A positive charge moving with a constant velocity V enters a region of a uniform magnetic field directed out of the page. What is the direction of the magnetic force on the charge?

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To analyze the magnetic force on a moving charge, we use the Lorentz force F = q (v × B).
Option a: There is no Lorentz force on the charge. This would be true only if either q = 0, or v and B are parallel (or one is zero). Here q is positive, v is to the right, and B is out of the page, so v is not parallel to B, so a zero force is incorrect.
Option b: To the top of the page. If we apply the right-hand rule for v × B: point the index finger in the direction of v (to the right), then curl or orient the middle finger toward B (out of the page). The thumb then points downward, not upward, so the force is not toward the top of the page; this option is incorrect.
Option c: To the bottom of the page. With v to the right and B out of the page, v × B points downward along the negative y-axis. Since the charge is positive, the force direction follows v × B itself, which is downward. This option is consistent with the cross product result and is a correct description of the force direction.
Option d: To the right. This would imply F is in the same direction as v, which would require B to be aligned with v (or q = 0) in the cross product; neither condition holds here. Therefore, this is incorrect.
Option e: To the left. This would result if the cross product produced a negative x-direction, but with v along +x and B along +z, the cross product yields a downward force, not leftward. Hence this option is incorrect.
In summary, evaluating each option against the v × B calculation shows that the downward (bottom of the page) direction is the correct outcome for a positive charge moving to the right in a magnetic field directed out of the page.

MUF0122 Physics Unit 2 - Semester 2, 2025 9.10 Lorentz force

A positive charge moving with a constant velocity V enters a region of a uniform magnetic field directed out of the page. What is the direction of the magnetic force on the charge?

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