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
$F=q v B \sin \theta$
If $\theta=0^{\circ}$ or $180^{\circ}$, then $\sin \theta=0$
$\therefore F=q v B \sin \theta=0$
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.