Momentum Of Electromagnetic Field Research Articles

Electromagnetic momentum in static fields and the Abraham–Minkowski controversy

Using a simple but quantitative example and requiring the conservation of total angular momentum, we have shown that Minkowski’s D×B/4πc cannot be accepted and that there is no inconsistency to accept Abraham’s E×H/4πc, as the general expression for the electromagnetic field momentum density in a stationary nonmagnetic medium.

Energy and Momentum in Electromagnetic Field for Charged Particles Moving with Constant Velocities

The relationship between the Lorentz force and the energy and momentum in the electromagnetic field is illustrated with some striking examples for systems of point charges moving at constant velocities. For these systems, the kinetic energy and momentum associated with particle mass do not change, while the external forces which balance the interparticle Lorentz forces give exactly the rate of change of energy, momentum, and angular momentum in the electromagnetic fields. Calculations along roughly these lines have been performed to order c−2 by Page and Adams. The present evaluations are noteworthy in that they are exact, and also in that the necessary electromagnetic field integrals over all space have been reduced to delta function integrations. In the limiting charge distributions involving infinite energy density at spatial infinity, the connection of the Lorentz force with electromagnetic energy and momentum is lost.

Some new results concerning the radiation pressure on the plasma-vacuum boundary

The radiation pressure is studied by means of the tensor of time-averaged stresses arising in plasma under the effect of a magnetostatic and an oscillating field. It is proved that the radiation pressure need not arise on the plasma-vacuum boundary even if the electromagnetic wave falling from vacuum is reflected substantially. The density of momentum flux defined by the stress tensor is compared with the density of the electromagnetic field momentum.

Linearity of Electromagnetic Field Energy and Momentum

It is shown that static electromagnetic fields have nonlinear energy and momentum due to the interaction between sources, while the apparent nonlinearity in energy and momentum densities of electromagnetic waves generated by noninteracting sources merely reflects a hitherto unsuspected degree of freedom of the energy-momentum four-tensor Tμν, which can undergo the following transformation without changing its physical meaning: Tμν→ T′μν = Tμν + Kμν, where the symmetric four-tensor Kμν is arbitrary except for the constraint δνKμν = 0. The force density fμ = δνTμν is preserved in this transformation. The implication of this transformation on fields everywhere satisfying the homogeneous wave equations is discussed.

Aharonov-Bohm Paradox

It is remarked that even in the classical limit the behavior of a charged particle interacting with a stationary current distribution exhibits paradoxical behavior. This comes from the inequality of action and reaction forces. It is shown that the vector potential term appearing in the expression for the canonical momenta represents the electromagnetic field momentum.