Consider the magnetic force \( \vec{F}=q(\vec{v}\times\vec{B}) \) on a moving charge.
Statement I: The vectors \( \vec{F} \) and \( \vec{v} \) are perpendicular to each other.
Statement II: The vectors \( \vec{v} \) and \( \vec{B} \) can have any angle between them.
Statement III: The vectors \( \vec{F} \) and \( \vec{B} \) are perpendicular to each other.
Choose the correct option.
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → All the statements are true
The magnetic force is a vector product of \( \vec{v} \) and \( \vec{B} \), and a vector product is perpendicular to both of the vectors it is formed from.
Statement I The vectors \( \vec{F} \) and \( \vec{v} \) are perpendicular to each other. — True. \( \vec{F}=q\,(\vec{v}\times\vec{B}) \) is perpendicular to \( \vec{v} \) at every instant. So the magnetic force does no work on the charge.
Statement II The vectors \( \vec{v} \) and \( \vec{B} \) can have any angle between them. — True. The charge can move in any direction in the field. The angle \( \theta \) between \( \vec{v} \) and \( \vec{B} \) only fixes the size of the force, \( qvB\sin\theta \). The force is zero when they are parallel or anti-parallel and largest when they are perpendicular.
Statement III The vectors \( \vec{F} \) and \( \vec{B} \) are perpendicular to each other. — True. The force is a vector product with \( \vec{B} \). So it is perpendicular to \( \vec{B} \) for any angle between \( \vec{v} \) and \( \vec{B} \).
NCERT (2026-27):
Magnetic Field, Lorentz Force – “(ii) The magnetic force q [ v × B ] includes a vector product of velocity and magnetic field. The vector product makes the force due to magnetic field vanish (become zero) if velocity and magnetic field are parallel or anti-parallel. The force acts in a (sideways) direction perpendicular to both the velocity and the magnetic field.”