I Electric field of a moving charge that's abruptly stopped

AI Thread Summary
The discussion centers on the behavior of the electric field surrounding a moving charge that is abruptly stopped, particularly referencing a figure that illustrates this phenomenon. Participants clarify that the field outside a sphere of radius ct reflects the particle's previous motion due to the limitations of causal connections in electromagnetic theory, as dictated by Maxwell's equations. The field does not assume an "apparent position" of the charge but rather depends on its past trajectory. The conversation emphasizes that physics operates on experimental evidence rather than intuitive reasoning. Ultimately, the conclusion is reached to accept the established principles of electromagnetism and continue studying the topic.
vish22
Messages
33
Reaction score
1
Hello everyone,

This is in reference to fig 5.19 (screen shot attached - please read the paragraph which says "Figure 5.19 shows the...").
I don't get why the field outside of the sphere of radius ct acts as though the particle would have continued its motion. Author's words : "The field outside the sphere of radius R = ct must be that which would have prevailed if the electron had kept on moving at its original speed. That is why we see the “brush”
of field lines on the right in Fig. 5.19 pointing precisely down to the posi-
tion where the electron would be if it hadn’t stopped."

Why does it act this way? Why does the field outside R=ct assume an "apparent position" of the charge? Why does it think the charge is at x = v*t and that it remains in its state of motion?

In my opinion, it would make more sense if the field (outside R=ct) acted as though the particle is in a state of motion (with uniform velocity v) at x=0, ie. The field outside R=ct must belong to that of a charge moving (with a uniform velocity v along the x-axis and situated at x=0), before transforming into an electrostatic field belonging to a charge that's stationary at x=0. The field will transform once it knows the particle has stopped. But before such a transformation occurs, the field should reflect the actual state of the particle right before it's abruptly stopped, no (neglect any deceleration effects)? I'm not sure why the field assumes an "apparent position" in this case.This just doesn't seem right to me - I'm not sure what to make of it.
 

Attachments

  • Screenshot_20220722-035411_Drive.jpg
    Screenshot_20220722-035411_Drive.jpg
    30.8 KB · Views: 161
Last edited by a moderator:
Physics news on Phys.org
vish22 said:
Why does it act this way?
Because that is what comes out of Maxwell’s equations. What is outside of the sphere is not causally connected to any part of the particle worldline after the change in motion, only parts before the change. The field will therefore be the same as if the particle motion did not change because the change simply does not have enough time to propagate.

vish22 said:
Why does the field outside R=ct assume an "apparent position" of the charge?
It doesn’t. It depends on where the particle was and how it was moving on the past lightcone of the event.

vish22 said:
Why does it think the charge is at x = v*t and that it remains in its state of motion?
It doesn’t. See above.

vish22 said:
In my opinion, it would make more sense if the field (outside R=ct) acted as though the particle is in a state of motion (with uniform velocity v) at x=0, ie.
Physics is not required to adhere to what you think would make sense. The theory of electromagnetism is based on Maxwell’s equations - a relativistic field theory. It behaves this way and has been very well tested experimentally.

vish22 said:
This just doesn't seem right to me - I'm not sure what to make of it.
See above. Physics depends on experimental evidence, not on what you think seems right.
 
See above. Physics depends on experimental evidence, not on what you think seems right.

Yes, yes absolutely.

For now I shall consider it as being experimentally proven and carry on my readings, thank you!
 
This is from Griffiths' Electrodynamics, 3rd edition, page 352. I am trying to calculate the divergence of the Maxwell stress tensor. The tensor is given as ##T_{ij} =\epsilon_0 (E_iE_j-\frac 1 2 \delta_{ij} E^2)+\frac 1 {\mu_0}(B_iB_j-\frac 1 2 \delta_{ij} B^2)##. To make things easier, I just want to focus on the part with the electrical field, i.e. I want to find the divergence of ##E_{ij}=E_iE_j-\frac 1 2 \delta_{ij}E^2##. In matrix form, this tensor should look like this...
Thread 'Applying the Gauss (1835) formula for force between 2 parallel DC currents'
Please can anyone either:- (1) point me to a derivation of the perpendicular force (Fy) between two very long parallel wires carrying steady currents utilising the formula of Gauss for the force F along the line r between 2 charges? Or alternatively (2) point out where I have gone wrong in my method? I am having problems with calculating the direction and magnitude of the force as expected from modern (Biot-Savart-Maxwell-Lorentz) formula. Here is my method and results so far:- This...
Back
Top