Q. When a charged particle moving with velocity $\overrightarrow{V}$ is subjected to a magnetic field of induction $\overrightarrow{B}$, the force on it is non-zero. This implies that
A) Angles between $\overrightarrow{V}$ and $\overrightarrow{B}$ can have any value other than zero and $180{^\circ}$
B) Angel between $\overrightarrow{V}$ and $\overrightarrow{B}$ is either zero or $180{^\circ}$
C) Angle between $\overrightarrow{V}$ and $\overrightarrow{B}$ is necessarily $90{^\circ}$
D) Angle between $\overrightarrow{V}$ and $\overrightarrow{B}$ can have any value other than $90{^\circ}$
Explanation
(a) Force acting on a charged particle moving with velocity $\overrightarrow{v}$ subjected to magnetic field $\overrightarrow{B}$ is given by
$\overrightarrow{F} = q\left( \overrightarrow{v} \times \overrightarrow{B} \right)$ or, $F = qvB\sin\theta$
(i) When $\theta = 0{^\circ},\ F = qvB\sin{0{^\circ}} = 0$
(ii) When $\theta = 90{^\circ},\ F = qv\sin{90{^\circ}} = qvB$
(iii) When $\theta = 180{^\circ},\ F = qvB\sin{180{^\circ}} = 0$
This implies force acting on a charged particle is non-zero, when angle between $\overrightarrow{v}$ and $\overrightarrow{B}$ can have any value other than zero and $180{^\circ}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.