A long, straight wire going through the origin is carrying a current of 2.90 A in the positive z-direction (see the figure attached).A current I flows in the +z-direction in a vertical rod that lies along the z-axis in an x y z coordinate space. A dashed-line circle of radius r is labeled vector B and lies in the x y plane.At a point a distance r = 1.10 m from the origin on the positive x-axis, find the magnitude and direction of the magnetic field. (a)magnitude of the magnetic field (in T) b) direction of the magnetic field+x-direction−x-direction +y-direction−y-direction+z-direction−z-direction At a point the same distance from the origin on the negative y-axis, find the magnitude and direction of the magnetic field. (c) magnitude of the magnetic field (in T) (d) direction of the magnetic field+x-direction−x-direction +y-direction−y-direction+z-direction−z-direction In the diagram, we observe a three-dimensional representation involving a current-carrying wire and a magnetic field:1. **Axes**: The diagram includes three coordinate axes labeled \(x\), \(y\), and \(z\). The \(z\)-axis is oriented vertically, with an arrow indicating an upward direction.2. **Current (\(I\))**: A straight wire carrying an electric current \(I\) is aligned with the \(z\)-axis. The current is directed upwards along this axis, as shown by the arrow.3. **Magnetic Field (\(\mathbf{B}\))**: Around the wire, a circular magnetic field is depicted. This field is represented by dashed lines forming concentric circles in the plane perpendicular to the wire. The circles suggest the magnetic field's circular nature due to the current in the wire, following the right-hand rule.4. **Plane**: A shaded plane is shown perpendicular to the wire. This plane can be considered the \(xy\)-plane.5. **Radius (\(r\))**: The distance from the wire to a point in the magnetic field is indicated as \(r\). This helps in visualizing the radial distance from the wire to any point on one of the circular magnetic field lines.This diagram illustrates the fundamental concept in electromagnetism that a current through a conductor produces a magnetic field, which encircles the conductor in closed loops.

a) B = u0I/2πr B = (4π×10-7×2.9)/(2π×1.1) B = 5.27×10-7 T b) by right hand thumb rule Place…

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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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A long, straight wire going through the origin is carrying a current of 2.90 A in the positive z-direction (see the figure attached).

A current I flows in the +z-direction in a vertical rod that lies along the z-axis in an x y z coordinate space. A dashed-line circle of radius r is labeled vector B and lies in the x y plane.

At a point a distance r = 1.10 m from the origin on the positive x-axis, find the magnitude and direction of the magnetic field.

(a)magnitude of the magnetic field (in T)

b) direction of the magnetic field

+x-direction

−x-direction

+y-direction

−y-direction

+z-direction

−z-direction

At a point the same distance from the origin on the negative y-axis, find the magnitude and direction of the magnetic field.

(d) direction of the magnetic field

+x-direction

−x-direction

+y-direction

−y-direction

+z-direction

−z-direction

In the diagram, we observe a three-dimensional representation involving a current-carrying wire and a magnetic field:

1. **Axes**: The diagram includes three coordinate axes labeled \(x\), \(y\), and \(z\). The \(z\)-axis is oriented vertically, with an arrow indicating an upward direction.

2. **Current (\(I\))**: A straight wire carrying an electric current \(I\) is aligned with the \(z\)-axis. The current is directed upwards along this axis, as shown by the arrow.

3. **Magnetic Field (\(\mathbf{B}\))**: Around the wire, a circular magnetic field is depicted. This field is represented by dashed lines forming concentric circles in the plane perpendicular to the wire. The circles suggest the magnetic field's circular nature due to the current in the wire, following the right-hand rule.

4. **Plane**: A shaded plane is shown perpendicular to the wire. This plane can be considered the \(xy\)-plane.

5. **Radius (\(r\))**: The distance from the wire to a point in the magnetic field is indicated as \(r\). This helps in visualizing the radial distance from the wire to any point on one of the circular magnetic field lines.

This diagram illustrates the fundamental concept in electromagnetism that a current through a conductor produces a magnetic field, which encircles the conductor in closed loops.

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