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Magnetic fields from current loops are a key concept in electromagnetism. The Biot-Savart law helps us calculate these fields, showing how moving charges create magnetism. Understanding this relationship is crucial for grasping the fundamentals of electromagnetic theory.

Current loops produce magnetic fields similar to bar magnets, with closed field lines and poles. However, their fields are generated by moving charges and can be easily controlled by adjusting the current. This principle is used in various applications, from simple electromagnets to complex scientific instruments.

Magnetic Field of a Current Loop

Biot-Savart law for current loops

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Top images from around the web for Biot-Savart law for current loops

  • 12.4 Magnetic Field of a Current Loop – University Physics Volume 2 View original

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  • Magnetic field of a current loop – TikZ.net View original

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  • 12.4 Magnetic Field of a Current Loop – University Physics Volume 2 View original

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  • Calculates produced by
  • Magnetic field at a point is sum of contributions from each
  • General form of Biot-Savart law: dB=μ04πIdl⃗×r^r2dB = \frac{\mu_0}{4\pi} \frac{I d\vec{l} \times \hat{r}}{r^2}
    • μ0\mu_0: 4π×10−7 T⋅m/A4\pi \times 10^{-7} \text{ T} \cdot \text{m/A}
    • II: current in conductor (measured in amperes)
    • dl⃗d\vec{l}: infinitesimal length element of conductor
    • r^\hat{r}: unit vector pointing from current element to point where magnetic field is calculated
    • rr: distance between current element and point where magnetic field is calculated
  • Simplified form of Biot-Savart law for magnetic field along axis of
    • Magnetic field at center of current loop: B=μ0I2RB = \frac{\mu_0 I}{2R}
      • RR: radius of current loop
    • Magnetic field at point along axis, distance zz from center: B=μ0IR22(R2+z2)3/2B = \frac{\mu_0 I R^2}{2(R^2 + z^2)^{3/2}}

Magnetic field lines of current loops

  • Form closed loops around current loop
    • Concentrated near center of loop, spread out away from loop
    • Perpendicular to plane of current loop at center
  • Direction of depends on current direction in loop
    • determines direction of magnetic field
      1. Point thumb in direction of current
      2. Fingers curl in direction of magnetic field
    • Current loop in xy-plane with counterclockwise current
      • point in positive z-direction inside loop
      • Magnetic field lines point in negative z-direction outside loop
  • Magnetic flux through the loop is related to the number of field lines passing through its area

Current loops vs bar magnets

  • Similarities
    • Similar shape with field lines forming closed loops
    • Both have north and where field lines are most concentrated
    • Field strength decreases with distance from center
  • Differences
    • Current loop magnetic field generated by moving charges (current)
      • Bar magnet magnetic field generated by alignment of within material
    • Current loop magnetic field easily controlled by changing current
      • Bar magnet magnetic field fixed and not easily changed
    • Current loop magnetic field typically weaker than bar magnet
      • Field strength depends on current and size of loop
  • Solenoids: tightly wound coils of wire that produce strong, uniform magnetic fields
  • Magnetic dipole moment: a measure of the strength and orientation of a current loop's magnetic field
  • Multiple current loops can be combined to create more complex magnetic field configurations

Key Terms to Review (19)

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.
B-field: The B-field, also known as the magnetic field, is a vector field that describes the magnetic influence exerted by electric currents and magnetic materials. It is a fundamental concept in electromagnetism and is crucial for understanding the behavior of charged particles and the operation of various electrical devices.
Current loop: A current loop is a closed path through which electric current flows, creating a magnetic field around it. This concept is crucial for understanding how loops of wire can produce magnetic fields, which play a vital role in electromagnetism and its applications. The strength and direction of the magnetic field generated by a current loop depend on factors such as the amount of current flowing and the shape of the loop.
Current-Carrying Conductor: A current-carrying conductor is an object, typically a wire or metal, that allows the flow of electric current through it. This term is particularly relevant in the context of understanding the magnetic field generated by a current loop, as described in the physics topic 12.4 Magnetic Field of a Current Loop.
Infinitesimal Current Element: An infinitesimal current element is an infinitely small segment of a current-carrying wire or conductor. It is a fundamental concept used in the analysis of the magnetic field generated by a current-carrying loop or circuit.
Magnetic domains: Magnetic domains are regions within a magnetic material where the magnetization is uniformly aligned in the same direction. These domains collectively determine the material's overall magnetic properties.
Magnetic Domains: Magnetic domains are microscopic regions within a magnetic material where the magnetic moments of individual atoms are aligned in the same direction. These aligned magnetic moments give rise to the overall magnetization of the material, which can be observed and measured at the macroscopic scale.
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 field lines: Magnetic field lines are imaginary lines that represent the direction and strength of a magnetic field. They emerge from the north pole of a magnet and enter the south pole, forming continuous loops.
Magnetic Field Lines: Magnetic field lines are the invisible lines that represent the direction and strength of a magnetic field. They are used to visualize and understand the behavior of magnetic fields, which are crucial in various topics related to electromagnetism and electromagnetic induction.
North Pole: The north pole is the point on the Earth's surface that is farthest north, where the Earth's axis of rotation meets its surface. It is one of the two points where the Earth's axis of rotation intersects its surface, the other being the south pole. The north pole is the location of the Earth's magnetic north, which is distinct from the geographic north pole.
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.
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.
South Pole: The south pole is one of the two points on the Earth's surface where the planet's axis of rotation meets its surface. It is the southernmost point on the globe and is the location of the Earth's magnetic south pole, which is the point where the Earth's magnetic field lines converge and exit the planet's surface.
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Glossary
Glossary
12.5 Ampère’s Law