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Related Concept Videos

Magnetic Fields01:27

Magnetic Fields

7.4K
A moving charge or a current creates a magnetic field in the surrounding space, in addition to its electric field. The magnetic field exerts a force on any other moving charge or current that is present in the field. Like an electric field, the magnetic field is also a vector field. At any position, the direction of the magnetic field is defined as the direction in which the north pole of a compass needle points.
A magnetic field is defined by the force that a charged particle experiences...
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Magnetic Field of a Solenoid01:18

Magnetic Field of a Solenoid

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A solenoid is a conducting wire coated with an insulating material, wound tightly in the form of a helical coil. The magnetic field due to a solenoid is the vector sum of the magnetic fields due to its individual turns. Therefore, for an ideal solenoid, the magnetic field within the solenoid is directly proportional to the number of turns per unit length and the current. Conversely, the magnetic field outside the solenoid is zero.
Consider a solenoid with 100 turns wrapped around a cylinder of...
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Magnetic Field Lines01:19

Magnetic Field Lines

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The representation of magnetic fields by magnetic field lines is very useful in visualizing the strength and direction of the magnetic field. Each of the magnetic field lines forms a closed loop. The field lines emerge from the north pole (N), loop around to the south pole (S), and continue through the bar magnet back to the north pole.
Magnetic field lines follow several hard-and-fast rules:
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Energy In A Magnetic Field01:24

Energy In A Magnetic Field

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If a magnetic field is sustained, there must be a current in a closed circuit or loop, implying some energy has been spent in creating the field. If this energy is not dissipated via the circuit's resistance, it is stored in the field.
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Magnetic Field Of A Current Loop01:16

Magnetic Field Of A Current Loop

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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 Field due to Moving Charges01:23

Magnetic Field due to Moving Charges

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A stationary charge creates and interacts with the electric field, while a moving charge creates a magnetic field.
Consider a point charge moving with a constant velocity. Like the electric field, the magnetic field at any point is directly proportional to the magnitude of the charge and inversely proportional to the square of the distance between the source point and the field point. However, unlike the electric field, the magnetic field is always perpendicular to the plane containing the line...
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Electric and Magnetic Field Devices for Stimulation of Biological Tissues
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Magnetic-field-induced localization in 2D topological insulators.

Pierre Delplace1, Jian Li, Markus Büttiker

  • 1Département de Physique Théorique, Université de Genève, CH-1211 Genève, Switzerland.

Physical Review Letters
|February 2, 2013
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Summary
This summary is machine-generated.

Localized helical edge states in quantum spin Hall insulators are achieved by breaking time-reversal symmetry with a magnetic field. Our model shows localization length depends on magnetic field strength, decreasing with B^{-2} at low fields and saturating at high fields.

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Area of Science:

  • Condensed Matter Physics
  • Materials Science
  • Quantum Mechanics

Background:

  • Helical edge states in quantum spin Hall insulators are crucial for spintronic applications.
  • Localization of these states is necessary for device functionality.
  • Time-reversal invariance must be broken to induce localization.

Purpose of the Study:

  • To develop a theoretical model for the localization of helical edge states.
  • To investigate the role of random magnetic fluxes in this localization process.
  • To determine the dependence of localization length on applied magnetic field.

Main Methods:

  • Development of a scattering theory model.
  • Analysis of helical edge state coupling to random magnetic fluxes.
  • Theoretical calculation of localization length as a function of magnetic field.

Main Results:

  • The localization length is inversely proportional to the square of a small magnetic field (B^{-2}).
  • The localization length saturates to a constant value at sufficiently large magnetic fields.
  • Specific estimations for HgTe/CdTe quantum wells are provided.

Conclusions:

  • Random magnetic fluxes provide a mechanism for localizing helical edge states.
  • The magnetic field dependence of localization length offers a tunable parameter for controlling edge state behavior.
  • The findings are relevant for designing spintronic devices based on quantum spin Hall insulators.