The motion of a charged particle in an electromagnetic field can be obtained from the Lorentz equation for the force on a particle in such a field. If the electric field vector is E and the magnetic field vector is B, the force on a particle of mass m that carries a charge q and has a velocity v is given by(adsbygoogle = window.adsbygoogle || []).push({});

F=qE+qv X B

(The X is the cross product.)

If there is no electric field and if the particle enters the magnetic field in a direction perpendicular to the lines of magnetic flux, show that the trajectory is a circle with radius

r=(mv)/(qB)=v/(omega)

where omega=qB/m, which is the cyclotron frequency.

Okay, if there's no electric field, then I drop the qE term, meaning F=qv X B. I set this equal to F=ma.

qv X B = ma

I think I should make a=dv/dt, and solve for v, then take the derivative to get the trajectory. But the cross product is really confusing me, and I don't really know how to simplify from there. Am I going in the right direction?

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# Homework Help: Lorentz equation?

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