Solved: PHYSICS Question for NEET

NEET PHYSICSEasy

When a charged particle with velocity $\vec{v}$ is subjected to an induction magnetic field $\vec{B}$ , the force on it is non-zero. What does this imply?

Angle between $\vec{v}$ and $\vec{B}$ is necessarily $90^{\circ}$ .

Angle between $\vec{v}$ and $\vec{B}$ can have any value other than $90^{\circ}$ .

Angle between $\vec{v}$ and $\vec{B}$ can have any value other than zero and $180^{\circ}$ .

Angle between $\vec{v}$ and $\vec{B}$ is either zero or $180^{\circ}$ .

Step-by-Step Solution

Lorentz Force Formula: The magnetic force $\vec{F}$ acting on a charge $q$ moving with velocity $\vec{v}$ in a magnetic field $\vec{B}$ is given by the vector product $\vec{F} = q(\vec{v} \times \vec{B})$ .
Magnitude: The magnitude of this force is $F = qvB \sin\theta$ , where $\theta$ is the angle between $\vec{v}$ and $\vec{B}$ .
Zero Force Condition: The force vanishes ( $F=0$ ) if $v=0$ , $B=0$ , or $\sin\theta = 0$ . The condition $\sin\theta = 0$ implies $\theta = 0^{\circ}$ or $\theta = 180^{\circ}$ (i.e., the particle moves parallel or anti-parallel to the magnetic field) .
Non-Zero Force Condition: For the force to be non-zero, $\sin\theta$ must not be zero. Therefore, the angle $\theta$ can have any value except $0^{\circ}$ and $180^{\circ}$ . It does not necessarily have to be $90^{\circ}$ (maximum force).

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