Magnetic Field: Coil

Introduction

Relevance of the Topic The study of Magnetic Field: Coil is a gateway to more advanced concepts in Physics, such as Electrodynamics, and practical applications in engineering, such as transformers and electric motors. The coil, a device built with a conductor wire wound in turns, becomes an efficient magnetic field when an electric current passes through its wire. Understanding the geometry and intensity of this field is essential not only for understanding how electricity and magnetism interact, but also for exploring its potential in numerous technologies.

Contextualization In the vast mosaic of Physics, the topic of Magnetic Field: Coil resides at the intersection between the study of electromagnetism and the behavior of electric current. It builds upon the basic principles established in the study of magnetic fields in straight conductors and reapplies these concepts in more complex circuits, focusing on the analysis of coil behavior. Understanding this topic is therefore essential for progression in the Physics curriculum, as it allows the connection between more basic and advanced topics, creating a more complete and integrated view of electromagnetism. Furthermore, this topic establishes the basis for understanding phenomena and technologies that depend on the interaction between magnetic fields and electric currents, such as the operation of an electric power generator.

Theoretical Development

Components

• Coil: A coil is an electromagnetic device composed of a conductor wire wound in a spiral. The geometry of this spiral, such as the number of turns and the loop diameter, directly influences the strength of the magnetic field produced.

• Conductor Wire and Electric Current: The electric current passes through the coil's conductor wire, generating a magnetic field around it. The intensity of this field is directly proportional to the current flowing through the wire.

• Solenoide Effect: The coil's geometry, when the width of the turns is negligible compared to its length, is called a solenoid. The solenoid has a uniform and directed internal magnetic field, similar to a bar magnet's field.

• Generated Magnetic Field: The Magnetic Field generated by a coil, when crossed by an electric current, is produced by the alignment of the magnetic fields of each turn. This resulting field is centralized and parallel to the coil's axis, similar to a bar magnet's field.

Key Terms

• Magnetic Field: Area of influence around a magnet or a moving electric current, in which electric charges and other magnets experience a magnetic force.

• Magnetic Induction (B): It is the vector quantity that measures the intensity of a magnetic field.

• Magnetic Force (F): Force acting on a moving electric charge or a magnet when they pass through a magnetic field.

• Solenoid: Configuration of a coil with a length much greater than the diameter, whose magnetic field inside behaves similarly to a bar magnet.

Examples and Cases

• Magnetic Field of an Infinite Solenoid: An infinite solenoid, with current I flowing through it, creates a magnetic field in the direction of its axis, whose intensity at each point inside the solenoid is given by B = μ₀nI, where μ₀ is the magnetic permeability of vacuum and n is the number of turns per unit length.

• Magnetic Field of a Real Coil: The magnetic field at the center of a coil with N turns and radius R is calculated by B = (μ₀nI / 2R)(N² / (N² + p²)), where p is the distance from the coil's center to the point where the field is measured.

• Force on a Coil in an External Magnetic Field: A coil with current I in an external magnetic field B experiences a force given by F = BNIl, where N is the number of turns of the coil, l is the size of the coil in the direction of the current, and I is the current in the coil.

Detailed Summary

Key Points:

• Definition of a Coil: The coil is an electromagnetic induction device composed of a conductor wire wrapped in turns. Each turn contributes to the total magnetic field creation of the coil.

• Magnetic Field of an Ideal Coil (Solenoid): If the width of the turns is negligible, the coil can be treated as an ideal solenoid. In an ideal solenoid, the magnetic field inside it is uniform and aligned with the coil's axis, similar to a bar magnet's field.

• Magnetic Field of a Real Coil: The magnetic field at the center of a real coil (not considered an ideal solenoid) is calculated using Ampère's Law. The magnitude of this field depends on factors such as the number of turns, the current passing through the coil, and the coil's radius.

• Force on a Coil in an External Magnetic Field: A coil with current I in an external magnetic field experiences a force, known as Lorentz force, given by the formula F = BNIl. In this formula, N is the number of turns of the coil, l is the length of the coil in the direction of the current, and I is the current in the coil.

Conclusions:

• The creation and manipulation of magnetic fields are a fundamental basis for many practical applications. The study of the coil, as a device that generates and allows the control of these fields, is a crucial step towards understanding electromagnetic phenomena and technologies.

• The force and magnetic field generated by a coil are affected by variables such as the number of turns, the electric current, and the coil's size. Understanding these interactions is vital for creating efficient electromagnetic devices.

Exercises:

1. Calculate the intensity of the magnetic field at the center of an infinite coil with a current of 5A. What would be the value if the current were doubled?

2. A coil with 100 turns and a radius of 0.05 m has a current of 10 A passing through it. Calculate the intensity of the magnetic field at the center of the coil and 0.05 m away from the center.

3. A coil is placed in a uniform magnetic field of 0.5 T. If the coil has a length of 0.1 m and a current of 5 A passing through it, what will be the force acting on the coil if the angle between the field vector and the current vector is 90 degrees?