Regarding applicability of Maxwell's equations on microscopic structures.

In summary, it depends on the energy scales and temperatures involved. You typically need very well engineered environments to see quantum effects in macroscopic objects.
  • #1
otaKu
27
2
So from what I seem to understand up until now, Maxwell's equations usually work while assuming that the fields are continuous and smooth instead of the actual complexity at the atomic scale. However, as we move more and more towards the microscopic realm, a point comes when we cannot ignore this miniscule field variations and we need to change our approach. What exactly is that length scale? Is there a specific term for it? What changes do we need to apply to the macroscopic equations to make them work at this regime? I apologise if some of the questions in the thread don't make any sense, I'm rather new to Electrodynamics, especially at the microscopic level and I was wondering about the length scale where things will get troublesome. Thanks.
 
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  • #2
There is no specific length scale for this. The ME always work, even for extremely small objects.
That said, the ME are -sort of- classical equations and there is e.g. no concept of a photon. Hence, to describe quantum effects you need a formalism known as quantum electrodynamics (QED) which is what you would e.g. use in quantum optics.
However, QED effects can -and frequently are- seen in macroscopic objects. A good example would the microwave resonators used in cavity-QED experiments which are many centimeters in size.
What determines whether you see quantum effects in an experiment is not the physical size of the objects, it is rather the energy scales (and temperatures) involved; typically you need very well engineered environments.
 
  • #3
f95toli said:
There is no specific length scale for this. The ME always work, even for extremely small objects.
That said, the ME are -sort of- classical equations and there is e.g. no concept of a photon. Hence, to describe quantum effects you need a formalism known as quantum electrodynamics (QED) which is what you would e.g. use in quantum optics.
However, QED effects can -and frequently are- seen in macroscopic objects. A good example would the microwave resonators used in cavity-QED experiments which are many centimeters in size.
What determines whether you see quantum effects in an experiment is not the physical size of the objects, it is rather the energy scales (and temperatures) involved; typically you need very well engineered environments.
So is it safe for me to assume that I probably won't have to deal with quantum electrodynamics if I am dealing with conventional electronic devices such as LEDs and HEMTs?
 

1. What are Maxwell's equations and how are they used in science?

Maxwell's equations are a set of four fundamental equations in electromagnetism that describe the relationships between electric and magnetic fields. They are used extensively in many areas of science to understand and predict the behavior of electromagnetic phenomena.

2. Can Maxwell's equations be applied to microscopic structures?

Yes, Maxwell's equations can be applied to microscopic structures. However, at the microscopic level, the equations may need to be modified to account for quantum effects.

3. What are some examples of microscopic structures where Maxwell's equations are applicable?

Maxwell's equations can be used to study the behavior of electromagnetic fields in materials such as atoms, molecules, and nanoparticles. They are also applicable to the study of electromagnetic waves in vacuum, such as light.

4. Are there any limitations to the applicability of Maxwell's equations on microscopic structures?

Yes, there are limitations to the applicability of Maxwell's equations on microscopic structures. These equations were developed for macroscopic systems and may not accurately describe the behavior of electromagnetic fields at the atomic scale. Additionally, they do not take into account quantum effects which may be significant at the microscopic level.

5. How do scientists account for the limitations of Maxwell's equations on microscopic structures?

To account for the limitations of Maxwell's equations on microscopic structures, scientists may use other theories, such as quantum electrodynamics, which take into account both electromagnetic and quantum effects. They may also use computational methods to simulate and study the behavior of electromagnetic fields at the microscopic level.

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