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Is it true, what he's saying from 04:28 to 04:56 ? I have my doubts, but I thought I'd better ask here.
Abstract said:Electromagnetic fields carry energy, momentum, and angular momentum. The momentum density, ##\epsilon_0 (\mathbf{E} \times \mathbf{B})##, accounts (among other things) for the pressure of light. But even static fields can carry momentum, and this would appear to contradict a general theorem that the total momentum of a closed system is zero if its center of energy is at rest. In such cases, there must be some other (nonelectromagnetic) momenta that cancel the field momentum. What is the nature of this “hidden momentum” and what happens to it when the electromagnetic fields are turned off?
clem said:I just want to repeat again
Obviously we have some misunderstanding here. The correct Ohm's Law isclem said:Your lengthy post about things I hadn't brought up indicates that we are talking at cross purposes.
For now, I just want to repeat again that keeping ##{\bf j}## constant while ##{\bf\gamma E}## varies contradicts
##{\bf j=\gamma\sigma E.}##
Wikipedia: the circulating flow of energy contains an angular momentum.[14] This is the cause of the magnetic component of the Lorentz force which occurs when the capacitor is discharged. During discharge, the angular momentum contained in the energy flow is depleted as it is transferred to the charges of the discharge current crossing the magnetic field.
vanhees71 said:To understand this well-known example ... you have to treat it relativistically.
vanhees71 said:Sure, a changing ##\vec{E} \times \vec{B}## means there's change in energy flow/momentum density with time and this means some net force is acting on the system.
Momentum from static E and H fields is a concept in physics that describes the transfer of momentum from electromagnetic fields that are not changing over time. This means that the fields are not producing any waves or radiation, but are instead stationary.
Momentum from static E and H fields is different from other forms of momentum because it is not associated with the motion of particles or objects. Instead, it is related to the energy and momentum of electromagnetic fields themselves.
Momentum from static E and H fields plays a crucial role in understanding the behavior of electromagnetic fields and their interactions with matter. It also has practical applications in technologies such as particle accelerators and electromagnetic propulsion systems.
Momentum from static E and H fields can be calculated using the Poynting vector, which describes the direction and magnitude of energy flow in an electromagnetic field. The momentum is then calculated by dividing the energy by the speed of light.
Yes, momentum from static E and H fields can be observed in real life through experiments and observations of electromagnetic fields. It is also used in practical applications such as the manipulation of particles in particle accelerators and the propulsion of spacecraft using electromagnetic fields.