Final answer:
The magnetic field must be applied into the page, perpendicular to both the motion of the alpha particle and the gravitational force, following the right-hand rule for deflection balance.
Step-by-step explanation:
To ensure the alpha particle is undeflected by the gravitational force and moves in a straight path between the two uncharged, horizontal metal plates, a magnetic field must be applied in such a direction that the magnetic force balances the gravitational pull. The direction of the magnetic field can be determined using the right-hand rule. If an alpha particle is moving to the left and gravity is pulling it downward, to find the direction of the required magnetic field, you would point your thumb to the left (direction of velocity), and your middle finger downward (direction of the force due to gravity). Your index finger, which points in the direction of the magnetic field, would then be pointing directly into the page. Therefore, the magnetic field must be applied into the page to ensure that the alpha particle remains undeflected.