Distance of a Point Charge: Solving for Initial Distance Using Relativity

[Zack K]

Homework Statement

You make repeated measurements of the electric field $\vec E$ due to a distant charge, and you find it is constant in magnitude and direction. At time $t=0$ your partner moves the charge. The electric field doesn't change for a while, but at time $t=24$ ns you observe a sudden change. How far away was the charge originally?

Homework Equations

Maybe $\gamma= \frac {1} {\sqrt {1-\frac {v^2} {c^2}}}$?
$\vec E=\frac {kq} {|\vec r|^2}\hat r$

The Attempt at a Solution

Someone in my class said that you have to use relativity to solve the problem, hence why I put the equation to get a gamma factor. The textbook did go into relativistic electric fields at the end of the chapter but didn't go into too much detail. I was thinking that you would use the equation for the gamma factor to solve for v, then use that and multiply by time to get the initial distance. But to do that you would have to know what your gamma factor is, which I don't. What also confuses me is how can your electric field not change when you are moving the charge? I'm guessing it has something to do with time dilation. Sorry for the ramble

 

[Zack K]

Sigh... It's just d=vt, v being the speed of light.

 

[SammyS]

Sigh... It's just d=vt, v being the speed of light.

Yup. So the answer is d ≈ 24 ft.
c ≈ 0.9835 ft/ns , so about 1 foot per nanosecond.