When a charged particle with velocity $\vec{v}$ is subjected to an induction magnetic field $\vec{B}$, the for

Question

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?

Accepted Answer

1. **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 $\vec{F} = q(\vec{v} 	imes \vec{B})$ .
2. **Magnitude:** The magnitude of this force is $F = qvB \sin	heta$, where $	heta$ is the angle between $\vec{v}$ and $\vec{B}$.
3. **Zero Force Condition:** The force vanishes ($F=0$) if $v=0$, $B=0$, or $\sin	heta = 0$. The condition $\sin	heta = 0$ implies $	heta = 0^{\circ}$ or $	heta = 180^{\circ}$ (i.e., the particle moves parallel or anti-parallel to the magnetic field) .
4. **Non-Zero Force Condition:** For the force to be **non-zero**, $\sin	heta$ must not be zero. Therefore, the angle $	heta$ can have any value **except** $0^{\circ}$ and $180^{\circ}$. It does not necessarily have to be $90^{\circ}$ (maximum force).

Step-by-Step Solution

Practice All PHYSICS Questions