Electric field at the surface of a filament.

[miew]

On a nylon filament 0.01cm in diameter and 4cm long there are 5.0e-8 extra electrons distributed uniformly over the surface. What is the electric field strength at the surface of the filament?
a) In the rest frame of the filament?
b) In a frame in which the filament is moving at a speed 0.9c in a direction parallel to its length.

Homework Equations

E-field for cylinder: E= Q/(2piLr[tex]\epsilon[/tex])

The Attempt at a Solution

First I calculated the charge which is Q=(#electrons)(1.6e-19)=8e-11C and I plugged that in the E formula. I got E= 3.59e5N/C
For b) i calculated the new length which is 4/(1-(0.9)^2)^(1/2) and I did the same process.

I just wanted to know if that is right or not. I am a little confused.
Thank !

 

[AvroArrow]

Yes, your calculation is correct. For part (b), since the filament is moving at a speed close to the speed of light, its length will appear shorter in the rest frame, so you have to use the new length in the equation.