Question

When a charged particle moving with velocity $\vec{v}$ is subjected to a magnetic field of induction $\vec{B}$ the force on it is non-zero. This implies that

• A. angle between $\vec{v}$ and $\vec{B}$ is necessarily $90^{\circ }$
• B. angle between $\vec{v}$ and $\vec{B}$ can have any value other than $90^{\circ }$
• C. angle between $\vec{v}$ and $\vec{B}$ can have any value other than zero and $180^{\circ }$
• D. angle between $\vec{v}$ and $\vec{B}$ is either zero or $180^{\circ }$

Answer 1

Answer: (C)

When a charged particle $q$ is moving in a uniform magnetic field $\vec{B}$ with velocity $\vec{v}$ such that angle between $\vec{v}$ and $\vec{B}$ be $\theta$, then due to interaction between the magnetic field produced due to moving charge and magnetic force applied, the charge $q$ experiences a force which is given by
$F=qvB\sin \theta$
If $\theta =0^{\circ }$ or $180^{\circ }$, then $\sin \theta =0$
$\therefore F=qvB\sin \theta =0$
Since, force on charged particle is non-zero, so angle between $\vec{v}$ and $\vec{B}$ can have any value other than zero and $180^{\circ }$.
Note : Force experienced by the charged particle is Lorentz force.