I have just begun my Introduction to Quantum Mechanics course in my undergrad and I am trying to understand the uncertainty principle on a fundamental level. I think the best way to understand the fundamentals of this principle is to question the principle and understand why doing so is wrong.
Consider the following thought experiment:
I have a setup consisting of two independent regions. Region A with an electric field along the positive x-axis, lets say, and Region B with a magnetic field, also along the positive x-axis. In Region A I have a cathode and the electric field causes a potential difference thereby accelerating the electrons from rest to a particular velocity (along positive x-axis).
Let us just focus on a single electron. I know the exact velocity (magnitude and direction) to which this electron is accelerated to (energy conservation). Now this electron is going to enter the magnetic field in a direction that is parallel to the field. I know that the electron is going to move in a straight line in the magnetic field, without losing any energy as the magnetic field does zero work. So I know the exact momentum of the electron at all times as this momentum is not going to change as long as the electron is inside the magnetic field. So uncertainty in momentum is zero. Since I know the exact trajectory of the electron, the uncertainty in position is also zero and I know both of these simultaneously.
So it appears like this though experiment violates the Heisenberg uncertainty principle.
What is the flaw in my argument? Why can't this happen?