A charged particle moves with velocity v⃗ in a uniform magnetic field B⃗. The magnetic force exp

step 1 Okay, the question is a charge particle moves with the velocity V vector in a uniform magnetic f

A charged particle moves with velocity v⃗ in a uniform...

A charged particle moves with velocity $\vec{v}$ in a uniform magnetic field $\vec{B}$. The magnetic force experienced by the particle is
(A) always zero.
(B) never zero.
(C) zero if $\vec{B}$ and $\vec{v}$ are perpendicular.
(D) zero if $\vec{B}$ and $\vec{v}$ are parallel.

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Key Concepts

Lorentz Force

The Lorentz force describes the force on a charged particle moving in electromagnetic fields. It is governed by the equation F = q(v × B), where q is the charge, v is the velocity vector, and B is the magnetic field vector. This force is perpendicular to both v and B, and its magnitude depends on the sine of the angle between these vectors.

Vector Cross Product

The vector cross product is an operation that takes two vectors and produces a third vector perpendicular to both. Its magnitude is given by |v||B|sin(?), where ? is the angle between the two vectors. This implies that if the vectors are parallel (? is 0 or 180 degrees), the cross product—and consequently the magnetic force—is zero.

Magnetic Field Orientation

The effectiveness of the magnetic force depends on the relative orientation between the particle's velocity and the magnetic field. When the velocity is parallel or antiparallel to the magnetic field, the sine of the angle is zero, which means the magnetic force also becomes zero.

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