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Potential Due to a Magnetized Object

Potential Due to a Magnetized Object

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.
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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.
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Paramagnetism

Paramagnetism

Paramagnets are materials with unpaired electrons that possess a finite magnetic moment. In the absence of a magnetic field, these moments are randomly oriented, and thus the net moment is zero. Under an external field, a torque acting on the moments tends to align them along the field's direction. However, the random thermal motion of electrons produces a torque opposite to the external field and tries to disorient the moments. These two competing effects align only a few moments along the...

Magnetic Force

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In addition to the electric forces between electric charges, moving electric charges exert magnetic forces on each other. A magnetic field is created by a moving charge or a group of moving charges known as the electric current. A magnetic force is experienced by a second current or moving charge in response to this magnetic field. Fundamentally, interactions between moving electrons in the atoms of two bodies produce magnetic forces between them.
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Magnetic Field due to Moving Charges

Magnetic Field due to Moving Charges

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...

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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Measuring Magnetically-Tuned Ferroelectric Polarization in Liquid Crystals

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Paraelectricity in magnetized massless QED.

Efrain J Ferrer¹, Vivian de la Incera, Angel Sanchez

¹Department of Physics, University of Texas at El Paso, 500 W. University Avenue, El Paso, Texas 79968, USA.

Physical Review Letters

|August 27, 2011

Summary

Strong paraelectricity is observed in massless quantum electrodynamics (QED) under a magnetic field. This effect, linked to electric dipole moments, can probe magnetic catalysis of chiral symmetry breaking.

Area of Science:

* Quantum electrodynamics (QED)
* Condensed matter physics
* High-energy physics

Background:

* Massless quantum electrodynamics (QED) is a fundamental theory in particle physics.
* Chiral symmetry breaking is a key phenomenon in quantum field theories.
* Magnetic fields can influence the behavior of quantum fields.

Purpose of the Study:

* To investigate the phenomenon of paraelectricity in massless QED with a magnetic field.
* To explore the role of magnetic catalysis in chiral symmetry breaking.
* To identify potential experimental probes for these phenomena.

Main Methods:

* Theoretical analysis of massless QED in a magnetic field.
* Examination of the infrared region and lowest Landau level effects.

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* Investigation of dynamical mass generation and anomalous magnetic moment.

* Calculation of electric susceptibility and its dependence on the fine-structure constant.

Main Results:

* A chiral-symmetry-broken phase exhibiting strong paraelectricity was identified.
* Large anisotropic electric susceptibility was observed in the infrared region.
* Dynamical mass and anomalous magnetic moment were generated via magnetic catalysis.
* The nonperturbative nature of the effect was confirmed through dependence on the fine-structure constant.
* Strong paraelectricity was linked to electric dipole moments in the chiral condensate.

Conclusions:

* The chiral-symmetry-broken phase of massless QED in a magnetic field shows significant paraelectricity.
* Magnetic catalysis is a key mechanism driving these effects.
* The observed electric susceptibility can serve as a probe for magnetic catalysis of chiral symmetry breaking in physical systems.