12.3 Magnetic Force between Two Parallel Currents
3 min read•june 24, 2024
Parallel current-carrying wires create magnetic fields that interact, causing attraction or repulsion. The force between them depends on current direction, magnitude, wire length, and separation. This interaction forms the basis for defining the , the of electric current.
Understanding these forces is crucial for electrical engineering and physics applications. The relationship between current and magnetic fields showcases the fundamental connection between electricity and magnetism, a cornerstone of electromagnetic theory.
Magnetic Force between Parallel Currents
Magnetic interaction of parallel wires
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- Parallel current-carrying wires generate magnetic fields that interact with each other
- Magnetic fields encircle the wires according to the (point thumb in current direction, fingers curl in field direction)
- Field strength decreases with distance from the wire ()
- Interaction depends on relative current directions
- Same direction currents attract due to opposite field directions between wires
- Opposite direction currents repel due to same field directions between wires
- Force magnitude depends on current magnitudes, wire length, and separation distance
- Proportional to product of current magnitudes ()
- Proportional to wire length ()
- Inversely proportional to separation distance ()
- Force direction is always perpendicular to the plane containing the wires
- Attraction pulls wires together perpendicular to their length
- Repulsion pushes wires apart perpendicular to their length
Ampere definition using wire forces
- is the base SI unit for electric current
- Defined in terms of the force between two parallel wires
- Consider two infinitely long, thin, parallel wires separated by 1 meter in
- If equal currents in the wires produce an attractive force of N per meter of length, each current is defined as 1 ampere
- This definition connects the ampere to a measurable force between current-carrying wires
- Provides a practical way to standardize the ampere based on a magnetic interaction
- Highlights the relationship between electric current and magnetic fields
Force calculation for parallel wires
- The magnetic force per unit length between parallel current-carrying wires is given by:
-
- T⋅m/A is the
- and are the currents in the two wires in amperes
- is the separation distance between the wires in meters
-
- Multiply the force per unit length by the wire length to get the total force
- Use the to determine the force direction
- Point right thumb in the direction of the first current ()
- Curl fingers in the direction of the second current ()
- Extended index finger points in the direction of the force on the second wire
- Reverse the roles of and to find the force direction on the first wire
- The force experienced by the wires is an example of the
Related Electromagnetic Concepts
- : The current loop in a wire creates a magnetic dipole, which interacts with external magnetic fields
- Magnetic flux: The amount of passing through a given area, which can change due to the motion of
- : The process by which changing magnetic fields can induce currents in nearby conductors, including parallel wires
- : A measure of the strength and orientation of a magnetic dipole, which affects the interaction between current-carrying wires
Key Terms to Review (31)
Ampere: An ampere (A) is the unit of electric current in the International System of Units (SI). It is defined as the flow of one coulomb of charge per second.
Ampere: The ampere (symbol: A) is the base unit of electric current in the International System of Units (SI). It is defined as the constant flow of one coulomb of electric charge per second, and it is a fundamental quantity in the study of electromagnetism and electrical circuits.
Ampère's Law: Ampère's law is a fundamental principle in electromagnetism that relates the magnetic field generated by an electric current to the magnitude and direction of that current. It is one of the four Maxwell's equations, which together describe the relationships between electric and magnetic fields and electric charges and currents.
André-Marie Ampère: André-Marie Ampère was a French mathematician and physicist who made significant contributions to the study of electromagnetism. He is considered the father of electromagnetism and is known for his work on the relationship between electricity and magnetism, which led to the development of Ampère's law.
Electromagnetic Induction: Electromagnetic induction is the process by which a changing magnetic field induces an electromotive force (EMF) in a conductor, causing an electric current to flow. This phenomenon is fundamental to the operation of many electrical devices and is crucial in understanding the relationship between electricity and magnetism.
Ferromagnetic: Ferromagnetism is a type of magnetism that occurs in certain materials, where the magnetic moments of the atoms spontaneously align, resulting in a strong and persistent magnetic field. This phenomenon is the basis for the magnetic properties of materials like iron, nickel, and cobalt, which are commonly referred to as ferromagnetic materials.
Ferromagnetic material: A ferromagnetic material is a substance that exhibits strong magnetic properties due to the alignment of its atomic magnetic moments. These materials can retain magnetization even after an external magnetic field is removed.
Helmholtz Coils: Helmholtz coils are a pair of circular coils arranged coaxially, with a constant distance between them, used to generate a uniform magnetic field in the region between the coils. This configuration is widely employed in various applications, including particle accelerators, magnetic resonance imaging (MRI), and the study of magnetic fields.
I: In physics, 'I' represents electric current, which is the flow of electric charge in a circuit. It is measured in amperes (A) and plays a critical role in understanding magnetic interactions, especially when considering how parallel currents influence each other through magnetic forces. The behavior of 'I' in circuits is foundational for applying laws that govern magnetic fields and forces between currents.
James Clerk Maxwell: James Clerk Maxwell was a renowned Scottish physicist who made significant contributions to the understanding of electromagnetism, the nature of light, and the foundations of modern physics. His work laid the groundwork for many of the key concepts and theories that are central to the topics of 2.4 Distribution of Molecular Speeds, 6.4 Conductors in Electrostatic Equilibrium, 11.1 Magnetism and Its Historical Discoveries, 12.3 Magnetic Force between Two Parallel Currents, 13.4 Induced Electric Fields, 13.5 Eddy Currents, and 16.1 Maxwell's Equations and Electromagnetic Waves.
Lorentz Force: The Lorentz force is the force exerted on a charged particle when it moves through a magnetic field. It is a fundamental concept in electromagnetism that describes the interaction between electric and magnetic fields and the motion of charged particles.
Lorentz force equation: The Lorentz force equation describes the force experienced by a charged particle moving through an electric and magnetic field. It is given by $\mathbf{F} = q(\mathbf{E} + \mathbf{v} \times \mathbf{B})$, where $q$ is the charge, $\mathbf{E}$ is the electric field, $\mathbf{v}$ is the velocity of the particle, and $\mathbf{B}$ is the magnetic field.
Magnetic Dipole: A magnetic dipole is a pair of equal and opposite magnetic poles separated by a small distance. It is the fundamental unit of magnetism and is responsible for the magnetic fields generated by current-carrying loops, permanent magnets, and atomic/molecular structures.
Magnetic Field: A magnetic field is a region of space where magnetic forces can be detected. It is a fundamental concept in electromagnetism, describing the invisible lines of force that surround and permeate magnetic materials, electric currents, and changing electric fields. The magnetic field plays a crucial role in various topics within the study of college physics.
Magnetic Force between Two Parallel Currents: The magnetic force between two parallel current-carrying wires is described by the formula F = (μ0I1I2L)/(2πr), where μ0 is the permeability of free space, I1 and I2 are the currents in the two wires, L is the length of the wires, and r is the distance between the wires. This formula allows for the calculation of the attractive or repulsive force between the two parallel currents.
Magnetic moment: The magnetic moment is a vector quantity that represents the strength and direction of a magnetic source, such as a current-carrying loop or a magnetic dipole. It quantifies how much torque a magnetic field exerts on the magnetic source, indicating its tendency to align with an external magnetic field. This concept is crucial for understanding the behavior of charged particles in magnetic fields and the interaction between currents in parallel conductors.
Parallel Currents: Parallel currents refer to the flow of electric currents in the same direction, side-by-side, through separate conductors. This concept is crucial in understanding the magnetic force between two conductors carrying electric currents, as described in the topic of 'Magnetic Force between Two Parallel Currents'.
Paramagnetic: Paramagnetic materials are substances that are weakly attracted to an external magnetic field and can become magnetized in the presence of that field. This property arises from the atomic-level magnetic moments of the material's constituent atoms or molecules.
Paramagnetic material: A paramagnetic material is a substance that becomes magnetized in the presence of an external magnetic field and loses its magnetism when the field is removed. This effect is due to the alignment of unpaired electron spins within the material.
Permeability of free space: Permeability of free space, denoted as $\mu_0$, is a physical constant that describes the extent to which a magnetic field can penetrate and affect a vacuum. Its value is $4\pi \times 10^{-7}$ Tm/A.
Permeability of Free Space: The permeability of free space, denoted as $\mu_0$, is a fundamental physical constant that describes the magnetic properties of a vacuum or free space. It is a measure of the ability of free space to support the formation of a magnetic field in response to an electric current or changing electric field.
Pinch effect: The pinch effect is the compression of a plasma column by magnetic forces generated by electric currents within the plasma. It occurs when parallel currents in a plasma attract each other, leading to a reduction in the cross-sectional area of the plasma.
Right-hand rule: The right-hand rule is a mnemonic used to determine the direction of the magnetic field surrounding a current-carrying conductor. Point your thumb in the direction of the current and curl your fingers; your fingers indicate the direction of the magnetic field lines.
Right-Hand Rule: The right-hand rule is a mnemonic device used to determine the direction of various quantities related to electromagnetism, such as the direction of magnetic fields, the motion of charged particles in magnetic fields, and the direction of the magnetic force on a current-carrying conductor. It provides a simple and intuitive way to visualize and remember these directional relationships.
SI unit: An SI unit is a standard measurement unit defined by the International System of Units, which is used globally to ensure consistency in scientific measurements. These units provide a common framework for scientists and engineers, allowing them to communicate and compare results effectively across different fields of study. The adoption of SI units facilitates the understanding of physical quantities, such as force, mass, and electric current, which are essential in examining various phenomena including the magnetic force between parallel currents.
Solenoid: A solenoid is a coil of wire designed to create a uniform magnetic field in its interior when an electric current passes through it. It is commonly used in electromagnets, inductors, and valves.
Solenoid: A solenoid is a tightly wound coil of wire, often cylindrical in shape, that produces a magnetic field when an electric current passes through it. Solenoids are fundamental components in the study of electromagnetism and have applications in various areas of physics, including magnetic fields, magnetic force, and electromagnetic induction.
Tesla: The tesla (T) is the SI unit of magnetic flux density, representing the strength of a magnetic field. One tesla is defined as one weber per square meter.
Tesla: The tesla (T) is the unit of magnetic flux density, or magnetic field strength, in the International System of Units (SI). It is named after the Serbian-American inventor Nikola Tesla, who made significant contributions to the field of electromagnetism. The tesla is a fundamental unit that is essential in understanding and describing various electromagnetic phenomena and their applications.
Vacuum: A vacuum is a space devoid of matter, with extremely low pressure and density compared to the surrounding environment. It is an important concept in the study of electromagnetism and the behavior of charged particles.
μ0: μ0, also known as the permeability of free space or the vacuum permeability, is a fundamental physical constant that represents the magnetic permeability of free space or a vacuum. It is a crucial parameter in the study of electromagnetism and the behavior of magnetic fields.