Concept:The macroscopic magnetic force (Lorentz force) acting on a moving point charge is defined fundamentally by the vector cross product of velocity and the magnetic field.
Formula:$$ \mathbf{F} = q(\mathbf{v} \times \mathbf{B}) $$
Solution:- The force \( \mathbf{F} \) is a vector that is always strictly perpendicular to both the velocity vector \( \mathbf{v} \) and the magnetic field vector \( \mathbf{B} \).
- In mathematics, a vector that is perpendicular to two other vectors is found using the cross product.
- The magnitude is scaled by the scalar value of the electric charge \( q \).
- Therefore, the correct standard expression is \( \mathbf{F} = q(\mathbf{v} \times \mathbf{B}) \).
Why other options are incorrect:Option C incorrectly places the charge in the denominator. Options B and D mathematically misarrange the vector relations and isolate the scalar charge \( q \) using invalid vector division.
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