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A charged particle is moving in a uniform magnetic field. Then ______.

Asked in GUJCET 2016 · Lorentz force and work done

• (1) its momentum and kinetic energy both change
• (2) its momentum changes but kinetic energy does not change
• (3) neither the momentum nor kinetic energy changes
• (4) kinetic energy changes but momentum does not change

Step-by-step solution

Why the other options are wrong

• (1) The kinetic energy cannot change. The magnetic force q⃗v×⃗B is perpendicular to ⃗v at every instant, so ⃗F·⃗v=0 and no work is done on the particle.
• (3) Only a particle moving exactly along the field escapes with nothing changed. In general q⃗v×⃗B is non-zero and keeps turning the velocity, so the direction of ⃗p — and therefore ⃗p itself — changes.
• (4) This has it exactly backwards. Work needs a force component along the velocity, which the magnetic force never has; a force across the velocity is precisely what changes the direction of the momentum.

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