EM field and wave interactions of a point charge

In summary, when one point charge is moved, the electromagnetic field changes its appearance at the new location. This change in appearance propagates at the speed of light and constitutes an EM wave.
  • #1
mishima
556
34
I've been thinking of 2 point charges separated by some distance in static equilibrium. When one charge is moved from rest, the EM field would change the way it looks at the location of the other point charge. This "changing in the looks" of the EM field as I understand propagates from the first charge at the speed of light and constitutes an EM wave. This is easy to see using a computer simulation that allows dragging charges around. When the change in the EM field reaches the other point charge it accelerates, trying to restore equilibrium.

So, I know about cases where an excited atom returns to its ground state and how to calculate the frequency and wavelength of the emitted photon. I'm wondering how I might do that with the somewhat unreal situation above. Could I just consider the work done on the second charge to be equal to the light's energy, then divide by Planck's constant to get frequency (if both charges had charge e)? Thanks.
 
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  • #2
The nature of the light will depend on how the charges move. In such general situation as you described, the motion would be most probably aperiodic, so the light will move in all directions in a complicated way. One cannot assign frequency to it in such situation (one can resolve it into Fourier components, but the result would be complicated as well.)

Frequency is a quantity which refers to periodic wave, like sine wave. In order to get such wave, the charges have to move periodically - in circles in synchrotron, or around each other, like in excited state of hydrogen atom, or oscillate rectilinearly as in antenna.
 
  • #3
Thanks, I never thought of it that way.
 
  • #4
No problem. From your post, it seems you learned bit about quanta. The Planck constant and the connection between the energy and frequency is important, but rather subtle and not entirely clear, so I recommend to learn bit about the classical theory of light (wave optics/electrodynamics ) which is quite clear and natural, and only then move on to learn about the quantum theory.
 
  • #5


I would first like to commend you on your curiosity and exploration of electromagnetic fields and wave interactions. Your understanding of the propagation of EM waves and their effects on charged particles is accurate.

In terms of calculating the frequency and wavelength of the emitted EM wave in your scenario, it is important to note that the movement of the charges would not just result in a single frequency or wavelength. The EM wave emitted would actually contain a range of frequencies and wavelengths, depending on the specific motion and acceleration of the charges.

To accurately calculate the frequency and wavelength of the emitted EM wave, you would need to consider the specifics of the motion and acceleration of the charges, as well as factors such as the distance between the two charges, their masses, and their charges. This would require a more complex mathematical approach, using equations such as Maxwell's equations and the Lorentz force law.

Alternatively, you could also use the work done on the second charge as a starting point, but this would only give you an estimate of the frequency and wavelength of the emitted EM wave. It would not take into account the specific details of the motion and acceleration of the charges.

In conclusion, while your approach is a good starting point, it is important to consider all the relevant factors and use more advanced mathematical methods to accurately calculate the frequency and wavelength of the emitted EM wave in your scenario.
 

1. What is an EM field?

An electromagnetic (EM) field is a physical field produced by electrically charged objects. It consists of electric and magnetic components that oscillate at right angles to each other and travel through space at the speed of light.

2. How does a point charge interact with an EM field?

A point charge is a theoretical concept used in physics to represent a single, isolated electric charge. When a point charge interacts with an EM field, it experiences a force due to the electric and magnetic fields. This force is known as the Lorentz force and is given by the equation F = q(E + v x B), where q is the charge, E is the electric field, v is the velocity of the charge, and B is the magnetic field.

3. What are the properties of an EM wave?

An EM wave has several properties, including wavelength, frequency, amplitude, and velocity. Wavelength is the distance between two peaks or troughs of the wave, frequency is the number of oscillations per second, amplitude is the maximum displacement of the electric and magnetic fields, and velocity is the speed at which the wave travels through space.

4. How does an EM wave interact with a point charge?

When an EM wave encounters a point charge, it induces a force on the charge due to the oscillating electric and magnetic fields of the wave. This force causes the charge to accelerate and emit its own EM waves, creating a feedback loop between the charge and the wave.

5. What are some applications of understanding EM field and wave interactions of a point charge?

Understanding EM field and wave interactions of a point charge is crucial in many areas of science and technology. It is used in the design and operation of electronic devices, such as antennas and circuitry. It also plays a significant role in fields like telecommunications, radar technology, and medical imaging. Additionally, understanding these interactions is essential in studying and explaining fundamental physical phenomena, such as light and electricity.

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