Think about the magnitude of the physics quantity is very important when we study physics.
Did you notice that the radius is very small: m
And the period of one resolution is very small,too. s.
So the electron will make almost turns in one second.
There is no way you can observed such trajectory with your eye or ordinary device.
And the velocity is very large. m/s.
If only 1% of velocity component is along the field line, the electron will move along the field line with speed m/s km/s.
So on average, the electron will move along the field line. That is also how electrons move between sourth pole and north pole-- following the field line of earth's magnetic field.
When the magnetic field is very strong, it will force electron moving back -- that need more physics analysis.
(or check out [url=http://www.phy.ntnu.edu.tw/ntnujava/index.php?topic=182.0]Helmholtz coil / particle trapped in magnetic mirror field[/url])