A charged particle enters at right angles into a uniform magnetic field as shown: What should be the nature of charge on the particle if it begins to move in a direction pointing vertically out of the page due to its interaction with the magnetic field?

To move out of the page (towards you), the magnetic force must be in that direction.

For a positive charge: Use the right-hand rule. If the magnetic field is into the page and the velocity is towards the right, the force will be directed out of the page.

For a negative charge: The force direction will be opposite to the palm of your right hand. If the magnetic field is into the page and the velocity is towards the right, the force will be directed into the page.

Since the particle moves vertically out of the page, the particle must be positively charged if the magnetic field is into the page.

Thus, if the particle begins to move out of the page, the charge on the particle is positive.