Introduction

Relevance of the Topic

The study of Electricity and, more precisely, the 'Work of the Electric Force' is of paramount importance within the realm of Physics. Understanding the concepts that surround this topic is fundamental to comprehend everything from everyday natural phenomena, such as lightning, to advanced technological applications, like the functioning of electronic circuits.

Electric force, represented by Coulomb's Law, is one of the four fundamental interactions of nature, along with gravitational force, weak force, and strong force. It is responsible for the interactions between charged particles, being the 'glue' that holds the structure of matter together. The 'work' of this force, in turn, corresponds to the transfer of energy between these particles, being the basis of numerous physical phenomena and practical applications.

Contextualization

In the vast field of Physics, Electricity is at the core of the sub-discipline Electromagnetism, one of the most relevant and comprehensive ones. Within the curriculum of the 2nd year of High School Physics, the study of Electricity is a crucial step in deepening the understanding of natural phenomena and interactions between particles of matter.

After the theory on electrization by contact and by induction, as well as the study of the concepts of electric charge, electric field, and electric potential, the topic 'Work of the Electric Force' naturally emerges as a next step. Here, we will expand the knowledge about electric force and its relation to the movement of charges, establishing a solid foundation for the discussion of topics such as electric current, electric resistance, and energy in circuits.

The study of this topic, therefore, provides a crucial bridge between the basic concepts of Electricity and more advanced applications, preparing the ground for forays into the study of equally relevant topics, such as the Joule effect, Ohm's law, and Kirchhoff's law.

Theoretical Development

Components

• Electric Force (Coulomb's Law): The fundamental force in the interaction between two electric charges. It is a long-range force that acts at a distance, never in direct contact. The amount of force is directly proportional to the magnitude of the charges and inversely proportional to the square of the separation between the charges.

  • The formula for the electric force between two charges is F = k * (|q1| * |q2|) / r^2, where F is the force, k is the Coulomb constant, q1 and q2 are the charges of the particles, and r is the distance between them.

• Work of the Electric Force: The work done by the electric force to move a charge from one point to another is equal to the potential difference (voltage) between these two points, multiplied by the charge. In other words, W = q * ΔV, where W is the work, q is the charge, and ΔV is the potential difference.

• Electric Potential: The electric potential at a point in space is defined as the work done per unit charge to move a charged particle from infinite reference to that point. It is calculated using the expression V = k * q / r, where V is the potential, k is the Coulomb constant, q is the charge, and r is the distance.

Key Terms

• Work: In Physics, work is the transfer of energy through the application of a force. It is defined as the scalar product between the applied force and the resulting displacement in the direction of the force.

• Electric Charge: An intrinsic property of particles that make up matter, such as electrons and protons, which generates and interacts with electric fields.

• Potential Difference (or Voltage): Refers to the difference in electric potential energy per unit charge between two points in an electric field.

Examples and Cases

• Example 1: A charge moved in a uniform electric field: When a charge q is moved between two points a and b in a uniform electric field E, the work done by the electric force is calculated as W = q * ΔV = q * E * d, where d is the distance between points a and b.

• Example 2: Charge moved in a circuit: In the context of an electric circuit, the battery provides a voltage source that does work to move the electrons (charge) along the circuit. The work done by the battery is equal to the charge q multiplied by the voltage V (W = qV). Here, voltage is another way to refer to the potential difference.

Remember: 'Electricity is like the math of energy. It is a universal language that describes everything, from the movement of a single electron to the explosive energy of stars.' - Aaron Albright

Detailed Summary

Key Points

• Electric Force (Coulomb's Law): It is crucial to understand that electric force is the fundamental force that governs the interaction between two electric charges. It is based on Coulomb's Law, which states that this force is directly proportional to the product of the charges and inversely proportional to the square of the distance between them. Understanding this law, and the electric force it describes, is a foundation for the entire study of Electricity.

• Work of the Electric Force: The concept of work, in this context, refers to the ability of the electric force to transfer energy by moving a charge from one point to another. The work done is given by the product of the charge by the potential difference (voltage) between the points, W = q * ΔV. This is a key concept to understand how electrical energy is transferred and transformed in various contexts, from lighting a bulb to the operation of a motor.

• Electric Potential: Electric potential is another powerful tool to understand Electricity. This concept provides us with an alternative way to think about the interaction between charges, describing the potential energy that a charge possesses due to the presence of other charges. In the study of the work of the electric force, the potential difference between two points (that is, the variation in potential when moving a charge from one point to another) is what matters.

Conclusions

• The 'Work of the Electric Force' is a key topic in Physics that allows us to understand the transfer of energy in electrical phenomena and their applications. Coulomb's Law is the basis for understanding electric force, while the concept of work helps us understand how this force acts to transfer energy. Electric potential, in turn, provides an additional perspective on the interaction between charges.

• Fully understanding electric force and its work allows us to comprehend a wide range of phenomena and applications, from the static electricity we feel when touching a doorknob on a dry winter day to the complex operation of electronic devices and circuits.

Exercises

1. Calculate the work done by the electric force to move a charge of 5 μC through a potential difference of 20 V.

2. Two particles, one with a charge of +5 μC and the other with a charge of -2 μC, are separated by a distance of 10 cm in a vacuum. Calculate the force and the work done by the electric force if they are released and approach each other.

3. In a region of a uniform electric field of 200 N/C, a charge of -3 μC is moved 10 m in the opposite direction of the field. Calculate the work done by the electric force.