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The Abraham–Lorentz force is the source of the radiation resistance of a radio antenna radiating radio waves. There are pathological solutions of the Abraham–Lorentz–Dirac equation in which a particle accelerates in advance of the application of a force, so-called pre-acceleration solutions.
It arises from the observation that accelerating non-relativistic particles with associated magnetic moment emit radiation. The Abraham–Lorentz force is the average force that an accelerating charged particle feels in the recoil from the emission of radiation. The introduction of quantum effects leads one to quantum electrodynamics.
By combining the Lorentz force law above with the definition of electric current, the following equation results, in the case of a straight stationary wire in a homogeneous field: [30] =, where ℓ is a vector whose magnitude is the length of the wire, and whose direction is along the wire, aligned with the direction of the conventional current I.
The radiation must exert an additional force on the charged particle. This force is known as Abraham-Lorentz force while its non-relativistic limit is known as the Lorentz self-force and relativistic forms are known as Lorentz-Dirac force or Abraham-Lorentz-Dirac force. The radiation reaction phenomenon is one of the key problems and ...
[13] [14] [2] This is called the Abraham–Lorentz force. The recoil force is in a direction opposite to the electric field in the antenna accelerating the electron, reducing the average velocity of the electrons for a given driving voltage, so it acts as a resistance opposing the current.
Thus, the Newtonian equation for the particle (=) must contain a dissipative force (damping term), which takes into account this energy loss. In the causal interpretation of electromagnetism, Hendrik Lorentz and Max Abraham proposed that such a force, later called Abraham–Lorentz force , is due to the retarded self-interaction of the particle ...
Continuous charge distribution. The volume charge density ρ is the amount of charge per unit volume (cube), surface charge density σ is amount per unit surface area (circle) with outward unit normal n̂, d is the dipole moment between two point charges, the volume density of these is the polarization density P.
Figure 3. Predictions of speed dependence of transverse electromagnetic mass according to the theories of Abraham, Lorentz, and Bucherer. In 1902, Max Abraham published a theory based on the assumption that the electron was a rigid, perfect sphere, with its charge being distributed evenly on its surface. As explained above, he introduced the so ...