ind the magnitude of the magnetic field, in T, at a point between the wires: (0,0,2.22 cm).

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Chapter1: Units, Trigonometry. And Vectors
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**Educational Content: Magnetic Field of Perpendicular Current-Carrying Wires**

**Problem Description:**

Two "infinite" thin wires are perpendicular to each other:

- **Wire 1** is aligned parallel to the x-axis and carries a current \( I_1 = 564 \, \text{A} \) in the negative x-direction. The center of wire 1 is located at the point \((0, 0, 7.26 \, \text{cm})\).

- **Wire 2** is centered along the y-axis and carries a current \( I_2 = 408 \, \text{A} \) in the positive y-direction.

**Objective:**

Calculate the magnitude of the magnetic field, in Tesla, at a specific point between the wires: \((0, 0, 2.22 \, \text{cm})\).

**Explanation for Diagrams (if applicable):**

- **Diagram 2** would likely illustrate the spatial configuration and orientation of both wires in three-dimensional space, showing Wire 1 parallel to the x-axis and Wire 2 parallel to the y-axis. 
- The point of interest \((0, 0, 2.22 \, \text{cm})\) lies along the z-axis, indicating where the magnetic field's magnitude due to both wires needs to be calculated. 
- Vectors may depict the direction of current in each wire, while coordinate markers help in visualizing the specific point for magnetic field calculation.

**Key Concepts:**

- The magnetic field due to a long, straight current-carrying wire can be determined using Ampère's Law, considering the influence of both wires at the given point.
- Superposition principle can be used to find the resultant magnetic field combining contributions from both wires.

**Calculation Steps:**

1. Apply the Biot-Savart Law or Ampère’s Law for each wire to determine the magnetic field contribution from each at the point \((0, 0, 2.22 \, \text{cm})\).
2. Use vector addition to find the net magnetic field at the specified point, considering the directions of the magnetic fields created by each wire.

This setup offers an insightful exercise into electromagnetic theory, especially focusing on interactions between magnetic fields from orthogonal current-carrying conductors.
Transcribed Image Text:**Educational Content: Magnetic Field of Perpendicular Current-Carrying Wires** **Problem Description:** Two "infinite" thin wires are perpendicular to each other: - **Wire 1** is aligned parallel to the x-axis and carries a current \( I_1 = 564 \, \text{A} \) in the negative x-direction. The center of wire 1 is located at the point \((0, 0, 7.26 \, \text{cm})\). - **Wire 2** is centered along the y-axis and carries a current \( I_2 = 408 \, \text{A} \) in the positive y-direction. **Objective:** Calculate the magnitude of the magnetic field, in Tesla, at a specific point between the wires: \((0, 0, 2.22 \, \text{cm})\). **Explanation for Diagrams (if applicable):** - **Diagram 2** would likely illustrate the spatial configuration and orientation of both wires in three-dimensional space, showing Wire 1 parallel to the x-axis and Wire 2 parallel to the y-axis. - The point of interest \((0, 0, 2.22 \, \text{cm})\) lies along the z-axis, indicating where the magnetic field's magnitude due to both wires needs to be calculated. - Vectors may depict the direction of current in each wire, while coordinate markers help in visualizing the specific point for magnetic field calculation. **Key Concepts:** - The magnetic field due to a long, straight current-carrying wire can be determined using Ampère's Law, considering the influence of both wires at the given point. - Superposition principle can be used to find the resultant magnetic field combining contributions from both wires. **Calculation Steps:** 1. Apply the Biot-Savart Law or Ampère’s Law for each wire to determine the magnetic field contribution from each at the point \((0, 0, 2.22 \, \text{cm})\). 2. Use vector addition to find the net magnetic field at the specified point, considering the directions of the magnetic fields created by each wire. This setup offers an insightful exercise into electromagnetic theory, especially focusing on interactions between magnetic fields from orthogonal current-carrying conductors.
### Diagram Description

**Diagram 2: Parallel Wires and Currents**

This diagram illustrates two parallel wires, labeled as Wire 1 and Wire 2, positioned in a three-dimensional coordinate system with axes x, y, and z.

- **Wire 1**: 
  - Positioned vertically along the z-axis.
  - Carries a current labeled \( I_1 \).
- **Wire 2**: 
  - Oriented horizontally along the x-axis.
  - Carries a current labeled \( I_2 \).

The distance between the two wires is denoted by \( d \). The diagram indicates that currents \( I_1 \) and \( I_2 \) flow in the positive directions of their respective axes.

### Key Features:
- **Axes**: 
  - The x-axis runs horizontally.
  - The y-axis runs into the plane.
  - The z-axis runs vertically upwards.
  
- **Current Directions**:
  - \( I_1 \) flows upward along Wire 1 in the z-direction.
  - \( I_2 \) flows to the right along Wire 2 in the x-direction.

This diagram is typically used to explain electromagnetic interactions between two parallel currents, such as the magnetic forces that arise and their potential effects on the wires.
Transcribed Image Text:### Diagram Description **Diagram 2: Parallel Wires and Currents** This diagram illustrates two parallel wires, labeled as Wire 1 and Wire 2, positioned in a three-dimensional coordinate system with axes x, y, and z. - **Wire 1**: - Positioned vertically along the z-axis. - Carries a current labeled \( I_1 \). - **Wire 2**: - Oriented horizontally along the x-axis. - Carries a current labeled \( I_2 \). The distance between the two wires is denoted by \( d \). The diagram indicates that currents \( I_1 \) and \( I_2 \) flow in the positive directions of their respective axes. ### Key Features: - **Axes**: - The x-axis runs horizontally. - The y-axis runs into the plane. - The z-axis runs vertically upwards. - **Current Directions**: - \( I_1 \) flows upward along Wire 1 in the z-direction. - \( I_2 \) flows to the right along Wire 2 in the x-direction. This diagram is typically used to explain electromagnetic interactions between two parallel currents, such as the magnetic forces that arise and their potential effects on the wires.
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