# Where do discontinuities in the electromagnetic field occur?

• I
• cuallito
In summary, the conversation discusses the occurrence of point charges along boundaries and their theoretical existence in superconductors, which can carry infinite current. It is noted that jumps in the normal component of the electric field can occur along conducting surfaces, carrying surface charge density. However, superconductors must be treated differently as they cannot be described by simply making the resistance zero. The London theory is mentioned as an effective theory for superconductors. The conversation also touches on the issue of finite wavelengths and the resulting lack of discontinuity at the microscopic level.

#### cuallito

Obviously at point charges, but where along boundaries? Would they theoretically occur in superconductors since they can carry infinite current (J -> infinity)?

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

PeroK
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
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