Electric Field of Moving Charge: Effects on Distance

[jartsa]

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?

 

[A.T.]

then I start moving away or towards the charge,

So which one?

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?

 

[jartsa]

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.

 

[A.T.]

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.

 

[Ibix]

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.