Final answer:
The magnetic field that causes a west-moving proton to curve upward must have a component into the page or southward. Using the right-hand rule, you can understand and predict the behavior of charges in magnetic fields, as the thumb represents the magnetic field direction when the fingers curl from the velocity direction to the force direction for positive charges.
Step-by-step explanation:
If a proton, moving west, curves upward upon entering a magnetic field, we can use the right-hand rule to deduce the direction of the magnetic field. For a positive charge like a proton, the fingers of your right hand point in the direction of the velocity (west), and you curl them in the direction of the force experienced by the proton (upward), then your thumb points in the direction of the magnetic field. Since the proton curves upward, the magnetic field must have a component into the page or south when looking from a top-down perspective.
In the contexts provided, if a proton moves in the -x-direction and encounters a magnetic field pointing in the +x-direction, applying the right-hand rule would tell us that the magnetic force is zero since the motion is parallel to the magnetic field lines. On the other hand, for a proton moving west to east with a given kinetic energy in Earth's magnetic field, the magnetic force can be calculated considering the horizontal and vertical components of the magnetic field and the velocity of the proton.