### 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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