Practice portal › Moving Charges and Magnetism › Motion of a Charge in a Magnetic Field
Asked in GSEB Board July 2017 · Circular motion: radius, period and energy
Given: a charged particle moving in a magnetic field.
Idea: the magnetic force is ⃗F=q(⃗v×⃗B), which is perpendicular to ⃗v at every instant.
Work in a small displacement: dW=⃗F· d⃗r=⃗F·⃗v dt=0, since ⃗F⊥⃗v.
By the work-energy theorem the kinetic energy changes only by the work done on the particle, and that is zero.
So the kinetic energy, and with it the speed, stays constant; only the direction of motion changes.
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