Magnetic forces are always perpendicular to the direction of motion. Because the Lorentz force $F$ is derived from the cross product of velocity $v$ and the magnetic field $B$, the resulting force vector is orthogonal to the particle's instantaneous displacement. In physics, work is only performed when a force has a component in the direction of motion; since the magnetic force lacks this component, it does no work ( $W=0$ ). Consequently, while a magnetic field can deflect a particle and change its trajectory, it cannot change the particle's kinetic energy or speed.
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title Zero Work and Maximum Speed
Resulmation: 3D Lorentz Force and Work Done
: The magnetic force does zero work on a particle undergoing cyclotron motion in a uniform magnetic field
IllustraDemo: Cyclotron Magnetic Steering and Electric Kicks
Ex-Demo: The Mechanics of Cyclotron Acceleration
Narr-graphic: Physics and Mechanics of cyclotron motion
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%% Proof and Derivation
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