A charged particle is projected with velocity $$v0$$ along positive $$x-axis$$. The magnetic field B is directed along negative $$z-axis$$ between x $$=$$ $$0$$ and x $$=$$ L. The particle emerges out (at$$ x $$=$$ $$L) at an angle of $$60$$º with the direction of projection. Find the velocity with which the same particle were projected (at$$ x $$=$$ $$0) along positive $$x-axis$$ so that when it emerges out (at$$ x $$=$$ $$L), the angle made by it is $$30$$º with the direction of projection

Question

A charged particle is projected with velocity $$v0$$ along positive $$x-axis$$. The magnetic field B is directed along negative $$z-axis$$ between x $$=$$ $$0$$ and x $$=$$ L. The particle emerges out (at$$ x $$=$$ $$L) at an angle of $$60$$º with the direction of projection. Find the velocity with which the same particle  were projected (at$$ x $$=$$ $$0) along positive $$x-axis$$ so that when it emerges out (at$$ x $$=$$ $$L), the angle made by it is $$30$$º with the direction of projection

Infinity Learn · Accepted Answer

In ∆OABAB $$=$$ L $$=$$ $$constantOB=r=mvqBsin$$⁡θ$$=Lr$$⇒$$L=rsin$$⁡θ$$=constant$$ or vsin⁡θ$$=$$ constant $$v0sin$$⁡$$60$$∘$$=v$$′$$sin$$⁡$$30$$∘v′$$=3v0$$

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