Glossary

Ampère's law connects electric currents to the magnetic fields they create. It's a key principle in electromagnetism, showing that moving charges generate magnetic fields proportional to the current's strength.

For straight wires, the strength decreases as you move away. The helps visualize field direction: point your thumb along the current, and your curled fingers show the field's circulation.

Ampère's Law and Magnetic Fields

Ampère's law and magnetic fields

Top images from around the web for Ampère's law and magnetic fields

  • Electrodynamics/Ampere's Law - Wikibooks, open books for an open world View original

    Is this image relevant?

  • 22.9 Magnetic Fields Produced by Currents: Ampere’s Law – College Physics View original

    Is this image relevant?

  • Electrodynamics/Ampere's Law - Wikibooks, open books for an open world View original

    Is this image relevant?

1 of 3

Top images from around the web for Ampère's law and magnetic fields

  • Electrodynamics/Ampere's Law - Wikibooks, open books for an open world View original

    Is this image relevant?

  • 22.9 Magnetic Fields Produced by Currents: Ampere’s Law – College Physics View original

    Is this image relevant?

  • Electrodynamics/Ampere's Law - Wikibooks, open books for an open world View original

    Is this image relevant?

1 of 3
  • Ampère's law establishes a fundamental relationship between electric currents and the magnetic fields they generate
  • States the magnetic field around a is directly proportional to the total passing through the area enclosed by the loop
  • Mathematically expressed as ∮[B](https://www.fiveableKeyTerm:B)⃗⋅dl⃗=μ0Ienc\oint \vec{[B](https://www.fiveableKeyTerm:B)} \cdot d\vec{l} = \mu_0 I_{enc}
    • ∮B⃗⋅dl⃗\oint \vec{B} \cdot d\vec{l} represents the of the magnetic field B⃗\vec{B} along the closed loop
    • IencI_{enc} denotes the total current enclosed by the loop
    • μ0\mu_0 is the , a constant equal to 4π×10−7 [T](https://www.fiveableKeyTerm:T)⋅[m/A](https://www.fiveableKeyTerm:m/A)4\pi \times 10^{-7} \text{ [T](https://www.fiveableKeyTerm:T)} \cdot \text{[m/A](https://www.fiveableKeyTerm:m/A)}
  • Demonstrates that electric currents (moving charges) serve as sources of magnetic fields
  • The strength of the generated magnetic field is directly proportional to the magnitude of the electric current
  • Ampère's law is a key principle in electromagnetism, alongside , , and the
  • Ampère's law is particularly useful in , where currents and magnetic fields are time-independent

Magnetic fields around straight wires

  • For an carrying a [I](https://www.fiveableKeyTerm:I)[I](https://www.fiveableKeyTerm:I), the magnetic field at a distance [r](https://www.fiveableKeyTerm:r)[r](https://www.fiveableKeyTerm:r) from the wire can be calculated using Ampère's law
  • The magnetic field magnitude is given by B=μ0I2πrB = \frac{\mu_0 I}{2\pi r}
    • BB represents the magnitude of the magnetic field
    • II is the current flowing through the wire
    • rr is the perpendicular distance from the center of the wire to the point of interest
  • To derive this formula using Ampère's law:
    1. Choose a of radius rr centered on the wire as the path of integration
    2. Due to the of the situation, the magnetic field is constant in magnitude along the loop
    3. Simplify the line integral: ∮B⃗⋅dl⃗=B(2πr)\oint \vec{B} \cdot d\vec{l} = B(2\pi r), where 2πr2\pi r is the circumference of the loop
    4. Apply Ampère's law: B(2πr)=μ0IB(2\pi r) = \mu_0 I, equating the line integral to the enclosed current
    5. Solve for BB to obtain the final expression: B=μ0I2πrB = \frac{\mu_0 I}{2\pi r}
  • The magnetic field around a straight wire decreases inversely with increasing distance from the wire (falls off as 1/r1/r)
  • This result is useful for calculating magnetic fields in situations involving long, straight current-carrying wires (power lines, electrical cables)

Right-hand rule for current direction

  • The is a convention used to determine the direction of the magnetic field circulation in relation to the current direction when applying Ampère's law
  • To use the right-hand rule:
    1. Point your right thumb in the direction of the current flow
    2. Your fingers will naturally in the direction of the magnetic field circulation
  • When applying Ampère's law, the direction of the line integral (circulation) must be consistent with the right-hand rule
    • If the current is pointing out of the loop (towards you), the circulation is counterclockwise
    • If the current is pointing into the loop (away from you), the circulation is clockwise
  • The right-hand rule ensures that the relationship between the current direction and the magnetic field circulation is consistent with Ampère's law
  • This convention is crucial for correctly determining the direction of the magnetic field when solving problems involving Ampère's law (solenoids, toroidal coils)

Ampère's Law and Maxwell's Equations

  • Ampère's law is one of , which collectively describe the behavior of electric and magnetic fields
  • The curl of the magnetic field is related to the current density and the time-varying electric field
  • Ampère's law in its original form applies to steady currents, but Maxwell's equations extend it to include time-varying fields
  • , as described by Faraday's law, is closely related to Ampère's law in Maxwell's equations

Key Terms to Review (31)

Ampère-Maxwell law: The Ampère-Maxwell law is an extension of Ampère's Law that incorporates the concept of displacement current, linking electric fields and magnetic fields in electromagnetic theory. It states that the magnetic field around a closed loop is proportional to the electric current passing through the loop and the rate of change of the electric field in the region, forming a crucial part of the complete set of equations that describe electromagnetism.
Ampère’s law: Ampère’s law is a fundamental principle in electromagnetism that relates the integrated magnetic field around a closed loop to the electric current passing through the loop. Mathematically, it is expressed as $\oint_{C} \mathbf{B} \cdot d\mathbf{l} = \mu_{0} I_{enc}$, where $\mathbf{B}$ is the magnetic field, $d\mathbf{l}$ is an infinitesimal element of the loop, $\mu_{0}$ is the permeability of free space, and $I_{enc}$ is the total current enclosed by the loop.
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.
B: B is a fundamental physical quantity that describes the strength and direction of the magnetic field at a given point in space. It is a vector quantity, meaning it has both magnitude and direction, and is a crucial concept in the study of electromagnetism and the behavior of charged particles in magnetic fields.
Circular Loop: A circular loop refers to a closed, circular path that an electric current or magnetic field can travel along. This geometric shape is a fundamental concept in the study of electromagnetism, as it allows for the analysis and understanding of the magnetic fields generated by electric currents.
Closed Loop: A closed loop is a system where the output of a process is fed back as input, creating a continuous cycle of information and control. This concept is fundamental in understanding both Kirchhoff's Rules and Ampère's Law in the context of electric circuits and electromagnetic fields.
Curl: Curl is a vector calculus operator that describes the circulation or rotation of a vector field around a given point. It is a fundamental concept in electromagnetism and fluid dynamics, providing a measure of the local spinning motion of a vector field.
Cylindrical symmetry: Cylindrical symmetry occurs when an object or system remains invariant under rotations about a central axis. It is commonly used in the context of electric fields and charge distributions.
Electric Current: Electric current is the flow of electric charge through a conductive material, such as a metal wire. It is the movement of charged particles, typically electrons, within a circuit and is responsible for the generation and transmission of electrical energy.
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.
Faraday's law: Faraday's law states that a change in magnetic flux through a circuit induces an electromotive force (emf) in that circuit. This principle is crucial for understanding how magnetic fields interact with electric circuits and lays the foundation for many applications in electromagnetism.
Gauss's Law: Gauss's law is a fundamental principle in electromagnetism that relates the electric flux through a closed surface to the total electric charge enclosed within that surface. It provides a powerful tool for calculating the electric field produced by various charge distributions.
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.
Infinitely Long Straight Wire: An infinitely long straight wire is a theoretical model used in electromagnetism to simplify the analysis of the magnetic field generated by an electric current. This idealized wire extends infinitely in both directions, creating a uniform and predictable magnetic field pattern around it.
Line Integral: A line integral is a mathematical concept that represents the integration of a function along a specified curve or path. It is a fundamental tool in vector calculus and is used to quantify the cumulative effect of a vector field along a particular trajectory.
M/A: The term m/A stands for 'meters per Ampere' and is a measure of magnetic field strength per unit of electric current. This term is crucial in the context of Ampère's Law, which relates the integrated magnetic field around a closed loop to the electric current passing through that loop. Understanding m/A helps in analyzing how changes in current affect the magnetic field produced, which is essential for grasping electromagnetic principles.
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.
Magnetostatics: Magnetostatics is the study of static or time-independent magnetic fields, where the magnetic fields do not vary with time. It involves the analysis of magnetic fields produced by steady currents or permanent magnets, without considering the effects of time-varying electric or magnetic fields.
Maxwell's Equations: Maxwell's equations are a set of four fundamental equations in electromagnetism that describe the relationships between electric and magnetic fields and electric charges and currents. These equations form the foundation of classical electromagnetism and are essential for understanding a wide range of electromagnetic phenomena.
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.
R: The variable 'r' is a fundamental quantity that represents the distance between two points or objects in space. It is a vector quantity, meaning it has both magnitude and direction, and is commonly used in physics to describe the spatial relationship between interacting entities.
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.
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.
Steady Current: Steady current, also known as direct current (DC), is a constant and unidirectional flow of electric charge through a conductor. It is a fundamental concept in the study of electromagnetism and is a crucial component in Ampère's Law, which describes the relationship between a steady current and the magnetic field it generates.
Symmetry: Symmetry is the quality of being made up of exactly similar parts facing each other or around an axis, center, or edge. It is a fundamental concept in physics that describes the invariance of a system under certain transformations, such as translations, rotations, or reflections.
T: T, in the context of physics, typically refers to the symbol used to represent the magnetic field or magnetic flux density. It is a fundamental quantity in the study of electromagnetism and is closely related to Ampère's law, which describes the relationship between the magnetic field and the electric current that generates it.
Toroid: A toroid is a three-dimensional geometric shape that resembles a doughnut or an inner tube. It is characterized by a circular path or loop, with the cross-section of the loop typically circular or elliptical. Toroids are commonly encountered in various physics topics, including magnetic fields, electromagnetic induction, and self-inductance.
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 is used in various electromagnetic laws and equations.
© 2024 Fiveable Inc. All rights reserved.
AP® and SAT® are trademarks registered by the College Board, which is not affiliated with, and does not endorse this website.
Back
Practice QuizGlossary
Practice QuizGlossary
Next guide