### Magnetic Field and Currents in Long Straight Wires#### Problem Statement:In the figure, two long straight wires (shown in cross-section) carry currents \( i_1 = 20.1 \, \text{mA} \) and \( i_2 = 24.5 \, \text{mA} \) directly out of the screen. They are equal distances from the origin, where they set up a magnetic field \( \vec{B} \). To what value must current \( i_1 \) be changed in order to rotate \( \vec{B} \) 17.1° clockwise?#### Diagram Explanation:The diagram depicts a coordinate system with two currents:- \( i_1 \) represented by a dot at (0, 1) on the y-axis.- \( i_2 \) represented by a dot at (-1, 0) on the x-axis.These currents are illustrated as coming directly out of the screen, indicated by the dot symbol in the cross-section view.#### Solution Approach:1. **Understanding Magnetic Fields Around Wires:** - The magnetic field \( \vec{B} \) generated by a current-carrying wire is given by the right-hand rule. - The magnetic field created by \( i_1 \) and \( i_2 \) at the origin needs to be mathematically evaluated.2. **Combining Magnetic Fields:** - Since the wires are at equal distances from the origin, calculate the contribution of each current to the net magnetic field using vector addition.3. **Rotating the Magnetic Field:** - Changing \( i_1 \) causes a change in its magnetic field's strength, which affects the combined net magnetic field. - The desired rotation of the magnetic field vector by 17.1° clockwise will determine the new value of \( i_1 \).4. **Calculating the Required Current Change:** - Use trigonometric relations and vector analysis to compute the necessary modification in \( i_1 \).#### Interactive Element:- **Input Fields for Solution:** - A numerical input field for entering the new value of \( i_1 \). - A dropdown menu for selecting appropriate units (e.g., mA, A).#### Task:Enter the calculated value of \( i_1 \) that rotates the magnetic field \( \vec{B} \)

Answered: Image /qna-images/answer/8208a8db-6ab9-468c-862f-bfc7945b6b46.jpg

In the figure, two long straight wires (shown in cross section) carry currents i₁ = 20.1 mA and i2 = 24.5 mA directly out of the screen. They are equal distances from the origin, where they set up a magnetic field B. To what value must current in be changed in order to rotate B 17.1° clockwise? Number MI Units 13

In the figure, two long straight wires (shown in cross section) carry currents i₁ = 20.1 mA and i2 = 24.5 mA directly out of the screen. They are equal distances from the origin, where they set up a magnetic field B. To what value must current in be changed in order to rotate B 17.1° clockwise? Number MI Units 13

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 and Currents in Long Straight Wires

#### Problem Statement:
In the figure, two long straight wires (shown in cross-section) carry currents \( i_1 = 20.1 \, \text{mA} \) and \( i_2 = 24.5 \, \text{mA} \) directly out of the screen. They are equal distances from the origin, where they set up a magnetic field \( \vec{B} \). To what value must current \( i_1 \) be changed in order to rotate \( \vec{B} \) 17.1° clockwise?

#### Diagram Explanation:
The diagram depicts a coordinate system with two currents:

- \( i_1 \) represented by a dot at (0, 1) on the y-axis.
- \( i_2 \) represented by a dot at (-1, 0) on the x-axis.

These currents are illustrated as coming directly out of the screen, indicated by the dot symbol in the cross-section view.

#### Solution Approach:
1. **Understanding Magnetic Fields Around Wires:**
- The magnetic field \( \vec{B} \) generated by a current-carrying wire is given by the right-hand rule.
- The magnetic field created by \( i_1 \) and \( i_2 \) at the origin needs to be mathematically evaluated.

2. **Combining Magnetic Fields:**
- Since the wires are at equal distances from the origin, calculate the contribution of each current to the net magnetic field using vector addition.

3. **Rotating the Magnetic Field:**
- Changing \( i_1 \) causes a change in its magnetic field's strength, which affects the combined net magnetic field.
- The desired rotation of the magnetic field vector by 17.1° clockwise will determine the new value of \( i_1 \).

4. **Calculating the Required Current Change:**
- Use trigonometric relations and vector analysis to compute the necessary modification in \( i_1 \).

#### Interactive Element:
- **Input Fields for Solution:**
- A numerical input field for entering the new value of \( i_1 \).
- A dropdown menu for selecting appropriate units (e.g., mA, A).

#### Task:
Enter the calculated value of \( i_1 \) that rotates the magnetic field \( \vec{B} \)

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