires have current flowing perpendicular to the plane of the page. The wires go through the corners of a square, and their current magnitudes are identical. **Diagram:** There is a square diagram with vertices labeled 1, 2, 3, and 4 in a clockwise order starting from the top left corner. The axes are labeled: - The horizontal axis is the x-axis. - The vertical axis is the y-axis. - **Wire at Vertex 1:** \(I_1\) - **Wire at Vertex 2:** \(I_2\) - **Wire at Vertex 3:** \(I_3\) - **Wire at Vertex 4:** \(I_4\) **Given condition:** If \(I_1\) and \(I_4\) have current \(I\) flowing out of the page, and \(I_2\) and \(I_3\) have current \(I\) flowing into the page, what is the direction of the magnetic field at the center of the square? **Answer Choices:** - \( \, \, - \, y \) - \( \, \, + \, x \) - \( \, \, + \, z \) - \( \, \, - \, z \) - \( \, \, - \, x \) - \( \, \, \text{none of these} \) - \( \, \, + \, y \) Please select the correct direction for the magnetic field at the center which results from the given current configuration.
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