Two ions having masses in the ratio 1: 1 and | vedclass

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(A) Given ratios: $m_1: m_2 = 1: 1$,$q_1: q_2 = 1: 2$,and $v_1: v_2 = 2: 3$.When a charged particle moves in a uniform magnetic field perpendicular to

Vedclass · Accepted Answer

$4: 3$

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(A) Given ratios: $m_1: m_2 = 1: 1$,$q_1: q_2 = 1: 2$,and $v_1: v_2 = 2: 3$.When a charged particle moves in a uniform magnetic field perpendicular to the field,it follows a circular path with radius $r = \frac{mv}{Bq}$.Therefore,the ratio of the radii is given by $\frac{r_1}{r_2} = \left(\frac{m_1}{m_2}ight) \left(\frac{v_1}{v_2}ight) \left(\frac{q_2}{q_1}ight)$.Substituting the given values: $\frac{r_1}{r_2} = \left(\frac{1}{1}ight) 	imes \left(\frac{2}{3}ight) 	imes \left(\frac{2}{1}ight) = \frac{4}{3}$.Thus,the ratio of the radii is $4: 3$.

Two ions having masses in the ratio $1: 1$ and charges $1: 2$ are projected into a uniform magnetic field perpendicular to the field with speeds in the ratio $2: 3$. The ratio of the radii of circular paths along which the two particles move is :

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