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

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First, establish the vectors: the magnetic field B is directed out of the page, and the velocity v of the negative charge is upward. The Lorentz force on a charge is F = q (v × B).
Option a: To the top of the page. This would require v × B to point upward, but since v is already upward, we need to check the cross product; the correct cross product v × B points horizontally, not upward, so this option is incorrect.
Option b: To the right. If the charge were positive, v × B would point to the right (positive x) because up (y) cross out of the page (z) yields right (x). However, the particle is negatively charged, so the force is reversed, making this option wrong.
Option c: There is no Lorentz force on the charge. A moving charge in a magnetic field generally experiences a force unless v is zero or B is zero. Here both are nonzero, so this statement is false.
Option d: To the left. This is the correct outcome when you account for the negative charge: v × B = +x (to the right) for upward velocity and B out of the page, but q is negative, so F = q(v × B) points to the left. This is consistent with the right-hand rule followed by the sign flip for negative q.
Option e: To the bottom of the page. The cross product does not point downward in this configuration, so this choice is incorrect.
In summary, applying F = q(v × B) with v up, B out of the page, and q negative yields a force to the left, matching option d.

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

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

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