Introduction to Magnetism: Force in Wire with Current

Relevance of the Topic

Magnetism is an essential part of Physics, one of the fundamental forces that shape the world around us. Understanding this phenomenon is critical to explain a wide variety of physical and technical processes, from the interaction between subatomic particles to the operation of electric motors.

The study of Magnetic Force in Wires with Specific Current is particularly important as it lies at the connection between Magnetism and Electricity. It provides an integrative bridge between these two seemingly distinct areas, showing how electric current in a conductor generates a magnetic field, and how this field interacts with other conductors carrying current. Furthermore, it is essential for understanding the basic principles of electromagnetic instruments, such as galvanometers and ammeters.

Contextualization

In the curriculum, the study of Magnetism: Force in Wire with Current is situated after the introduction to concepts of electric field, electrification, and electric current, but before more complex topics, such as Electromagnetic Induction and Electromagnetic Waves. It fits into the broader context of electromagnetism, providing the conceptual basis for understanding how electrical and magnetic interactions work together to govern the behavior of matter and radiation.

Understanding this topic is also fundamental for a range of practical applications, from designing efficient electric motors to the operation of data storage devices, such as hard drives and memory cards. Thus, by mastering this content, students acquire important theoretical tools and problemsolving skills that can be applied in a variety of scientific and technological contexts.

Theoretical Development

Components

• Magnetic Field (B): It is a region of space where a magnetic object can influence other magnetic objects or current-carrying conductors. It is represented by the vector B, where its direction is indicated by field lines, its sense is from south to north (always), and its intensity is proportional to the force that a test magnetic object would feel if located at a particular point in the field.

• Magnetic Force (Fm): It is the force that a magnetic field exerts on a particle or an object in motion with electric charge. This force is perpendicular to both the object's velocity and the direction of the magnetic field. Its direction is determined by the right-hand rule: the thumb points in the direction of velocity, the fingers in the direction of the magnetic field, and the force will be in the direction where the palm of the hand is.

• Ampère-Maxwell Law: The fundamental law that relates the distribution of electric current to the spatial variation of the produced magnetic field. It establishes the principle of conservation of magnetism and is expressed by the mathematical equation ∇ x B = μo J, where B is the magnetic field, J is the current density, μo is the magnetic permeability of vacuum, and ∇ x B is the curl of B.

Key Terms

• Electric Current (I): Ordered flow of charged particles in a conductor. The current is measured in amperes (A) and its direction is considered the direction of movement of positive charge carriers.

• Wire with Current: Also called a conductor, it is a material that allows the free flow of electrons. When an electric current passes through a wire, it generates a magnetic field around it.

• Magnetic Force in Wires with Current: Phenomenon by which a wire carrying current may be deflected from its path by the action of an external magnetic field, due to the interaction between the current and the field. The expression for the intensity of this force is given by the Biot-Savart law.

Examples and Cases

• Force between two parallel wires: Two straight, long, parallel wires conducting currents in the same direction will magnetically interact, generating a mutual attractive force.

• Electric Motor: This is a practical example of the application of the principle of force in wire with current. The motor operates through the interaction of an external magnetic field with the magnetic field generated by the electric current in its rotor wires, resulting in a torque that causes the rotor's movement.

• Galvanometer: An instrument that uses magnetic force in wires with current to measure the current intensity in a circuit. The current to be measured generates a magnetic field that interacts with the magnetic field of a fixed permanent magnet, causing a torque that moves an indicating needle.

Each of these examples illustrates the practical application of the studied theory, highlighting the relevance of Magnetic Force in Wires with Current as a key concept in Physics and Electromagnetism.

Detailed Summary

Key Points

• Magnetic Force in Wire with Current: This is the force exerted by a magnetic field on a wire carrying electric current. The interaction of the current with the magnetic field can cause a deviation in the wire's path, and the resulting force follows the direction and sense determined by the right-hand rule.

• Magnetic Permeability of Vacuum (μo): It is a fundamental constant that appears in the Ampère-Maxwell Law, establishing the relationship between the distribution of electric current and the spatial variation of the magnetic field. It has an approximate value of 4π × 10^-7 N/A².

• Magnetic Field around a Wire with Current (B): When current passes through a wire, a circular magnetic field arises around it. The intensity of this field decreases as the distance from the wire increases. The direction of the field is determined by the current's direction, in accordance with the right-hand rule.

• Right-Hand Rule: This rule is used to determine the direction of the magnetic force or field in situations involving electric current and magnetic field. It stipulates that if the right hand's palm is placed in the direction of the current, the fingers will indicate the direction of the magnetic field.

Conclusions

• Electric current generates a magnetic field around it, and the wire conducting this current starts to interact with external magnetic fields, both receiving force from them and also generating magnetomotive force;

• The direction and sense of the magnetic force in a wire with current are determined by the current and the magnetic field, according to the right-hand rule;

• The Biot-Savart Law, which formulates the magnetic force in a wire with current, and the Ampère-Maxwell Law, which relates the current and the distribution of the magnetic field, are fundamental tools in the study of force in wire with current.

Suggested Exercises

1. Force in Wire with Current: Calculate the magnetic force acting on a straight wire, 30 cm long, carrying a current of 3 A and immersed in a magnetic field of intensity 0.8 T, when the angle between the current and the field is 45°.

2. Determine the Magnetic Field Generated by a Wire with Current: A straight, long wire is conducting a current of 2 A. Determine the intensity of the magnetic field produced by the wire at a distance of 10 cm from its axis.

3. Interpretation of Magnetic Force in an Electric Motor: Describe, step by step, the interaction of magnetic forces and electric forces that occur in an electric motor, and how this results in the rotor's movement. Use the concepts of force in wire with current and magnetic field to support your answer.