Two ions have equal masses but one is singly | vedclass

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(B) The radius of the circular path of a charged particle in a magnetic field is given by $r = \frac{mv}{qB}$.Since $m$,$v$,and $B$ are the same for b

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$b, d$

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(B) The radius of the circular path of a charged particle in a magnetic field is given by $r = \frac{mv}{qB}$.Since $m$,$v$,and $B$ are the same for both ions,we have $r \propto \frac{1}{q}$.Let $q_1 = e$ (singly ionized) and $q_2 = 2e$ (doubly ionized).Then,$\frac{r_1}{r_2} = \frac{q_2}{q_1} = \frac{2e}{e} = 2$.This implies $r_1 = 2r_2$. Thus,statement $(b)$ is correct.Since both ions are projected from the same point with the same velocity in the same magnetic field,their paths will be circles that pass through the point of projection and are tangent to the velocity vector at that point. As shown in the figure,the two circles will touch each other at the point of projection. Thus,statement $(d)$ is correct.

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