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Related Concept Videos

Gauss's Law: Cylindrical Symmetry01:20

Gauss's Law: Cylindrical Symmetry

A charge distribution has cylindrical symmetry if the charge density depends only upon the distance from the axis of the cylinder and does not vary along the axis or with the direction about the axis. In other words, if a system varies if it is rotated around the axis or shifted along the axis, it does not have cylindrical symmetry. In real systems, we do not have infinite cylinders; however, if the cylindrical object is considerably longer than the radius from it that we are interested in,...
Interference and Diffraction02:18

Interference and Diffraction

Interference is a characteristic phenomenon exhibited by waves. When two electromagnetic waves interact with their peaks and troughs coinciding, a resulting wave with enhanced amplitude is produced. This is known as constructive interference. In this case, the two waves interacting are in phase with each other.
Potential Due to a Polarized Object01:29

Potential Due to a Polarized Object

A neutral atom consists of a positively charged nucleus surrounded by a negatively charged electron cloud. When placed in an external electric field, the external electric force pulls the electrons and nucleus apart, opposite to the intrinsic attraction between the nucleus and the electrons. The opposing forces balance each other with a slight shift between the center of masses of the nucleus and the electron cloud, resulting in a polarized atom. On the other hand, a few molecules, like water,...
Gauss's Law: Spherical Symmetry01:26

Gauss's Law: Spherical Symmetry

A charge distribution has spherical symmetry if the density of charge depends only on the distance from a point in space and not on the direction. In other words, if the system is rotated, it doesn't look different. For instance, if a sphere of radius R is uniformly charged with charge density ρ0, then the distribution has spherical symmetry. On the other hand, if a sphere of radius R is charged so that the top half of the sphere has a uniform charge density ρ1 and the bottom half has a uniform...
Divergence and Curl of Electric Field01:25

Divergence and Curl of Electric Field

The divergence of a vector is a measure of how much the vector spreads out (diverges) from a point. For example, an electric field vector diverges from the positive charge and converges at the negative charge. The divergence of an electric field is derived using Gauss's law and is equal to the charge density divided by the permittivity of space. Mathematically, it is expressed as
Symmetry in Maxwell's Equations01:28

Symmetry in Maxwell's Equations

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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Related Experiment Video

Updated: Jun 15, 2026

Fabrication and Operation of a Nano-Optical Conveyor Belt
11:10

Fabrication and Operation of a Nano-Optical Conveyor Belt

Published on: August 26, 2015

Optical force on a cylindrical cloak under arbitrary wave illumination.

Hongsheng Chen1, Baile Zhang, Brandon A Kemp

  • 1The Electromagnetics Academy at Zhejiang University, Zhejiang University, Hangzhou 310027, China. hansomchen@zju.edu.cn

Optics Letters
|March 3, 2010
PubMed
Summary

This study analyzes optical forces within a cylindrical cloak. It reveals balanced forces and zero net momentum transfer from incident waves, despite internal ray trajectory changes.

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Area of Science:

  • Electromagnetism
  • Metamaterials
  • Optical Physics

Background:

  • Cylindrical cloaks are designed to guide electromagnetic waves around an object.
  • Understanding the internal forces within cloaks is crucial for their practical application.
  • Previous studies have focused on wave propagation, but optical force distribution requires further investigation.

Purpose of the Study:

  • To present the optical force distribution within a cylindrical cloak under arbitrary incident waves.
  • To analyze the interaction between induced surface currents, polarization charges, and incident waves.
  • To determine the net momentum transfer to the cloak.

Main Methods:

  • Theoretical analysis of optical forces.
  • Calculation of induced surface currents and polarization charges.
  • Application of Lorentz force principles to ray trajectories.

Main Results:

  • Opposite radiation pressures on the inner surface of the cloak due to surface currents and polarization charges.
  • Lorentz force can alter ray trajectories or reflect rays, potentially reducing carried energy.
  • The optical forces within the cloak are found to be symmetric and balanced.

Conclusions:

  • The total momentum transfer from incident waves to the cylindrical cloak is zero.
  • Despite internal force interactions, the cloak as a whole experiences no net momentum change.
  • The findings contribute to the fundamental understanding of wave-matter interactions in cloaking devices.