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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...

Magnetic Field Lines

Magnetic Field Lines

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:

Magnetostatic Boundary Conditions

Magnetostatic Boundary Conditions

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...

Divergence and Curl of Magnetic Field

Divergence and Curl of Magnetic Field

The magnetic field due to a volume current distribution given by the Biot–Savart Law can be expressed as follows:

Vector Components in the Cartesian Coordinate System

Vector Components in the Cartesian Coordinate System

Vectors are usually described in terms of their components in a coordinate system. Even in everyday life, we naturally invoke the concept of orthogonal projections in a rectangular coordinate system. For example, if someone gives you directions for a particular location, you will be told to go a few km in a direction like east, west, north, or south, along with the angle in which you are supposed to move. In a rectangular (Cartesian) xy-coordinate system in a plane, a point in a plane is...

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...

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Related Experiment Video

Updated: Aug 15, 2025

High-speed Particle Image Velocimetry Near Surfaces

High-speed Particle Image Velocimetry Near Surfaces

Published on: June 24, 2013

Spatial correlated vortex arrays.

Zhangrong Mei, Yonghua Mao, Jixian Wang

|January 6, 2023

Summary

This summary is machine-generated.

Partially coherent sources with helical phase structures can generate spatial correlated vortex arrays. These vortex patterns in the far field offer adjustable dimensions and shapes, controlled by coherence and topological charge.

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Related Experiment Videos

Last Updated: Aug 15, 2025

High-speed Particle Image Velocimetry Near Surfaces

High-speed Particle Image Velocimetry Near Surfaces

Published on: June 24, 2013

Experimental Investigation of the Flow Structure over a Delta Wing Via Flow Visualization Methods

Experimental Investigation of the Flow Structure over a Delta Wing Via Flow Visualization Methods

Published on: April 23, 2018

Experimental Investigation of Secondary Flow Structures Downstream of a Model Type IV Stent Failure in a 180° Curved Artery Test Section

Experimental Investigation of Secondary Flow Structures Downstream of a Model Type IV Stent Failure in a 180° Curved Artery Test Section

Published on: July 19, 2016

Area of Science:

Optics and Photonics
Quantum Optics
Laser Physics

Background:

Spatial correlated vortex arrays can emerge from random sources with multiple helical phase structures within a single beam.
Partially coherent light sources are crucial for controlling light beam properties.

Purpose of the Study:

To introduce and analyze two novel types of partially coherent sources with symmetric helical phase structures (Cartesian and polar).
To investigate the characteristics of the radiated fields from these sources.
To explore the formation of spatial correlated vortex arrays in the far field.

Main Methods:

Theoretical modeling of partially coherent sources with specific helical phase structures.
Analysis of the far-field characteristics of the radiated optical beams.
Investigating the interplay between coherence properties and topological charge.

Main Results:

Demonstration of the formation of lattice-like vortex patterns in the far field.
The dimension and shape of these vortex patterns are tunable.
The joint regulation of coherence and topological charge dictates the observed far-field features.

Conclusions:

Partially coherent sources with tailored helical phase structures provide a versatile method for generating controllable spatial correlated vortex arrays.
The findings offer new possibilities for optical manipulation and information encoding using vortex beams.