Final answer:
The possible directions for the proton's velocity to result in a force when the magnetic field is in the y-direction are the +z direction or the -z direction, as per the right-hand rule.
Step-by-step explanation:
The answer to the student's question involves understanding the relationship between velocity, magnetic field, and force as explained by the right-hand rule in the context of electromagnetic theory. If the magnetic field due to the proton is in the y direction, and we want to find a possible direction for the velocity of the proton that would result in a magnetic force, we can use the right-hand rule.
The right-hand rule states that if you point your fingers in the direction of the proton's velocity and curl them towards the direction of the magnetic field, your thumb will point in the direction of the force on a positively charged particle, such as a proton. Since we know the force is perpendicular to both the velocity and the magnetic field, the possible directions for the velocity could be either the +z direction (out of the page) or the -z direction (into the page). If the magnetic field is in the y direction and we want the resulting force to be perpendicular to it, the proton’s velocity should be in either the +z or -z direction.