Electric Field of Moving Charge: Effects on Distance

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Discussion Overview

The discussion revolves around the effects of a moving observer on the electric field of a point charge, particularly focusing on how distance and electric field strength are perceived as the observer moves towards or away from the charge. The conversation touches on concepts from special relativity, including length contraction and the relativity of simultaneity.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested

Main Points Raised

  • One participant suggests that moving towards or away from a point charge affects the perceived electric field strength due to the distance changing according to their perspective.
  • Another participant questions how length contraction could increase the distance to the charge, seeking clarification on the relationship between motion and perceived distance.
  • A participant introduces the Bell's spaceships thought experiment to illustrate changes in distance under different acceleration scenarios, noting complications when one spaceship is out of fuel.
  • Concerns are raised about the implications of simultaneity in the context of moving observers and how this affects the perceived position of the charge relative to the observer.
  • One participant references the electromagnetic tensor and Lorentz transformations to argue that the perceived position of the charge changes based on the observer's frame of reference and acceleration profile.

Areas of Agreement / Disagreement

Participants express differing views on the implications of length contraction and simultaneity, indicating that there is no consensus on how these concepts interact with the electric field of a moving charge.

Contextual Notes

The discussion includes unresolved assumptions about the nature of acceleration and the specific conditions under which the electric field is being analyzed. The participants do not reach a definitive conclusion regarding the effects of motion on the electric field.

jartsa
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First I stand next to a point charge, then I start moving away or towards the charge, which causes the charge to be further away from me according to me (my ruler contracts according to an inertial observer), and as electric field of a point charge decreases with distance, the electric field caused by the charge decreases at my position according to me.

Is that above thing right or wrong?
 
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jartsa said:
then I start moving away or towards the charge,
So which one?

jartsa said:
which causes the charge to be further away from me according to me (length contraction)
How would length contraction increase the distance to the charge?
 
A.T. said:
So which one?

Let's study both cases, first the easier one, whichever that is.

How would length contraction increase the distance to the charge?

Simple case: Bell's spaceships. Distance increases according to accelerating spaceships.
Complicated case: Bell's spaceships, but one spaceship is out of fuel, but that does not prevent the other spaceship from observing the Bell's spaceship type of change of distance.
 
jartsa said:
Bell's spaceships, but one spaceship is out of fuel, but that does not prevent the other spaceship from observing the Bell's spaceship type of change of distance.
If one ship doesn't accelerate (corresponding to the charge in your question?), the one behind it will crash into it. That is hardly an increase in distance.
 
You're forgetting the relativity of simultaneity. Put yourself at the origin and the charge at x=X. At time t=0 you accelerate instantaneously to velocity v. Plug the numbers into the Lorentz transforms. Yes, at t=0 the charge is at ##x'=\gamma X##. However, at t'=0, which is your current simultaneity convention, it is at ##x'=X/\gamma## - closer to you. For non-instantaneous acceleration you'd have to specify an acceleration profile to figure out how far you and the charge move during your acceleration phase.

You need to take a look at the electromagnetic tensor (see for example equation 1.58 in Carroll's GR notes - apologies for lack of link, but my phone is not cooperating with linking today) to determine what field you will see.
 

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