Final answer:
The force on a charged particle moving through a uniform magnetic field is perpendicular to both its velocity and the magnetic field, causing it to follow a circular path. The right-hand rule determines the direction of the force for positive charges and the left-hand rule for negative charges. Calculating the force involves the equation F = qvB sin(θ).
Step-by-step explanation:
Determining the Direction of the Force on a Charged Particle
When a charged particle moves through a uniform magnetic field, it experiences a force perpendicular to both the velocity of the particle and the magnetic field. This perpendicular force causes the charged particle to follow a curved path, which is circular if the initial motion is perpendicular to the field. The direction of the force can be determined using the right-hand rule, which is a visual tool for understanding the orientation of these three directions (velocity, magnetic field, and force). For a positive charge, the fingertips of the right hand point in the direction of the velocity, the palm faces the direction of the magnetic force, and the thumb points in the direction of the magnetic field. Conversely, for a negative charge like an electron, one would use the left-hand rule.
To answer case-specific questions pertaining to the direction of the force on a charged particle in a magnetic field, it would be necessary to apply the right-hand rule to each scenario given, keeping in mind the orientation of velocity and magnetic field vectors. For example, if an electron moves upward through a magnetic field directed into the page, the force on the electron would be to the left, as per the right-hand rule (or rather left-hand rule for negative charges).