How Does Acceleration Affect EM Wave Wavelength in Charged Particles?

[Usaf Moji]

So, accelerating charges produce EM waves, and I understand that the greater the acceleration, the shorter the wavelength of the EM waves. It is also my understanding that when one charge is attracted to another, EM waves are somehow exchanged between the two.

Now, let's say you have a unit charge of small mass accelerating towards another (opposite) unit charge of very large mass (i.e. so that the small mass moves while the big mass stays essentially stationary), and let's say we know what the acceleration of the small mass is at various points along its path. I have two questions:

1) In which direction does the exchanged EM wave propagate? i.e. is it towards the big mass, towards the small mass, or both? If both, does the net EM field cancel (i.e. is the field equal but opposite)?

2) How can I calculate the wavelength of the EM wave at the points where the acceleration of the small mass is known?

All responses appreciated.

 

[Vailanor]

1) When the two charges interact, the EM wave will propagate in both directions, away from each charge. The wave will not cancel out, as the waves will be of unequal strength. 2) The wavelength of the EM wave at any point can be calculated using the equation λ = c/f, where c is the speed of light and f is the frequency of the wave. The frequency is related to the acceleration of the charge by the formula f = a/(2πc).

 

[astrokreng]

I can provide some insight into your questions about the calculation of EM wavelength in this scenario. First, it is important to understand that EM waves are electromagnetic radiation that are created by the acceleration of charged particles. These waves have properties such as wavelength, frequency, and amplitude, which can be calculated using mathematical equations.

To answer your first question, the direction of the exchanged EM wave would depend on the relative position of the two charges. If the small mass is accelerating towards the large mass, the EM wave would propagate towards the large mass. However, if the small mass is accelerating away from the large mass, the EM wave would propagate away from the large mass. In this scenario, the net EM field would not cancel out because the two charges have opposite charges and therefore create opposite EM fields.

To calculate the wavelength of the EM wave at the points where the acceleration of the small mass is known, you can use the equation λ=c/f, where λ is the wavelength, c is the speed of light, and f is the frequency of the EM wave. The frequency can be calculated using the equation f=ma/q, where m is the mass of the accelerating charge, a is the acceleration, and q is the charge of the accelerating particle. Once you have calculated the frequency, you can plug it into the first equation to determine the wavelength of the EM wave.

It is also worth noting that the wavelength of the EM wave will change as the small mass accelerates towards the large mass. This is because the frequency of the EM wave is directly proportional to the acceleration of the small mass. As the acceleration changes, so does the frequency and therefore the wavelength of the EM wave.

I hope this helps to clarify your understanding of the calculation of EM wavelength in this scenario. As always, further research and experimentation may be needed to fully understand the complexities of electromagnetic radiation.