A charged particle is projected with velocity v in a uniform magnetic field making an angle of $$450$$ with the field. The particle followed a helical path of radius $$10$$ cm. If the same particle is projected with velocity $$2V$$ in the same magnetic field making an angle of $$600$$ with the field, radius of helical path followed by the particle will be

Question

A charged particle is projected with velocity v in a uniform magnetic field making an angle of $$450$$ with the field. The particle followed a helical path of radius $$10$$ cm. If the same particle is projected with velocity $$2V$$ in the same magnetic field making an angle of $$600$$ with the field, radius of helical path followed by the particle will be

Infinity Learn · Accepted Answer

$$(1)r=V$$ $$sin$$θω$$=V$$ $$sin$$θ$$QB/m$$∴   r ∝  V $$sin$$θ ∴   $$r10=2V$$ $$sin600V$$ $$sin450$$   ⇒  $$r=106$$  cm

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