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Magnetic Vector Potential

Magnetic Vector Potential

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.
Consider an ideal solenoid with n turns per unit length and radius R. If I is the current through the solenoid, the magnetic field inside the solenoid is expressed as the product of vacuum...

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.
The vector...

Magnetic Fields

Magnetic Fields

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...

π Electron Effects on Chemical Shift: Overview

π Electron Effects on Chemical Shift: Overview

An applied magnetic field causes loosely bound π-electrons in organic molecules to circulate, producing a local or induced diamagnetic field over a large spatial volume. As the molecules tumble in solution, the field generated by π-electrons in spherical substituents results in a zero net field. However, the net field generated by π-electrons in non-spherical substituents is not zero. The effect of this induced field depends on the orientation of the molecule with respect to B0, resulting in...

Electrostatic Boundary Conditions in Dielectrics

Electrostatic Boundary Conditions in Dielectrics

When an electric field passes from one homogeneous medium to another, crossing the boundary between the two mediums imparts a discontinuity in the electric field. This results in electrostatic boundary conditions that depend on the type of mediums the field propagates through.
Consider a case where both the mediums across a boundary are two different dielectric materials. Recall that the electric field and electric displacement are proportional and related through the material's permittivity.

Motional Emf

Motional Emf

Magnetic flux depends on three factors: the strength of the magnetic field, the area through which the field lines pass, and the field's orientation with respect to the surface area. If any of these quantities vary, a corresponding variation in magnetic flux occurs. If the area through which the magnetic field lines are passing changes, then the magnetic flux also changes. This change in the area can be of two types: the flux through the rectangular loop increases as it moves into the magnetic...

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Related Experiment Video

Updated: May 30, 2026

Advanced Experimental Methods for Low-temperature Magnetotransport Measurement of Novel Materials

Advanced Experimental Methods for Low-temperature Magnetotransport Measurement of Novel Materials

Published on: January 21, 2016

Electron optics with magnetic vector potential barriers in graphene.

Sankalpa Ghosh¹, Manish Sharma

¹Department of Physics, Indian Institute of Technology, Delhi, New Delhi-110016, India.

Journal of Physics. Condensed Matter : an Institute of Physics Journal

|August 11, 2011

Summary

Electron transport in graphene is analyzed with magnetic barriers, revealing unusual asymmetric transmission. Periodic barriers act as Bragg reflectors for resonant cavities and band structure analysis.

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Advanced Experimental Methods for Low-temperature Magnetotransport Measurement of Novel Materials

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Fabrication of Gate-tunable Graphene Devices for Scanning Tunneling Microscopy Studies with Coulomb Impurities

Fabrication of Gate-tunable Graphene Devices for Scanning Tunneling Microscopy Studies with Coulomb Impurities

Published on: July 24, 2015

Area of Science:

Condensed matter physics
Materials science
Nanotechnology

Background:

Graphene exhibits unique electronic properties due to its 2D structure.
Electron transport in graphene can be modulated by magnetic fields.
Understanding electron behavior at interfaces is crucial for device applications.

Purpose of the Study:

To investigate electron transport in graphene influenced by magnetic barriers.
To explore the effects of barrier arrangement on transmission symmetry.
To analyze the potential of periodic barriers as Bragg reflectors and in resonant cavities.

Main Methods:

Theoretical analysis of electron transport.
Modeling of delta-function-like magnetic barriers.
Application of transfer matrix formalism.
Calculation of Bragg reflector reflectivity.
Analysis of band structure for periodic potentials.

Main Results:

A single magnetic barrier induces non-specular refraction and asymmetric transmission.
Symmetry in transmission is restored with pairs of opposing barriers.
Periodic barrier arrangements function as effective Bragg reflectors.
Calculated reflectivity using transfer matrix formalism.
Associated band structures for infinite periodic structures were analyzed.

Conclusions:

Magnetic barriers offer a novel way to control electron transport in graphene.
Periodic magnetic barriers can be utilized for creating optical-like elements (Bragg reflectors, resonant cavities) in graphene.
The findings contribute to the understanding of electron dynamics in engineered graphene nanostructures.