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Related Concept Videos

General State of Stress01:21

General State of Stress

274
The general state of stress within a material can be accurately depicted using a stress tensor. This tensor encapsulates the internal forces distributed within a material subjected to external forces or deformations.
Specifically, consider a tetrahedral element where one face, labeled XYZ, is perpendicular to the line OA, and the remaining faces align with the coordinate axes with point O as the origin. At any point, such as point O, the stress tensor can be used to determine the stress...
274
Transformation of Plane Stress01:18

Transformation of Plane Stress

326
Studying stress transformation is essential in understanding how stress components within a material, like a cube under plane stress, change with rotation. This change is analyzed by considering a prismatic element within the cube. As the element rotates, the stress components acting on it—both normal and shearing stresses—change in magnitude and orientation. This change is quantified using trigonometric functions of the rotation angle, relating the forces acting on the rotated element's...
326
Components of Stress01:23

Components of Stress

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Stress analysis under multiple loading conditions is intricate, necessitating a comprehensive grasp of normal and shearing stresses. Consider a small cube at point O, subjected to stress on all six faces, visible or not. Normal stress components σx, σy, σz act perpendicularly to the x, y, and z axes. Shearing stress components τxy and τxz are exerted on faces perpendicular to these axes.
Interestingly, the hidden cube faces also experience these stresses, equal and...
258
Stress: General Loading Conditions01:15

Stress: General Loading Conditions

360
To grasp the intricacy of real-world conditions where multiple loads are applied simultaneously to a structure, one might visualize a section passing through a specific point within a body, aligned parallel to the xy plane. This section is subjected to various forces, including original loads, normal forces, and shearing forces.
The shearing force, possessing potential directionality within the plane of the section, is simplified into two component forces running parallel to the x and y axes....
360
Moment of a Force: Scalar Formulation01:18

Moment of a Force: Scalar Formulation

805
The moment of a force, also known as torque, measures the ability of the force to create rotational motion in a body about an axis. It is a vector quantity, meaning it has both magnitude and direction. This concept is used extensively in engineering, physics, and mechanics.
Consider a simple example of a flywheel being rotated about a point, O, by applying a force to it. In this case, the moment arm is the perpendicular distance between the point O and the line of action of the force. The...
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Symmetry in Maxwell's Equations01:28

Symmetry in Maxwell's Equations

3.5K
Once the fields have been calculated using Maxwell's four equations, the Lorentz force equation gives the force that the fields exert on a charged particle moving with a certain velocity. The Lorentz force equation combines the force of the electric field and of the magnetic field on the moving charge. Maxwell's equations and the Lorentz force law together encompass all the laws of electricity and magnetism. The symmetry that Maxwell introduced into his mathematical framework may not be...
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Interrogating imaginary optical force by the complex Maxwell stress tensor theorem.

Jinwei Zeng1,2, Jian Wang3,4

  • 1Wuhan National Laboratory for Optoelectronics and School of Optical and Electronic Information, Huazhong University of Science and Technology, Wuhan, 430074, Hubei, China.

Light, Science & Applications
|January 10, 2023
PubMed
Summary
This summary is machine-generated.

A new theorem for the Maxwell stress tensor relates imaginary optical force and canonical momentum. This is key for achieving perfect optical force efficiency in nanoparticles.

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Area of Science:

  • Optics
  • Nanotechnology
  • Theoretical Physics

Background:

  • Optical forces are crucial for manipulating nanoparticles.
  • Understanding the efficiency of optical forces requires detailed theoretical frameworks.

Purpose of the Study:

  • To develop a complex Maxwell stress tensor theorem.
  • To establish relationships between optical force components and momentum.
  • To enable the optimization of optical force efficiency.

Main Methods:

  • Formulation of the complex Maxwell stress tensor theorem.
  • Analysis of the reactive strength of canonical momentum.
  • Derivation of relationships for total optical force.

Main Results:

  • The theorem successfully relates imaginary optical force to canonical momentum.
  • Quantification of the reactive strength of canonical momentum.
  • Identification of parameters essential for perfect optical force efficiency.

Conclusions:

  • The developed theorem provides a fundamental link between optical forces and momentum.
  • This framework is essential for designing systems with maximum optical force efficiency.
  • Advances in nanoparticle manipulation and optical trapping are anticipated.