Two ions having same mass have charges in ratio 1: 2 . They are projected normally in a uniform magn

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4.Moving Charges and Magnetism

medium

Two ions having same mass have charges in the ratio $1: 2$. They are projected normally in a uniform magnetic field with their speeds in the ratio $2: 3$. The ratio of the radii of their circular trajectories is -

$4: 3$

$3: 1$

$2: 3$

$1: 4$

(JEE MAIN-2021)

Solution

$R =\frac{ mv }{ qB }$

$\Rightarrow \frac{ R _{1}}{ R _{2}}=\frac{\frac{ mv _{1}}{ q _{1} B }}{\frac{ mv _{2}}{ q _{2} B }}=\frac{ v _{1}}{ q _{1}} \times \frac{ q _{2}}{ v _{2}}=\frac{ q _{2}}{ q _{1}} \times \frac{ v _{1}}{ v _{2}}$

$=\frac{2}{ l } \times\left(\frac{2}{3}\right)=\frac{4}{3}$

Standard 12

Physics

In a mass spectrometer used for measuring the masses of ions, the ions are initially accelerated by an electric potential $V$ and then made to describe semicircular paths of radius $R$ using a magnetic field $B$. If $V$ and $B$ are kept constant, the ratio $\left( {\frac{{{\text{charge on the ion}}}}{{{\text{mass of the ion}}}}} \right)$ will be proportional to

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Two ions having same mass have charges in the ratio $1: 2$. They are projected normally in a uniform magnetic field with their speeds in the ratio $2: 3$. The ratio of the radii of their circular trajectories is -

Solution

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