Which of the following pairs of quantities are not always perpendicular?

Question

BlackTom AI · Accepted Answer

We need to evaluate each pair to see whether they are always perpendicular for a moving charged particle in a magnetic field.

Option a: Magnetic force and velocity of the charge.
- The magnetic force is given by F = q (v × B). This force is always perpendicular to the velocity v, because the cross product yields a vector perpendicular to both v and B. Therefore, F ⟂ v holds in all cases (ignoring the trivial case q = 0 where F = 0). This option describes a pair that is always perpendicular.

Option b: Magnetic field and acceleration of the charge.
- The acceleration a is F/m. Since F is perpendicular to both v and B, a is along F and thus also perpendicular to B (assuming F ≠ 0). If the force is zero (e.g., v = 0 or qB = 0), acceleration is zero, and the perpendicular relationship is not meaningful but vacuously true. In typical motion with a magnetic force, a ⟂ B, so this pair is generally perpendicular.

Option c: Magnetic field and magnetic force on the charge.
- The magnetic force F is perpendicular to the magnetic field B by definition of the cross product F ∝ v × B. Thus F ⟂ B in all cases where the force is nonzero. This pair is always perpendicular.

Option d: Magnetic field and velocity of the charge.
- The velocity v need not be perpendicular to the magnetic field B. If the velocity is parallel (or at some angle) to B, the cross product v × B becomes zero or not strictly constrained to be perpendicular to B. Consequently, B and v are not guaranteed to be perpendicular in general.

Summary of reasoning:
- Options a, b, and c describe relationships that hold (at least when the interaction is nontrivial): F ⟂ v, a ⟂ B (when force exists), and F ⟂ B. These are outcomes of the definitions and vector relationships in magnetic force.
- Option d does not have a guaranteed perpendicular relation, since v can be parallel or at any angle to B, and thus B and v are not necessarily perpendicular.

UCIC 202503 PHYS101 Quiz 11

Which of the following pairs of quantities are not always perpendicular?

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