A charge q moving with velocity \( \vec v \) in a magnetic field \( \vec B \) experiences a force \( \vec F \). Which pair of quantities are mutually perpendicular?
A. \( \vec F \) & \( \vec v \)
B. \( \vec F \) & \( \vec B \)
C. \( \vec v \) & \( \vec B \)
Choose the correct answer from the options given below:
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → A and B only
The magnetic force on a moving charge is \( \vec{F} = q(\vec{v}\times\vec{B}) \). A vector product is perpendicular to both of the vectors that form it.
A. \( \vec F \) & \( \vec v \) — perpendicular, since \( \vec{F} \) is perpendicular to \( \vec{v} \). This is why the magnetic force does no work and never changes the speed.
B. \( \vec F \) & \( \vec B \) — perpendicular, since \( \vec{F} \) is perpendicular to \( \vec{B} \).
C. \( \vec v \) & \( \vec B \) — not necessarily perpendicular. The charge may enter the field at any angle \( \theta \), and the force has magnitude \( qvB\sin\theta \); it is zero when \( \vec{v} \) is parallel to \( \vec{B} \).
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.”