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If the speed of a charged particle moving through a magnetic field is increased, then the angular frequency of its circular motion will ______.

Asked in GSEB Board March 2020 (old course) · Circular motion: radius, period and energy

Answer: (3) not change

Step-by-step solution

Idea: in a uniform field the magnetic force supplies the centripetal force, qvB=(mv²)/r.

So the radius is r=(mv)/(qB) — proportional to the speed.

Angular frequency: ω=v/r=v×(qB)/(mv)=(qB)/m.

The speed cancels: a faster particle simply runs round a proportionally larger circle in the same time.

So increasing the speed does not change the angular frequency.

Why the other options are wrong

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