The proton and electron experience forces to the left and right of the page, the particles would separate to the left and right respectively after the magnetic field is applied.
To know what would happen to each particle when a magnetic field pointing in the direction of the page is applied, we need to know the direction of the force acting on the particles due to this magnetic field according to fleming's left hand rule
This states that when the thumb, the middle-finger and fore-finger of the left-hand are held at right angles to each other, the magnetic field points in the direction of the fore-finger, the current (or direction of charge) points in the direction of the middle finger and the force on the conductor or charge points in the direction of the thumb.
Since the direction of the proton is up the page and the direction of the magnetic field is into the page, the direction of the force according to fleming's left hand rule is to the left of the page.
Since the direction of the electron is up the page (it is in the direction of the conventional current or positive charge in the other direction) and the direction of the magnetic field is into the page, the direction of the force according to fleming's left hand rule is to the right of the page.
Since both the proton and electron experience forces to the left and right of the page, the particles would separate to the left and right respectively after the magnetic field is applied.
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