Finite speed of signal transmission and conservation laws

[keithkras]

Hi all,
This is my first post, so please forgive me if this has already been discussed.
There is a question that has perplexed me for years, and I am hoping someone at this forum can shed light or point me in the right direction.
If two like charges separated by a distance, d, quickly and simultaneously move toward each other some small incremental distance, the new larger field strength of one particle on the other must take a finite amount of time to reach the other particle. So it should be possible for each particle to move to its closer position before the new larger field of the other 'takes effect'. So each particle moves in the weaker field E1, but then the fields increase to E2. How is the conservation of energy preserved?

Similarly, if they suddenly and simultaneously return to their original positions, they move back in the stronger field, then the weaker field catches up to them after some finite time.

Sorry if this is a stupid question. What am I missing here? Thanks!

 

[eljose79]

Thank you for bringing up this interesting question. It seems that you are referring to the phenomenon of electric field propagation and its impact on the movement of charged particles. This is a valid concern and has been a topic of study in the field of electromagnetism for many years.

Firstly, it is important to understand that the electric field is a vector quantity, meaning it has both magnitude and direction. When two like charges move towards each other, their individual electric fields also change in magnitude and direction. This change in the electric field propagates at the speed of light, meaning it takes a finite amount of time for the new field to reach the other particle. This is known as the propagation delay.

However, this delay does not affect the conservation of energy. This is because the energy of the system is still conserved even as the electric fields change. The movement of the particles is determined by the net force acting on them, which is the vector sum of all the electric fields at that particular moment. As the fields change, the net force also changes accordingly and the particles will move accordingly.

In the scenario you described, where the particles move towards each other and then return to their original positions, the same principle applies. The electric fields will change accordingly and the net force on the particles will also change, resulting in their movement.

In conclusion, the conservation of energy is not violated in this scenario as the change in electric fields and the resulting movement of the particles are all accounted for in the calculations of the net force. I hope this helps to clarify your doubts. If you have any further questions, please do not hesitate to ask.

 

[astrokreng]

Hello there,

Thank you for your question. It is actually a very interesting and valid one. The concept of finite speed of signal transmission is a fundamental aspect of physics and has implications for conservation laws.

In the scenario you described, where two like charges are moving towards each other, the new larger field strength of one particle on the other does indeed take a finite amount of time to reach the other particle. This means that the particles are not immediately affected by the new field strength and will continue to move in their original weaker field until the new field reaches them. This does not violate the conservation of energy because the energy is still conserved in the overall system. The energy of the particles may have changed, but the total energy of the system remains constant.

Furthermore, the conservation of energy is not violated when the particles suddenly and simultaneously return to their original positions. The weaker field catches up to them after some finite time, but this does not mean that the energy is lost. The energy is simply redistributed within the system, but the total amount remains the same.

In summary, the finite speed of signal transmission does not violate the conservation of energy. It simply means that there is a delay in the effects of the new field strength, but the overall energy of the system remains constant. I hope this helps to clarify your question. Keep exploring and questioning, that's what being a scientist is all about!