two identical charged particles moving with same speed enter a region of uniform magnetic field if one of these - Physics - Magnetism And Matter

Question

two identical charged particles moving with same speed enter a
region of uniform magnetic field if one of these enters normal to
the feild direction and the other along a direction at 30'c with
the field , what would be the ratio of their angular
frequencies?

Vijay Yadav · Accepted Answer

Force on moving charge particle in a magnetic field (uniform)

F = qvB sin θ

θ = Angle between direction of motion and magnetic field.

If θ = 90°

F₁ = qvB sin 90° = qvB

If θ = 30°

F₂ = qvB sin 30° $= \frac{1}{2} q v B$

We know angular frequency

$ω = \frac{q B}{m}$

Angular frequency does not depend on θ.

So, ratio of frequencies

$\frac{ω_{1}}{ω_{2}} = \frac{1}{1}$

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two identical charged particles moving with same speed enter a region of uniform magnetic field. if one of these enters normal to the feild direction and the other along a direction at 30'c with the field , what would be the ratio of their angular frequencies?