Three wires with (nonzero) current flowing shown below. i, i, i, The first wire experiences no force due to the current magnitudes of iz and ig: O i2 = 3i3 O i3 = i2 O none of these O i3 = 3i2 O it is impossible for the first wire to experiene O i3 = 2i2 O i2 = 2i3

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Chapter1: Units, Trigonometry. And Vectors
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**Problem Statement:**

Three wires with (nonzero) current flowing perpendicular to the page are spaced equally on a line as shown below.

![Diagram](diagram)

The first wire experiences no force due to the other two wires when the following is true regarding the current magnitudes of \(i_2\) and \(i_3\):

1. \(i_2 = 3i_3\)
2. \(i_3 = i_2\)
3. none of these
4. \(i_3 = 3i_2\)
5. it is impossible for the first wire to experience no force
6. \(i_3 = 2i_2\)
7. \(i_2 = 2i_3\)

**Explanation of Diagram:**

The diagram shows three wires arranged in a horizontal line, with currents \(i_1\), \(i_2\), and \(i_3\) respectively flowing perpendicularly into or out of the page. Each wire has a corresponding current labeled next to it. The spacing between each wire is equal.

**Concept:**

The net force on the first wire due to the other two wires must be zero for it to experience no force. This requires that the magnetic forces exerted on the first wire by the second and third wires cancel each other out. The directions and magnitudes of these forces are determined by the directions of the currents and the distances between the wires. 

**Answer Choices and Analysis:**

1. \(i_2 = 3i_3\)
2. \(i_3 = i_2\)
3. none of these
4. \(i_3 = 3i_2\)
5. it is impossible for the first wire to experience no force
6. \(i_3 = 2i_2\)
7. \(i_2 = 2i_3\)
Transcribed Image Text:**Problem Statement:** Three wires with (nonzero) current flowing perpendicular to the page are spaced equally on a line as shown below. ![Diagram](diagram) The first wire experiences no force due to the other two wires when the following is true regarding the current magnitudes of \(i_2\) and \(i_3\): 1. \(i_2 = 3i_3\) 2. \(i_3 = i_2\) 3. none of these 4. \(i_3 = 3i_2\) 5. it is impossible for the first wire to experience no force 6. \(i_3 = 2i_2\) 7. \(i_2 = 2i_3\) **Explanation of Diagram:** The diagram shows three wires arranged in a horizontal line, with currents \(i_1\), \(i_2\), and \(i_3\) respectively flowing perpendicularly into or out of the page. Each wire has a corresponding current labeled next to it. The spacing between each wire is equal. **Concept:** The net force on the first wire due to the other two wires must be zero for it to experience no force. This requires that the magnetic forces exerted on the first wire by the second and third wires cancel each other out. The directions and magnitudes of these forces are determined by the directions of the currents and the distances between the wires. **Answer Choices and Analysis:** 1. \(i_2 = 3i_3\) 2. \(i_3 = i_2\) 3. none of these 4. \(i_3 = 3i_2\) 5. it is impossible for the first wire to experience no force 6. \(i_3 = 2i_2\) 7. \(i_2 = 2i_3\)
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