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

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Consider the Lorentz force on a moving charge: F = q (v × B).

Option a: To the top of the page. This would occur if the cross product v × B pointed upward, but that only happens when v is not parallel to B. In the given setup, B is directed upward (to the top of the page), and the velocity V of the charge is also upward. Since v and B are parallel, their cross product is zero, so this direction is not produced by the magnetic force.

Option b: To the left. A leftward force would require a v × B vector pointing left. This would occur for a specific perpendicular orientation of v and B, but with v parallel to B (both upward), the cross product vanishes and no such horizontal force arises.

Option c: To the right. Similar to option b, a rightward force would require a particular perpendicular arrangement of v and B. Again, because v ∥ B here, the cross product is zero and no horizontal force appears.

Option d: To the bottom of the page. A downward force would require v × B to point downward, which is not the case since v and B are aligned upward; the cross product magnitude is zero, giving no net force downward.

Option e: There is no Lorentz force on the charge. Since v is directly parallel to B (both upward), the cross product v × B = 0, and the magnetic force F = q(v × B) = 0. Therefore, no magnetic force acts on the charge regardless of its positive sign, as the vanishing cross product yields zero force.

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

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

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