What is the longest wave-lenght of a photon particle in the nature and can it be longer?
There is no simply defined upper limit for the wavelength of light. I suppose one mught argue the length of the universe is a practical limit.
Why would the length of the universe be a limit? I am sure there are radio waves in my room right with wave lengths much bigger than my room. Am I missing something?
Also, in the cases of black holes and places in the universe too far away for us to view, aren't these red shifted into infinitely long wavelengths?
In theory there is no longest wavelength. As a practical matter, the length of the universe may be the longest in existence.
Your question is fundamentally flawed, I'm afraid because it's harder than that, in fact. Photons do not 'have a wavelength'. They are not classical particles but quantum entities. What you 'are allowed' to say is that the EM wave they are associated with, has a wavelength. There is no fundamental maximum for wavelength but EM at very low frequencies has very low energy photons and becomes harder and harder to detect because you just can't make receiving equipment that can 'extract' the signal out of the space it's travelling through. (The antenna would have to be several thousand km long to intercept a 50Hz signal)
In addition they would be very hard to generate.
why can battery-operated amplifiers and oscilloscopes pick up the mains noise (50 Hz in Europe) when you touch the input cable?
Not at all hard to generate - all you need to do is to move electrons around with a low frequency electric field. The problem is to generate and radiate enough power at that frequency to be detected remotely in the presence of the ubiquitous noise. All problems in life come down to Signal To Noise Ratio.
Because the em wave is not a 'launched wave, travelling free through space but guided on the wire. To launch a significant level of signal into space. from a circuit, it has to be 'matched', which requires a radiating structure that's not much smaller than one wavelength. A wire / person link is a totally different situation.
EM theory imposes no upper limit.
It will take an infinite time to generate a wave of infinite wavelength.
What on earth (or in the universe) do you have in mind with this question?
The other variant of my question would be what is the smallest frequency of an EM wave
a) in general ?
b) detetected ?
Same answers. The smallest frequency is zero (as far as EM theory is concerned) and it would take an infinite time to detect it.
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