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Asked in GSEB Board March 2019 · Lorentz force and work done
Idea: the magnetic force on a charge is ⃗F=q(⃗v×⃗B), and a cross product is perpendicular to both of its factors — in particular to ⃗v.
The rate at which a force does work is P=⃗F·⃗v, and that dot product is zero here.
No work done means no change of kinetic energy, however long the particle travels and whatever shape the path takes.
So the kinetic energy remains constant: the field changes the direction of the velocity, never its magnitude.
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