Imagine that you are sitting in a chamber with your back to one wall. An electron beam, moving horizontally from back wall towards the front wall, is deflected by a strong magnetic field to your right side. What is the direction of magnetic field?

The direction of the magnetic field can be determined by applying Fleming's left-hand rule.
The direction of the current is in the opposite direction to the movement of electron beam so it is from the front wall to the back wall. Therefore, the middle finger should point towards the back wall. Also, the direction of force is towards the right, so the thumb points right-side. This gives the direction of fore-finger as downwards Hence, the direction of the magnetic field inside the chamber is downward.