Detecting Electric Fields with Motion: Is the Field Moving?

[log0]

Let's say I've got a charged particle moving with constant velocity and multiple columns of electric field sensors parallel to its path. The sensors will trigger whenever a maximum passes by.

Will the sensors in a row be triggered at the same time? If they are, what does it mean for the field? Is it moving with the charge? If it does, what is it that is moving?

 

[David Lewis]

The sensors will be triggered sequentially, not simultaneously.

 

[Nugatory]

It is an interesting exercise to consider this problem using a frame in which the particle is at rest and the sensors are moving as well.

 

[jtbell]

It may help to look at Figure 26.4 on this page from the Feynman lectures:

http://www.feynmanlectures.caltech.edu/II_26.html

 

[log0]

It may help to look at Figure 26.4 on this page from the Feynman lectures:

http://www.feynmanlectures.caltech.edu/II_26.html

Thank a lot for the link.

I am looking at the case of the charge passing a row of sensors (y-axis):
z = 0
x - vt = 0

This means:
Ez = 0
Ex = 0
Ey = k / (sqrt(1-v^2) *y^2)

So the field not lagging behind, it is simply length contracted in the direction of motion.

Why would the sensors be triggered sequentially as stated by David? Am I missing something?

 

[rumborak]

Can you explain your rationale why you think they will be triggered all at exactly the same time? I mean, the particle is moving with a finite velocity, right?

 

[log0]

Can you explain your rationale why you think they will be triggered all at exactly the same time? I mean, the particle is moving with a finite velocity, right?

I am looking at the field lines or better equipotential lines of a charge. For a charge at rest they are circles. For a charge in motion they are ellipses aligned with the direction of motion (length contraction). The maximum will be measured when the sensors are closest to the circle or aligned ellipse. This happens at the moment when the charge is at the same height as the sensor row.

Now, I've been reading up on the retarded potential concept. My current understanding is that the length contracted field (aligned elliptic equipotential) is a composite image of what is going on. The more correct view is that each sensor sees the field at a different point in the past, depending on its distance at that time. Also the equipotential as seen by the sensor is a rotated (or skewed?) ellipse, with the rotation angle being half the angle towards the sensor.

So the sensors are triggered at the same time, but they are triggered by the retarded field from different points in time.

 

[rumborak]

Are you aware that these length contractions only become relevant at close to the speed of light?

 

[David Lewis]

Are you aware that these length contractions only become relevant at close to the speed of light?

Since a charged particle can exert a large electric force, moving electric fields are sensitive to relativistic effects. For example, the typical speed of electrons in household wiring is probably around 10¹³ times less than the speed of light. That would make Lorentz length contraction on the order of 10^-26. Yet the magnetic field surrounding the wire is easily measurable.