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Question

(A) The magnetic force $\vec{F}$ on a charged particle moving with velocity $\vec{v}$ in a magnetic field $\vec{B}$ is given by the Lorentz force form

Vedclass · Accepted Answer

$\vec{v} \cdot \vec{B} = 0$

Vedclass · Answer

(A) The magnetic force $\vec{F}$ on a charged particle moving with velocity $\vec{v}$ in a magnetic field $\vec{B}$ is given by the Lorentz force formula: $\vec{F} = q(\vec{v} 	imes \vec{B})$.The magnitude of this force is $F = qvB \sin 	heta$,where $	heta$ is the angle between the velocity vector $\vec{v}$ and the magnetic field vector $\vec{B}$.For the force to be maximum,$\sin 	heta$ must be maximum,which occurs when $	heta = 90^\circ$.When $	heta = 90^\circ$,the velocity vector $\vec{v}$ is perpendicular to the magnetic field vector $\vec{B}$.Mathematically,two vectors are perpendicular if their dot product is zero,i.e.,$\vec{v} \cdot \vec{B} = 0$.

$A$ charged particle is projected with velocity $\vec{v}$ in a uniform magnetic field $\vec{B}$. For the magnetic force on it to be maximum,which of the following is correct?

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