Magnetic field of moving solenoid

[BananaJose]

If a solenoid oriented on the z axis is carrying a steady current, I if will produce a constant B field inside of the solenoid. A charged particle with initial velocity perpendicular to the z axis will undergo cyclotron motion within the solenoid at a constant radius, r. What are the electric and magnetic fields as seen from the particles reference frame.

I think that the B field will remain the same as seen from the lab frame. is this correct? I don't see any reason why the B field would change.

 

[Simon Bridge]

Welcome to PF;
Is this homework?

Someone may expect that the relative motion is important because electric and magnetic fields are related through relativity.
Most courses concentrate on how moving electric fields get you magnetism. i.e.
http://physics.weber.edu/schroeder/mrr/MRRtalk.html

... since the B field is frame dependent in the examples on that site, you will need to explain how come it is not in this case or revise your opinion.