Lesson Plan | Traditional Methodology | Magnetic Field: Loop

Objectives

Duration: (10 - 15 minutes)

The purpose of this stage of the lesson plan is to provide a clear and general overview of what will be learned throughout the lesson. Defining the main objectives helps guide both the teacher and the students, ensuring that everyone is aware of the skills that will be developed and the knowledge that will be acquired. This also allows the teacher to structure the lesson in a way that effectively achieves these objectives, promoting a focused and directed learning environment.

Main Objectives

1. Calculate the magnetic field generated by a loop.

2. Solve problems that require calculating magnetic fields generated by loops.

Introduction

Duration: (10 - 15 minutes)

The purpose of this stage of the lesson plan is to spark student interest and situate them in the context of the theme that will be addressed. Providing a rich and detailed introduction not only helps capture students' attention but also establishes a solid foundation for the understanding of the concepts that will be explored later. Additionally, by relating the content to practical applications and curiosities, students can see the relevance of what they are learning, which can significantly increase engagement and motivation for learning.

Context

To start the lesson on the magnetic field generated by a loop, it is essential to contextualize the students within the universe of magnetic phenomena. Begin by explaining that magnetism is one of the fundamental forces of nature and is present in various aspects of our daily lives, from refrigerator magnets to the sophisticated magnetic resonance imaging equipment used in medicine. Highlight that one of the fundamental components of advanced studies in physics and engineering is understanding how magnetic fields are generated and manipulated, particularly in devices such as electric motors and generators.

Curiosities

Did you know that credit and debit cards use magnetic fields to store information? The magnetic stripe on cards consists of tiny magnetic particles that can be organized in a specific way to encode data. This is a practical and everyday example of how understanding magnetism and magnetic fields can have a direct impact on technology and modern life.

Development

Duration: (50 - 60 minutes)

The purpose of this stage of the lesson plan is to deepen students' understanding of the magnetic field generated by a loop. By detailing the theoretical concepts and solving practical problems, students can connect theory to practice, consolidating their learning. Guided problem-solving allows students to see the direct application of the formulas and principles, facilitating comprehension and retention of the content.

Covered Topics

1. Definition and Characteristics of a Loop: A loop is a conductive wire bent into a circular shape. Explain that when electric current passes through this wire, a magnetic field is generated around the loop. Highlight the importance of the radius of the loop and the intensity of the current in determining the magnetic field. 2. Biot-Savart Law: Introduce the Biot-Savart Law, which is fundamental for calculating the magnetic field generated by a current element. Highlight the mathematical formula and explain each of its components. This law is essential for understanding how the magnetic field varies as a function of position around the loop. 3. Magnetic Field at the Center of the Loop: Show the specific formula for calculating the magnetic field at the center of a circular loop, which is derived from the Biot-Savart Law. The formula is B = (μ₀ * I) / (2 * R), where B is the magnetic field, μ₀ is the permeability of free space, I is the current, and R is the radius of the loop. Explain each term and how they influence the magnetic field. 4. Superposition of Magnetic Fields: Explain the principle of superposition, which allows the calculation of the resultant magnetic field from several loops or other current elements. Highlight the importance of the direction and sense of the individual magnetic fields in determining the resultant field. 5. Practical Examples and Problem Solving: Present practical examples of how to calculate the magnetic field generated by a loop. Solve problems step by step, highlighting the application of the formulas and principles discussed earlier. Ensure that students note each step of the resolution to facilitate understanding.

Classroom Questions

1. Calculate the magnetic field at the center of a circular loop with a radius of 0.05 m, carrying a current of 10 A. 2. A circular loop with a radius of 0.1 m is carrying a current of 5 A. What is the magnetic field at the center of the loop? 3. Two circular loops of the same radius, 0.1 m, are carrying currents of 5 A and 3 A, respectively. Calculate the magnetic field at the midpoint between the two loops, knowing that they are separated by a distance of 0.2 m.

Questions Discussion

Duration: (15 - 20 minutes)

The purpose of this stage of the lesson plan is to consolidate students' learning by reviewing and discussing the solutions to the proposed questions. This moment allows for clarifying doubts, reinforcing concepts, and ensuring that students fully understand the content addressed. Through discussion and active engagement, students have the opportunity to reflect on what they have learned and apply concepts critically and practically.

Discussion

• Calculate the magnetic field at the center of a circular loop with a radius of 0.05 m, carrying a current of 10 A.

To solve this question, use the formula for the magnetic field at the center of a circular loop:

B = (μ₀ * I) / (2 * R)

Substituting the provided values:

B = (4π x 10⁻⁷ T·m/A * 10 A) / (2 * 0.05 m)

B = (4π x 10⁻⁷ * 10) / 0.1

B = 4π x 10⁻⁵ T

B ≈ 1.256 x 10⁻⁴ T

Therefore, the magnetic field at the center of the loop is approximately 1.256 x 10⁻⁴ Tesla.

• A circular loop with a radius of 0.1 m is carrying a current of 5 A. What is the magnetic field at the center of the loop?

To solve this question, we again use the formula:

B = (μ₀ * I) / (2 * R)

Substituting the provided values:

B = (4π x 10⁻⁷ T·m/A * 5 A) / (2 * 0.1 m)

B = (4π x 10⁻⁷ * 5) / 0.2

B = 2π x 10⁻⁵ T

B ≈ 6.28 x 10⁻⁵ T

Therefore, the magnetic field at the center of the loop is approximately 6.28 x 10⁻⁵ Tesla.

• Two circular loops of the same radius, 0.1 m, are carrying currents of 5 A and 3 A, respectively. Calculate the magnetic field at the midpoint between the two loops, knowing that they are separated by a distance of 0.2 m.

First, calculate the magnetic field generated by each loop at the midpoint. The formula for the magnetic field of a loop at a distance x from its center along its axis is:

B = (μ₀ * I * R²) / [2 * (R² + x²)^(3/2)]

For the first loop (I₁ = 5 A):

B₁ = (4π x 10⁻⁷ T·m/A * 5 A * 0.1 m²) / [2 * (0.1 m² + 0.1 m²)^(3/2)]

B₁ = (2π x 10⁻⁶) / [2 * (0.01 + 0.01)^(3/2)]

B₁ = (2π x 10⁻⁶) / [2 * (0.02)^(3/2)]

B₁ = (2π x 10⁻⁶) / [2 * (0.002828)]

B₁ ≈ 1.11 x 10⁻⁵ T

For the second loop (I₂ = 3 A):

B₂ = (4π x 10⁻⁷ T·m/A * 3 A * 0.1 m²) / [2 * (0.1 m² + 0.1 m²)^(3/2)]

B₂ = (6π x 10⁻⁷) / [2 * (0.02)^(3/2)]

B₂ ≈ 6.67 x 10⁻⁶ T

Since both magnetic fields have the same direction, the resultant field at the midpoint is the sum of the fields:

B = B₁ + B₂

B ≈ 1.11 x 10⁻⁵ T + 6.67 x 10⁻⁶ T

B ≈ 1.78 x 10⁻⁵ T

Therefore, the magnetic field at the midpoint between the two loops is approximately 1.78 x 10⁻⁵ Tesla.

Student Engagement

1. 樂 Ask the students: Why is the magnetic field at the center of a loop inversely proportional to the radius of the loop? 2. 樂 Reflection: How does the intensity of the current affect the magnetic field generated by a loop? 3. 樂 Discussion: How can the principle of superposition of magnetic fields be applied in practical devices, such as electric motors? 4. 樂 Ask the students: What would be the effect on the magnetic field if we increase the number of loops while keeping the same current and radius? 5. 樂 Reflection: What are the practical applications of the magnetic field generated by loops in our daily lives?

Conclusion

Duration: (10 - 15 minutes)

The purpose of this stage of the lesson plan is to review and consolidate the main points covered during the lesson, ensuring that students have a clear and cohesive understanding of the content. Additionally, this stage reinforces the practical relevance of the topic, motivating students to value and apply the knowledge acquired in real contexts.

Summary

• Magnetism is a fundamental force of nature present in various aspects of everyday life.
• A loop is a conductive wire bent into a circular shape that generates a magnetic field when carrying electric current.
• The Biot-Savart Law allows calculating the magnetic field generated by a current element.
• The formula B = (μ₀ * I) / (2 * R) calculates the magnetic field at the center of a circular loop.
• The principle of superposition allows calculating the resultant magnetic field from several loops or other current elements.
• Problem-solving examples illustrated the application of the formulas and principles discussed.

The lesson connected theory with practice by presenting fundamental concepts about the magnetic field generated by a loop and demonstrating them through practical examples and problem resolutions. This allowed students to visualize the direct application of the formulas and principles learned, facilitating comprehension and retention of the content.

The topic is of great importance for daily life, as knowledge about magnetic fields generated by loops is present in various technologies, such as electric motors, generators, and medical magnetic resonance imaging equipment. Furthermore, understanding these concepts is essential for the development of new technologies and advancements in electrical and electronic engineering.