Lesson Plan | Traditional Methodology | Electricity: Electric Potential Energy

Objectives

Duration: (10 - 15 minutes)

The purpose of this stage is to provide a clear and detailed overview of the lesson objectives, ensuring that students understand the importance of grasping electric potential energy. This will help focus the students' attention on the crucial points of the content and prepare them for solving problems related to the topic.

Main Objectives

1. Explain the concept of electric potential energy and its relevance in electrical systems.

2. Demonstrate how to calculate the electric potential energy of a charge in an electric field.

3. Teach the application of the concept of electric potential energy to determine the speed of a moving charge.

Introduction

Duration: (10 - 15 minutes)

The purpose of this stage is to engage students with the concept of electric potential energy in an understandable way, connecting theoretical content to practical and everyday examples. This will help spark students' interest and make learning more relevant and meaningful, preparing them to understand subsequent concepts in detail and apply them to problem-solving.

Context

To start the lesson on Electric Potential Energy, it is important to contextualize the concept within the universe of Physics and electricity. Electric potential energy is a form of energy stored in a system due to the position of electric charges. This concept is analogous to gravitational potential energy, where energy is stored due to the position of an object in a gravitational field. To illustrate, imagine an electric charge in an electric field, similar to a ball at the top of a hill; the potential energy depends on the charge's position in the field, just as gravitational potential energy depends on the height of the ball on the hill. This concept is fundamental to understanding how electricity works in everyday devices, such as batteries, capacitors, and electronic appliances.

Curiosities

Did you know that electric potential energy is the reason why lightning occurs during storms? The potential difference between the cloud and the Earth creates a huge amount of electric potential energy, which is explosively released as a lightning bolt. Additionally, electric potential energy is also the principle behind the operation of batteries in our smartphones and laptops, storing energy that can be used later.

Development

Duration: (50 - 60 minutes)

The purpose of this stage is to deepen students' understanding of electric potential energy through detailed explanations and practical examples. This will enable students to apply the concepts learned to solve specific problems, consolidating their knowledge and skill in using electric potential energy to calculate the speeds of moving charges.

Covered Topics

1. Concept of Electric Potential Energy: Explain that electric potential energy is the energy stored due to the position of an electric charge in an electric field. Detail that this energy depends on the position of the charge and the intensity of the electric field. 2. Formula of Electric Potential Energy: Present the formula U = k * (q1 * q2) / r, where U is the electric potential energy, k is the electrostatic constant, q1 and q2 are the charges, and r is the distance between the charges. Explain each term of the formula and how they relate. 3. Relation to Electric Work: Explain that electric potential energy can be converted into work when a charge moves within the electric field. Illustrate how the work needed to move a charge from one point to another is equal to the difference in electric potential energy between the two points. 4. Conservation of Energy: Discuss the principle of energy conservation in the context of moving charges in an electric field. Explain that the total energy (kinetic + potential) of an isolated charge in an electric field remains constant if no external forces are acting on it. 5. Practical Application: Demonstrate how to calculate the speed of a charge that was initially at rest and has moved from its initial position using energy conservation. Use a numerical example to illustrate the process step by step.

Classroom Questions

1. Calculate the electric potential energy between two charges of 3 µC and 5 µC separated by a distance of 0.2 meters in a vacuum. 2. A charge of 2 µC is moved from point A to point B in an electric field. The difference in electric potential energy between the points is 4 mJ. What is the work done on the charge? 3. A charge of 1 µC is released from rest at a point where the electric potential energy is 10 mJ. What will be the speed of the charge when it reaches another point where the electric potential energy is 2 mJ? (Consider the charge's mass as 2 mg).

Questions Discussion

Duration: (20 - 25 minutes)

The purpose of this stage is to ensure that students consolidate their understanding of electric potential energy, reviewing the detailed explanations of the solved questions and promoting discussion and reflection on the topic. This helps solidify knowledge, clarify doubts, and connect theoretical content to practical and everyday situations.

Discussion

• ✅ Question 1: Calculate the electric potential energy between two charges of 3 µC and 5 µC separated by a distance of 0.2 meters in a vacuum.

Solution: Formula: U = k * (q1 * q2) / r Where k = 8.99 x 10^9 N·m²/C² (electrostatic constant), q1 = 3 x 10^-6 C, q2 = 5 x 10^-6 C, and r = 0.2 m Substituting the values: U = 8.99 x 10^9 * (3 x 10^-6 * 5 x 10^-6) / 0.2 U = 8.99 x 10^9 * 15 x 10^-12 / 0.2 U = 674.25 x 10^-3 J U = 0.67425 J Result: The electric potential energy between the charges is 0.67425 joules.

• ✅ Question 2: A charge of 2 µC is moved from point A to point B in an electric field. The difference in electric potential energy between the points is 4 mJ. What is the work done on the charge?

Solution: The work done on the charge is equal to the difference in electric potential energy between the points. W = ΔU Where ΔU = 4 mJ = 4 x 10^-3 J Result: The work done on the charge is 4 mJ or 4 x 10^-3 joules.

• ✅ Question 3: A charge of 1 µC is released from rest at a point where the electric potential energy is 10 mJ. What will be the speed of the charge when it reaches another point where the electric potential energy is 2 mJ? (Consider the charge's mass as 2 mg).

Solution: Principle of energy conservation: E_total = E_kinetic + E_potential Initial total energy (E_total initial) = Initial potential energy (E_potential initial) Final total energy (E_total final) = Final kinetic energy (E_kinetic final) + Final potential energy (E_potential final) E_total initial = E_total final E_potential initial = 10 mJ = 10 x 10^-3 J E_potential final = 2 mJ = 2 x 10^-3 J ΔE_potential = E_potential initial - E_potential final = 8 x 10^-3 J ΔE_potential = E_kinetic final E_kinetic final = 1/2 * m * v^2 m = 2 mg = 2 x 10^-6 kg 8 x 10^-3 J = 1/2 * 2 x 10^-6 kg * v^2 v^2 = (8 x 10^-3 J) / (1 x 10^-6 kg) v^2 = 8 x 10^3 v = √(8 x 10^3) v ≈ 89.44 m/s Result: The speed of the charge will be approximately 89.44 m/s.

Student Engagement

1.  Reflection Questions:

Why is electric potential energy important in devices like batteries and capacitors? How does the conservation of energy apply to the motion of charges in an electric field? What other everyday situations can be explained by the concept of electric potential energy? What are the consequences of a very high potential difference in natural systems, like storms? How can we relate the concept of electric potential energy to the work done in an electrical system?

Conclusion

Duration: (5 - 10 minutes)

The purpose of this stage is to summarize and consolidate the main concepts presented during the lesson, reinforcing students' learning. Additionally, by connecting theory with practice and highlighting the relevance of the topic, the conclusion helps solidify knowledge and demonstrate the practical application of the concepts studied, promoting a deeper and more meaningful understanding.

Summary

• Electric potential energy is the energy stored due to the position of an electric charge in an electric field.
• The formula for electric potential energy is U = k * (q1 * q2) / r.
• Electric potential energy can be converted into work when a charge moves within the electric field.
• The principle of conservation of energy applies to the motion of charges in an electric field: the total energy (kinetic + potential) of an isolated charge remains constant if no external forces act on it.
• The practical application of the concept includes calculating the speed of a moving charge using energy conservation.

The lesson connected theory to practice by explaining fundamental concepts of electric potential energy and applying them to solve practical problems, such as calculating the speed of a moving charge. Detailed numerical examples and solved questions helped illustrate how theoretical concepts translate into real and practical applications in the field of electricity.

Understanding electric potential energy is crucial for everyday life, as it is present in various devices and natural phenomena. For example, the energy stored in smartphone and laptop batteries enables their operation, and the potential difference causes natural events such as lightning during storms. These examples highlight the practical importance and everyday relevance of the topic.