Final answer:
The sign of the charged particle is determined by the right-hand rule, which relates the particle's velocity, the magnetic field, and the direction of the magnetic force. Positive charges are deflected in the direction of the palm of the right hand when following the rule.
Step-by-step explanation:
This asks about the sign of a charged particle entering a uniform magnetic field, given its velocity and the force acting on it. The direction of the magnetic force on a charged particle is given by the right-hand rule: point your thumb in the direction of the particle's velocity (u), your fingers in the direction of the magnetic field (B), and your palm will point in the direction of the force (F) exerted on a positive charge. If the force is in the opposite direction, the charge is negative. In the cases provided, the particles' deflections and forces in relation to their velocity and the magnetic field direction help determine the sign of the charge. For instance, in the first scenario, if a particle is deflected to the north when the magnetic field is horizontal from east to west, and the particle is moving downward, it implies that the particle is positively charged according to the right-hand rule.