If the resulting trajectory of the charged particle is a circle, what is ω, the angular frequency of the circular motion?

Fmag = qvB

Also have in mind that Centripetal acceleration is: ar = v2/R

centripetal force will be :Fc = mv2/R

And velocity is: v = ωR

Remember that the magnetic force is the centripetal force then: 

Fmag = Fc
qvB = mv2/R
qB = mv/R

Next you need to substitute for velocity:

qB = mωR/R
qB = mω

ω = qB/m

The value of circular velocity or frequency is .

Explanation:

The charged particle is moving in a circular path.

Let the charge of the particle is . The radius of the circular path is . The velocity of the particle is and it is moving in a magnetic field is .

Now, the magnetic force experienced by the charged particle is,

(assuming the magnetic field is perpendicular to the direction of motion)

Now, the centripetal force experienced by the particle will be,

Velocity of the particle can be written as (in the form of angular velocity) .

Now, equating the magnetic and centripetal force to get the value of circular velocity,

So, the value of circular velocity or frequency is .

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