College Physics
11th Edition
ISBN: 9781305952300
Author: Raymond A. Serway, Chris Vuille
Publisher: Cengage Learning
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Transcribed Image Text:### 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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