Question

Explain why the magnetic force on a charged particle cannot change the linear speed and the kinetic energy of the particle

Answer 1

The magnetic force on a particle carrying a charge q and moving with a velocity $\overrightarrow{v}$ in a magnetic field of induction $\overrightarrow{B}$ is $\overrightarrow{F_m}$= q. At every instant, $\overrightarrow{F_m}$ is perpendicular to the linear velocity $\overrightarrow{v}$ and $\overrightarrow{B}$.

Therefore, a non—zero magnetic force may change the direction of the velocity and the dot product .$\overrightarrow{F_m}.\overrightarrow{v}$ = = 0.

But $\overrightarrow{F_m}.\overrightarrow{v}$ is the power, i.e., the time rate of doing work. Hence, the work done by the magnetic force in every short displacement of the particle is zero.

The work done by a force produces a change in kinetic energy. Zero work means no change in kinetic energy. Thus, although the magnetic force changes the direction of the velocity $\overrightarrow{v}$, it cannot change the linear speed and the kinetic energy of the particle.