SOLVED Centripetal force in magnetic field

[moment1337]

Hello. I have currently just started styding magnetism. My book states that an electic charge moving perpendicular to the magnetic field will cause the particle to move in a circular motion. This formula describes the motion of the particle:

qvB=mv²/r

According to the formule F=qvBsinα, the magnetic force will vary as the particle moves in the magnetic field, because the velocity changes, am I right? In that case the centripetal force will not be constant throughout the entire motion, and the particle won't move in a perfect circle. How come that the particle regardless of this move in a perfect circle? Where am I missing out?

 

[moment1337]

I did not remember to think in 3 dimension. facepalm