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Two ions have equal masses but one is singly ionized and the other is doubly ionized. They are projected from the same place in a uniform magnetic field with the same velocity perpendicular to the field.

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The two circles touch each other

The two circles do not touch each other

The circle described by the singly-ionized charge will have a radius double that of the other circle

Both ions will move along circles of equal radii

answer is B, D.

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Detailed Solution

$Bqϑ = \frac{m^{2}}{r} \Rightarrow r = \frac{mϑ}{Bq}$

$\Rightarrow r \propto \frac{1}{q}, \frac{r_{1}}{r_{2}} = \frac{q_{2}}{q_{1}} = \frac{2 e}{e} = 2 \Rightarrow r_{1} = 2 r_{2}$

As they are projected from the same place, the circular touch each other.

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