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Related Concept Videos

Magnetic Fields01:27

Magnetic Fields

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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 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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Electromagnetic Fields01:30

Electromagnetic Fields

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Electric fields generated by static charges, often referred to as electrostatic fields, are characteristically different from electric fields created by time-varying magnetic fields. While the former is a conservative field, implying that no net work is done on a test charge if it goes around in a complete loop in the field, the latter is, by definition, not a conservative field; net work is done, and it is proportional to the rate of change of magnetic flux.
However, the observation of...
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Potential Due to a Magnetized Object01:24

Potential Due to a Magnetized Object

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Magnetic dipoles in magnetic materials are aligned when placed under an external magnetic field. For paramagnets and ferromagnets, dipole alignment occurs in the direction of the magnetic field. However, the dipoles align opposite to the field in the case of diamagnets. This state of magnetic polarization due to the external field is called magnetization. Magnetization is defined as the dipole moment per unit volume. It plays a similar role to polarization in electrostatics.
The vector...
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Magnetostatic Boundary Conditions01:28

Magnetostatic Boundary Conditions

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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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Magnetic Vector Potential01:15

Magnetic Vector Potential

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In electrostatics, the electric field can be written as the negative gradient of the potential. In magnetostatics, the zero divergence of the magnetic field ensures that the magnetic field can be expressed as the curl of a vector potential. This potential is known as the magnetic vector potential.
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Scanning SQUID Study of Vortex Manipulation by Local Contact
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Nonlocal pseudopotentials and magnetic fields.

Chris J Pickard1, Francesco Mauri

  • 1TCM Group, Cavendish Laboratory, Madingley Road, Cambridge CB3 0HE, United Kingdom.

Physical Review Letters
|November 13, 2003
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Summary
This summary is machine-generated.

This study presents a method for electron-magnetic field coupling in pseudopotential calculations. It enables accurate magnetic susceptibility computations for molecules using density functional theory.

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Area of Science:

  • Computational Physics
  • Quantum Chemistry
  • Materials Science

Background:

  • Accurate electronic structure calculations are crucial for understanding material properties.
  • Describing electron-electron interactions in magnetic fields requires robust theoretical frameworks.
  • Norm-conserving pseudopotential approximations simplify calculations but need careful implementation for magnetic fields.

Purpose of the Study:

  • To develop and validate a method for incorporating nonuniform magnetic fields into norm-conserving pseudopotential calculations.
  • To enable reliable computation of magnetic properties, such as magnetic susceptibility, for molecules.
  • To provide a computationally efficient approach for electronic structure studies involving magnetic fields.

Main Methods:

  • Derivation of electron-nonuniform magnetic field coupling within the norm-conserving pseudopotential approximation.
  • Application of the method to calculate molecular magnetic susceptibility using density functional theory (DFT) and the local density approximation.
  • Comparison of results with all-electron DFT calculations and other pseudopotential formalisms.

Main Results:

  • A validated method for describing electron coupling to smooth, nonuniform magnetic fields in pseudopotential calculations.
  • Accurate calculation of magnetic susceptibility for molecules using the developed approach.
  • Demonstration of the method's reliability through comparison with established high-quality computational results.

Conclusions:

  • The proposed method effectively extends the norm-conserving pseudopotential approximation to include magnetic field effects.
  • This approach offers a computationally viable route for studying magnetic properties of molecules and materials.
  • The findings contribute to advancing electronic structure calculations in the presence of magnetic fields.