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cuallito
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Obviously at point charges, but where along boundaries? Would they theoretically occur in superconductors since they can carry infinite current (J -> infinity)?
In practice the resistance of the conductor allows the wave to slightly penetrate. I think the problem in general is that the wavelength is finite and so there is no discontinuity at the microscopic level. For instance, total internal reflection in a prism is accompanied by reactive fields in the air behind the reflecting surface.vanhees71 said:One example are jumps of the normal component of the electric field along conducting surfaces, carrying a surface charge density. The jump is ##E_{n1}-E_{n2}=\sigma/\epsilon_0##.
Superconductors must be treated differently. They cannot be described by simply making the resistance 0 (or the electric conductivity to ##\infty##). A nice effective theory is the London theory:
https://en.wikipedia.org/wiki/London_equations
Electromagnetic field discontinuities refer to abrupt changes or breaks in the electromagnetic field, which is a physical field that is created by electrically charged particles and is responsible for the interaction between charged particles.
Electromagnetic field discontinuities can occur at boundaries between different materials, at sharp corners or edges, or in regions where there is a change in the electric or magnetic field intensity or direction.
Electromagnetic field discontinuities occur due to the discontinuity in the physical properties of the materials or the geometry of the field. These discontinuities can arise from the presence of different materials, changes in the shape or size of objects, or the presence of sources or sinks of electric or magnetic fields.
The effects of electromagnetic field discontinuities can vary depending on the specific situation. In some cases, they can cause reflections, refractions, or diffractions of electromagnetic waves, which can affect the propagation of the waves. They can also lead to the accumulation of charges or the generation of electric or magnetic fields.
Electromagnetic field discontinuities are studied and analyzed using mathematical models and simulations. These models take into account the physical properties of the materials and the geometry of the field to predict the behavior of the electromagnetic field at the discontinuity. Experimental techniques, such as measuring the electric and magnetic fields, can also be used to study electromagnetic field discontinuities.