Comparing Electric Field Intensity in Moving Systems F & F

In summary, the conversation discusses two inertial systems, F and F', and an electric charge Q at the origin. Both systems measure the intensity of the electric field at a sphere centered at the origin after one second. The field measured by F is spherical, while the field measured by F' will have both electric and magnetic components, which cannot be easily related to a length contraction. The conversation also mentions interesting footnotes and links for further reading.
  • #1
jonjacson
447
38
Imagine that we have an intertial system F, and there is an electric charge Q at the origin. Obviously the field is symmetric and spherical in this reference system.

Imagine another inertial system F' that is moving at constant speed v to the right respect to F, and at t=t'=0 both origins coincide.

After one second both systems will measure the intensity of the electric field at an sphere centered at the origin of coordinates (obviously we are talking about an sphere in their own systems of reference).

According to the measurements of F the field created by Q is spherical, What will be the field measured by F'?

My guess is this:

2wf90cx.jpg


The points x' are contracted, and obviously closer to the charge Q at the origin.
We know that the instensity of the field is stronger if you are closer to the source, and weaker if you are further away, the system F' will perform measurements closer to the origin than F, Will F' get higher values for the intensity of the electric field?

Black is F, at rest, F' is green. I have represented in black an sphere in F, and an sphere in F' seen by F.
 
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  • #3
mfb said:
F' will measure a field with both electric and magnetic components, and the relation is not as easy as a length contraction.
Here are the transformations for electric and magnetic fields.

Thanks, there are interesting footnotes and links too.
 

Related to Comparing Electric Field Intensity in Moving Systems F & F

1. What is the difference between electric field intensity in a stationary system and a moving system?

The electric field intensity in a moving system is affected by the relative motion between the system and the observer, while in a stationary system, it is not affected by motion. This is due to the concept of relativity, where the electric field is dependent on the frame of reference.

2. How does the electric field intensity change in a moving system?

In a moving system, the electric field intensity is affected by the Lorentz transformation, which takes into account the relative velocity between the system and the observer. This means that the magnitude and direction of the electric field can change based on the frame of reference.

3. What is the formula for calculating electric field intensity in a moving system?

The formula for calculating electric field intensity in a moving system is given by E' = γ(E + v x B), where E' is the electric field intensity in the moving system, γ is the Lorentz factor, E is the electric field intensity in the stationary system, v is the relative velocity between the observer and the system, and B is the magnetic field.

4. How does the speed of the moving system affect the electric field intensity?

The speed of the moving system affects the electric field intensity by increasing the magnitude of the electric field. This is due to the Lorentz factor, which increases as the relative velocity between the system and the observer increases.

5. What are some real-world applications of comparing electric field intensity in moving systems?

One real-world application is in the study of particle accelerators, where particles are accelerated to high speeds and the electric field intensity must be accurately calculated to ensure the particles follow the intended path. Another application is in the theory of relativity, where the comparison of electric field intensity in moving systems is used to explain the effects of relative motion on physical phenomena.

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