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Magnetic Damping01:17

Magnetic Damping

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Eddy currents can produce significant drag on motion, called magnetic damping. For instance, when a metallic pendulum bob swings between the poles of a strong magnet, significant drag acts on the bob as it enters and leaves the field, quickly damping the motion.
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A charged particle experiences a force when moving through a magnetic field. Consider the field to be uniform and the charged particle to move perpendicular to it. If the field is in a vacuum, the magnetic field is the dominant factor determining the motion. Since the magnetic force is perpendicular to the direction of motion, a charged particle follows a curved path. The particle continues to follow this curved path until it forms a complete circle. Another way to look at this is that the...
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Force On A Current Loop In A Magnetic Field01:17

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Magnetic forces on wires carrying current are most frequently applied in motors. A DC motor is a device that converts electrical energy into mechanical work. In motors, wire loops are enclosed in a magnetic field. When current flows through the loops, the magnetic field applies torque, which causes the shaft to rotate. The direction of the current is reversed once the loop's surface area is lined up with the magnetic field, causing a constant torque on the loop. During the process,...
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An electric field suffers a discontinuity at a surface charge. Similarly, a magnetic field is discontinuous at a surface current. The perpendicular component of a magnetic field is continuous across the interface of two magnetic mediums. In contrast, its parallel component, perpendicular to the current, is discontinuous by the amount equal to the product of the vacuum permeability and the surface current. Like the scalar potential in electrostatics, the vector potential is also continuous...
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Consider a circular loop with a radius a, that carries a current I. The magnetic field due to the current at an arbitrary point P along the axis of the loop can be calculated using the Biot-Savart law.
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Magnetic Susceptibility and Permeability01:31

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In linear magnetic materials, like paramagnets and diamagnets, magnetization is proportional to the magnetic field intensity. The constant of proportionality, a dimensionless number, is called magnetic susceptibility. The value of the susceptibility depends on the type of material.
When diamagnetic materials are placed under an external magnetic field, the moments opposite to the field are induced. Hence, the susceptibility for diamagnets has a minimal negative value of 10-5–10-6. Since...
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Related Experiment Video

Updated: May 17, 2025

Optimizing Magnetic Force Microscopy Resolution and Sensitivity to Visualize Nanoscale Magnetic Domains
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Magnetic Tunneling Between Disc-Shaped Obstacles.

Søren Fournais1, Léo Morin1

  • 1Department of Mathematics, University of Copenhagen, Universitetsparken 5, 2100 Copenhagen Ø, Denmark.

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|April 24, 2025
PubMed
Summary
This summary is machine-generated.

We derived formulas for semiclassical tunneling in 2D with magnetic fields. Our method applies to general obstacle configurations, yielding Harper's equation for lattice-placed discs.

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Area of Science:

  • Mathematical Physics
  • Quantum Mechanics
  • Condensed Matter Physics

Background:

  • Semiclassical tunneling is crucial for understanding quantum phenomena.
  • Magnetic fields significantly alter quantum tunneling behavior.
  • Previous studies often simplified obstacle configurations.

Purpose of the Study:

  • To derive formulas for semiclassical tunneling in 2D with constant magnetic fields.
  • To develop a general reduction method for systems with multiple obstacles.
  • To investigate spectral properties and effective operators for specific configurations.

Main Methods:

  • Analysis of the magnetic Neumann Laplacian in the complement of discs.
  • Development of a reduction method to an interaction matrix.
  • Derivation of asymptotic formulas for spectral gaps.
  • Construction of an effective operator for lattice configurations.

Main Results:

  • A general reduction method applicable to various obstacle arrangements.
  • An asymptotic formula for the spectral gap with two discs.
  • Derivation of Harper's equation for discs arranged in a regular lattice.
  • Identification of challenges including non-trivial angular momentum and eigenvalue crossings.

Conclusions:

  • The developed method provides a powerful tool for studying magnetic tunneling in complex geometries.
  • The connection to Harper's equation highlights the relevance to condensed matter systems.
  • The findings offer new insights into quantum phenomena influenced by magnetic fields and boundary conditions.