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Related Concept Videos

Motion Of A Charged Particle In A Magnetic Field01:22

Motion Of A Charged Particle In A Magnetic Field

A charged particle experiences a force when moving through a magnetic field. Consider the field to be uniform and the charged particle to move perpendicular to it. If the field is in a vacuum, the magnetic field is the dominant factor determining the motion. Since the magnetic force is perpendicular to the direction of motion, a charged particle follows a curved path. The particle continues to follow this curved path until it forms a complete circle. Another way to look at this is that the...
Electric Field of a Charged Disk01:23

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The simplest case of a surface charge distribution is the uniformly charged disk. Calculating its electric field also helps us calculate the electric field of a large plane of charge.
The system's symmetry is in the cylindrical directions across the plane of the charge. As a result, the electric fields created by various surface charge elements nullify each other in the direction parallel to the surface. Thereby, the resulting electric field is perpendicular to the plane. Since the disk is...
Magnetic Field due to Moving Charges01:23

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...
Continuous Charge Distributions01:17

Continuous Charge Distributions

Imagine a bucket of water. It contains many molecules, of the order of 1026 molecules. Thus, although it contains discrete elements (molecules) at the microscopic level, macroscopically, it can be considered continuous. Small volume elements of water, infinitesimal compared to the bulk of the bucket's volume, still contain many molecules. Under this framework, quantized matter is approximated as continuous for practical purposes.
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Energy Associated With a Charge Distribution01:21

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Gauss's law states that the electric flux through any closed surface equals the net charge enclosed within the surface. This law is beneficial for determining the expressions for the electric field for a particular charge distribution if the electric flux is known.
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Finite Element Modelling of a Cellular Electric Microenvironment
08:23

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Published on: May 18, 2021

Dynamics of a charged particle.

Fritz Rohrlich1

  • 1Syracuse University, Syracuse, New York 13244-1130, USA. rohrlich@syr.edu

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|June 4, 2008
PubMed
Summary

This study derives physically correct equations of motion for classical charged particles by refining the Lorentz-Abraham-Dirac equations. A key condition ensures finite-sized charges behave as point particles, resolving known physical inconsistencies.

Area of Science:

  • Classical Electrodynamics
  • Theoretical Physics
  • Particle Physics

Background:

  • The Lorentz-Abraham-Dirac (LAD) equations describe the motion of classical charged particles but contain physical inconsistencies.
  • Classical charged particles cannot be true point particles due to Coulomb field divergences.
  • Existing models of finite radius charge distributions do not yield differential equations of motion.

Purpose of the Study:

  • To derive physically correct equations of motion for classical charged particles.
  • To address the limitations of the LAD equations and the concept of point particles.
  • To reconcile finite charge distributions with tractable equations of motion.

Main Methods:

  • Physical arguments are used to derive corrected equations of motion from the LAD equations.

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  • A fundamental condition is imposed on the external force to handle the particle's finite charge distribution.
  • The nonrelativistic case is discussed first, followed by the relativistic case for clarity.

    • Main Results:

    • Physically correct equations of motion for classical charged particles are derived.
    • A condition is established for finite-sized charge distributions to be treated as point charges by external forces.
    • The findings align with established results in theoretical physics, such as those by H. Spohn.

    Conclusions:

    • The derivation provides a physically sound framework for describing the motion of classical charged particles.
    • The imposed condition on external forces is crucial for resolving theoretical challenges related to charge distribution.
    • This work offers a consistent approach to classical charged particle dynamics, applicable in both nonrelativistic and relativistic regimes.