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Question: Answered & Verified by Expert
When a charged particle moving with velocity $\overrightarrow{\mathbf{v}}$ is subjected to a magnetic field of induction $\overrightarrow{\mathbf{B}}$, the force on it is non-zero. This implies that
PhysicsMagnetic Effects of CurrentJIPMERJIPMER 2008
Options:
  • A angle between $\overrightarrow{\mathbf{v}}$ and $\overrightarrow{\mathbf{B}}$ is necessarily $90^{\circ}$
  • B angle between $\overrightarrow{\mathbf{v}}$ and $\overrightarrow{\mathbf{B}}$ can have any value other than $90^{\circ}$
  • C angle between $\overrightarrow{\mathbf{v}}$ and $\overrightarrow{\mathbf{B}}$ can have any value other than zero and $180^{\circ}$
  • D angle between $\overrightarrow{\mathbf{v}}$ and $\overrightarrow{\mathbf{B}}$ is either zero or $180^{\circ}$
Solution:
1077 Upvotes Verified Answer
The correct answer is: angle between $\overrightarrow{\mathbf{v}}$ and $\overrightarrow{\mathbf{B}}$ can have any value other than zero and $180^{\circ}$
When a charged particle $q$ is moving in a uniform magnetic field $\overrightarrow{\mathbf{B}}$ with velocity $\overrightarrow{\mathbf{v}}$ such that angle between $\overrightarrow{\mathbf{v}}$ and $\overrightarrow{\mathbf{B}}$ 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 $\sin \theta=0$
$\therefore \quad F=q v B \sin \theta=0$
Since, force on charged particle is non-zero, so angle between $\overrightarrow{\mathbf{v}}$ and $\overrightarrow{\mathbf{B}}$ can have any value other than zero and $180^{\circ}$.
Note : Force experienced by the charged particle is Lorentz force.

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