**Magnetic Field Generated by Current-Carrying Wire****Problem Statement:**A long straight wire placed on the y-axis carries a current of 1.59 A in the +y direction. The coordinate system is shown in the figure. What is the magnetic field generated by the current at the point (x, y, z) = (2.50 m, 1.50 m, 0 m)? (in T; use a positive sign if the magnetic field points in the +z direction and a negative sign if it points in the −z direction)**Coordinate System:**The figure illustrates the coordinate system:- The x-axis is labeled with +x direction to the right.- The y-axis is labeled with +y direction upwards.- The z-axis is depicted with +z direction coming out of the page (illustrated by a circle with a dot), and the -z direction going into the page (illustrated by a circle with a cross).**Solution Approach:**To determine the magnetic field generated by a current-carrying wire at a given point, you can use the Biot-Savart Law or Ampère's Law. In this case, consider the following:- The current \(I\) flowing through the wire is 1.59 A in the +y direction.- The position where the magnetic field is to be determined is (x, y, z) = (2.50 m, 1.50 m, 0 m).By applying the right-hand rule for the direction of the magnetic field due to a straight current-carrying wire, you wrap your right hand's fingers in the direction of the current (+y direction), your thumb points in that direction, and your fingers curl in the direction of the magnetic field. At the specified point, the magnetic field will either point in the +z or -z direction depending on its location relative to the wire. **Steps to Follow:**1. Use the right-hand rule to determine the direction of the magnetic field at the given point.2. Calculate the magnetic field using the Biot-Savart Law or Ampère's Law.3. Determine whether the field points in the +z or -z direction based on the coordinate system.The final result will take the form of \(B_z = \pm \text{value in T}\), where the sign indicates the direction according to the problem's requirements.**Note:**For instructional

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(L10) A long straight wire placed on the y axis carries a current of 1.59 A in the ty direction. The coordinate system is shown in the figure. What is the magnetic field generated by the current at the point (x, y, z) = (2.50 m, 1.50 m, 0 m)? (in T; use positive sign if the magnetic field points in the +z direction and negative sign if it points in the −z direction)

(L10) A long straight wire placed on the y axis carries a current of 1.59 A in the ty direction. The coordinate system is shown in the figure. What is the magnetic field generated by the current at the point (x, y, z) = (2.50 m, 1.50 m, 0 m)? (in T; use positive sign if the magnetic field points in the +z direction and negative sign if it points in the −z direction)

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

**Magnetic Field Generated by Current-Carrying Wire**

**Problem Statement:**

A long straight wire placed on the y-axis carries a current of 1.59 A in the +y direction. The coordinate system is shown in the figure. What is the magnetic field generated by the current at the point (x, y, z) = (2.50 m, 1.50 m, 0 m)? (in T; use a positive sign if the magnetic field points in the +z direction and a negative sign if it points in the −z direction)

**Coordinate System:**

The figure illustrates the coordinate system:
- The x-axis is labeled with +x direction to the right.
- The y-axis is labeled with +y direction upwards.
- The z-axis is depicted with +z direction coming out of the page (illustrated by a circle with a dot), and the -z direction going into the page (illustrated by a circle with a cross).

**Solution Approach:**

To determine the magnetic field generated by a current-carrying wire at a given point, you can use the Biot-Savart Law or Ampère's Law. In this case, consider the following:

- The current \(I\) flowing through the wire is 1.59 A in the +y direction.
- The position where the magnetic field is to be determined is (x, y, z) = (2.50 m, 1.50 m, 0 m).

By applying the right-hand rule for the direction of the magnetic field due to a straight current-carrying wire, you wrap your right hand's fingers in the direction of the current (+y direction), your thumb points in that direction, and your fingers curl in the direction of the magnetic field. At the specified point, the magnetic field will either point in the +z or -z direction depending on its location relative to the wire.

**Steps to Follow:**

1. Use the right-hand rule to determine the direction of the magnetic field at the given point.
2. Calculate the magnetic field using the Biot-Savart Law or Ampère's Law.
3. Determine whether the field points in the +z or -z direction based on the coordinate system.

The final result will take the form of \(B_z = \pm \text{value in T}\), where the sign indicates the direction according to the problem's requirements.

**Note:**

For instructional

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