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Two very long parallel wires in the xy-plane, a distance 2a apart, are parallel to the y-axis and carry equal currents I as shown in the figure. The +z direction points perpendicular to the xy-plane out of the page. If the current in one wire flows in the +y direction and the current in the other wire flows in the opposite direction, which one of the graphs shown in the figure below could represent the z component of the total magnetic field, while moving along the x-axis? (Caution: These graphs are not magnetic field lines.)

Two very long parallel wires in the xy-plane, a distance 2a apart, are parallel to the y-axis and carry equal currents I as shown in the figure. The +z direction points perpendicular to the xy-plane out of the page. If the current in one wire flows in the +y direction and the current in the other wire flows in the opposite direction, which one of the graphs shown in the figure below could represent the z component of the total magnetic field, while moving along the x-axis? (Caution: These graphs are not magnetic field lines.)

Introductory Circuit Analysis (13th Edition)
Introductory Circuit Analysis (13th Edition)
13th Edition
ISBN:9780133923605
Author:Robert L. Boylestad
Publisher:Robert L. Boylestad
Chapter1: Introduction
Section: Chapter Questions
Problem 1P: Visit your local library (at school or home) and describe the extent to which it provides literature...
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**Problem: Magnetic Field of Parallel Wires** Two very long parallel wires in the \(xy\)-plane, a distance \(2a\) apart, are parallel to the \(y\)-axis and carry equal currents \(I\) as shown in the figure. The \(+z\) direction points perpendicular to the \(xy\)-plane out of the page. If the current in one wire flows in the \(+y\) direction and the current in the other wire flows in the opposite direction, which one of the graphs shown in the figure below could represent the \(z\) component of the total magnetic field while moving along the \(x\)-axis? (*Caution: These graphs are not magnetic field lines.*) ### Explanation of Graphs 1. **Graph (1):** - The plot shows two peaks at \(x = -a\) and \(x = a\) with a dip in the center. This indicates a positive \(B_z\) on either side of the wires. 2. **Graph (2):** - This graph presents a central peak at \(x = 0\) with values falling toward \(x = -a\) and \(x = a\). The symmetry suggests a reaction to the wires at these positions. 3. **Graph (3):** - Displays a linear crossing pattern with a change in sign near \(x = -a\) and \(x = a\). 4. **Graph (4):** - This graph has a minimum at \(x = 0\), forming a ‘U’ shape with dips at \(x = -a\) and \(x = a\). 5. **Graph (5):** - Shows a hill-like shape with peaks at \(x = -a\) and \(x = a\), implying negative \(B_z\) values approaching the wires. In this problem, you are to determine which graph correlates with the described current arrangement and its impact on the \(z\) component of the magnetic field around the \(x\)-axis.
Transcribed Image Text:**Problem: Magnetic Field of Parallel Wires** Two very long parallel wires in the \(xy\)-plane, a distance \(2a\) apart, are parallel to the \(y\)-axis and carry equal currents \(I\) as shown in the figure. The \(+z\) direction points perpendicular to the \(xy\)-plane out of the page. If the current in one wire flows in the \(+y\) direction and the current in the other wire flows in the opposite direction, which one of the graphs shown in the figure below could represent the \(z\) component of the total magnetic field while moving along the \(x\)-axis? (*Caution: These graphs are not magnetic field lines.*) ### Explanation of Graphs 1. **Graph (1):** - The plot shows two peaks at \(x = -a\) and \(x = a\) with a dip in the center. This indicates a positive \(B_z\) on either side of the wires. 2. **Graph (2):** - This graph presents a central peak at \(x = 0\) with values falling toward \(x = -a\) and \(x = a\). The symmetry suggests a reaction to the wires at these positions. 3. **Graph (3):** - Displays a linear crossing pattern with a change in sign near \(x = -a\) and \(x = a\). 4. **Graph (4):** - This graph has a minimum at \(x = 0\), forming a ‘U’ shape with dips at \(x = -a\) and \(x = a\). 5. **Graph (5):** - Shows a hill-like shape with peaks at \(x = -a\) and \(x = a\), implying negative \(B_z\) values approaching the wires. In this problem, you are to determine which graph correlates with the described current arrangement and its impact on the \(z\) component of the magnetic field around the \(x\)-axis.
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