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(A) The Lorentz magnetic force $\vec{F}_m$ acting on a particle of charge $q$ moving with velocity $\vec{V}$ in a magnetic field $\vec{B}$ is given by

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zero

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(A) The Lorentz magnetic force $\vec{F}_m$ acting on a particle of charge $q$ moving with velocity $\vec{V}$ in a magnetic field $\vec{B}$ is given by the formula: $\vec{F}_m = q(\vec{V} 	imes \vec{B})$.Since the magnetic force is always perpendicular to the velocity vector $\vec{V}$ (because the cross product $\vec{V} 	imes \vec{B}$ is perpendicular to both $\vec{V}$ and $\vec{B}$), the force is always perpendicular to the displacement $d\vec{r}$ of the particle.The work done $W$ by a force is given by the integral $W = \int \vec{F} \cdot d\vec{r}$.Since $\vec{F}_m \perp d\vec{r}$, the dot product $\vec{F}_m \cdot d\vec{r} = 0$.Therefore, the work done by the magnetic force on a charged particle is always zero.

Lorentz magnetic force is acting on a particle of charge $q$ moving with velocity $\vec{V}$ in magnetic field $\vec{B}$. The work done by this force on the charged particle is

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