Lesson Plan | Traditional Methodology | Magnetic Field: Wire

Objectives

Duration: (10 - 15 minutes)

The purpose of this stage is to provide a clear and objective overview of what will be learned during the lesson. By presenting the main objectives, students will be able to better understand the focus of the content and the importance of the skills that will be developed, ensuring greater effectiveness in the teaching and learning process.

Main Objectives

1. Calculate the magnetic field generated by a current-carrying wire.

2. Solve problems involving the calculation of magnetic fields generated by wires carrying currents.

Introduction

Duration: (10 - 15 minutes)

The purpose of this stage is to situate students in the context of the lesson, showing the relevance of the theme and how it applies to practical everyday situations. By sparking initial interest and curiosity among students, it is hoped to increase engagement and motivation to learn the content that will be covered.

Context

To begin the lesson on the Magnetic Field generated by a wire, it is important to establish a solid foundation of what a magnetic field is and how it is generated. Explain that a magnetic field is a region around a magnet where magnetic forces can be observed. When an electric current flows through a wire, it generates a magnetic field around that wire. This is a fundamental phenomenon with countless applications in modern technology, such as in electric motors, generators, and transformers.

Curiosities

Did you know that the magnetic field generated by a current-carrying wire is the basis for the operation of speakers? In everyday life, we use headphones and speakers that convert electrical signals into sound thanks to this phenomenon. Moreover, the Earth also has a magnetic field generated by currents in its core, which protects us from harmful solar particles.

Development

Duration: (40 - 50 minutes)

The purpose of this stage is to deepen students' understanding of the magnetic field generated by a current-carrying wire, providing a detailed explanation of the theoretical and practical concepts. By addressing essential topics and solving practical problems, students will be able to effectively apply the knowledge acquired, consolidating their understanding of the content.

Covered Topics

1. Biot-Savart Law: Explain that the Biot-Savart Law is a fundamental formula in physics that describes the magnetic field generated by an electric current. Detail the mathematical expression of the law and its physical significance, emphasizing the proportionality between the magnetic field and the electric current. 2. Magnetic Field of a Straight Wire: Detail how to calculate the magnetic field generated by a straight wire using the Biot-Savart Law. Explain the formula B = (μ₀ * I) / (2π * r), where B is the magnetic field, μ₀ is the magnetic permeability of vacuum, I is the current, and r is the distance from the wire. 3. Right-Hand Rule: Demonstrate the right-hand rule to determine the direction of the magnetic field around a wire. Explain that the thumb points in the direction of the current and the fingers curl in the direction of the magnetic field. 4. Practical Applications: Discuss some practical applications of the magnetic field generated by current-carrying wires, such as in electric motors, transformers, and magnetic storage devices. Provide specific examples to illustrate these applications. 5. Problem Solving: Present practical examples of problems that involve calculating the magnetic field generated by current-carrying wires. Solve the problems step by step, explaining each stage in detail to ensure that students understand the process.

Classroom Questions

1. Calculate the magnetic field at a distance of 5 cm from a long wire carrying a current of 10 A. 2. Determine the direction of the magnetic field generated by a wire carrying a current upwards, using the right-hand rule. 3. In a circular wire with a radius of 10 cm and a current of 5 A, calculate the magnetic field at the center of the circle.

Questions Discussion

Duration: (20 - 25 minutes)

The purpose of this stage is to consolidate the knowledge acquired by the students, reviewing and discussing the answers to the presented problems. By involving students in reflections and discussions, it is expected to reinforce the understanding of the content and stimulate critical thinking about the practical and theoretical applications of the concepts learned.

Discussion

• Question 1: Calculate the magnetic field at a distance of 5 cm from a long wire carrying a current of 10 A.

• To solve this question, use the formula for the magnetic field generated by a straight wire: B = (μ₀ * I) / (2π * r).

• Substituting the values: B = (4π * 10⁻⁷ T·m/A * 10 A) / (2π * 0.05 m).

• Simplifying: B = (4π * 10⁻⁶ T·m) / (2π * 0.05 m).

• Resulting in: B = 4 * 10⁻⁶ T / 0.1 m = 4 * 10⁻⁵ T.

• Therefore, the magnetic field at a distance of 5 cm from the wire is 4 * 10⁻⁵ Tesla (or 40 µT).

• Question 2: Determine the direction of the magnetic field generated by a wire carrying a current upwards, using the right-hand rule.

• According to the right-hand rule, if the thumb of the right hand points in the direction of the current (upwards), the curled fingers indicate the direction of the magnetic field.

• Thus, curling the fingers around the wire, the magnetic field will form concentric circles around the wire, with a counterclockwise direction in the horizontal plane when viewed from above.

• Question 3: In a circular wire with a radius of 10 cm and a current of 5 A, calculate the magnetic field at the center of the circle.

• For a circular wire, the formula for the magnetic field at the center is B = (μ₀ * I) / (2r).

• Substituting the values: B = (4π * 10⁻⁷ T·m/A * 5 A) / (2 * 0.1 m).

• Simplifying: B = (2 * 10⁻⁶ T·m) / 0.1 m = 2 * 10⁻⁵ T.

• Therefore, the magnetic field at the center of the circle is 2 * 10⁻⁵ Tesla (or 20 µT).

Student Engagement

1. What is the importance of understanding the direction of the magnetic field around a wire? Give practical examples. 2. How would the magnetic field vary if we doubled the current in the wire? And if we halved the distance? 3. Discuss the technological applications that utilize the magnetic field generated by wires. How can this understanding contribute to future innovations? 4. What is the difference between the magnetic field generated by a straight wire and by a circular wire? In which practical situations is each more applicable? 5. What are some challenges that engineers and scientists face when working with magnetic fields generated by electric currents?

Conclusion

Duration: (10 - 15 minutes)

The purpose of this stage is to review and consolidate the knowledge acquired by the students, ensuring that they fully understand the concepts addressed in the lesson. By recapping the main points and discussing the practical relevance of the content, it is hoped to reinforce learning and application of the concepts in everyday situations.

Summary

• Magnetic field: definition and generation by electric currents.
• Biot-Savart Law and its formula for calculating the magnetic field.
• How to calculate the magnetic field generated by a straight wire and a circular wire.
• Right-hand rule to determine the direction of the magnetic field.
• Practical applications of the magnetic field generated by current-carrying wires.
• Resolution of practical problems involving magnetic field calculations.

The lesson connected theory with practice by explaining the fundamental concepts of the magnetic field generated by electric currents and providing detailed examples of calculations and practical problems. The demonstrations and solved problems helped students visualize and apply the theoretical concepts in real situations, such as in electric motors and magnetic storage devices.

Understanding the magnetic field generated by current-carrying wires is essential for many modern technologies, such as electric motors, transformers, and communication systems. Moreover, understanding this phenomenon can lead to future innovations in various areas of engineering and science. For instance, the speakers we use daily operate based on this principle, and the Earth is protected from harmful solar particles by its natural magnetic field.