Moving Charges and Magnetism - Result Question 12

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12. 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 path of radius $R$ using a magnetic field $B$. If $V$ and $B$ are kept constant, the ratio $(\frac{\text{ charge on the ion }}{\text{ mass of the ion }})$ will be proportional to

======= ####12. 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 path of radius $R$ using a magnetic field $B$. If $V$ and $B$ are kept constant, the ratio $(\frac{\text{ charge on the ion }}{\text{ mass of the ion }})$ will be proportional to

3e0f7ab6f6a50373c3f2dbda6ca2533482a77bed:content/english/neet-pyq-chapterwise/physics/moving-charges-and-magnetism/moving-charges-and-magnetism—result-question-12.md (a) $1 / R^{2}$

(b) $R^{2}$

(c) $R$

(d) $1 / R$

[2007]

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Answer:

Correct Answer: 12. (a)

Solution:

  1. (a) In mass spectrometer, when ions are accelerated through potential $V$

$\frac{1}{2} m v^{2}=q V$

As the magnetic field curves the path of the ions in a semicircular orbit

$ \begin{equation*} B q v=\frac{m v^{2}}{R} \Rightarrow v=\frac{B q R}{m} \tag{ii} \end{equation*} $

Substituting (ii) in (i)

$\frac{1}{2} m[\frac{B q R}{m}]^{2}=q V$

or $\frac{q}{m}=\frac{2 V}{B^{2} R^{2}}$

Since $V$ and $B$ are constants,

$\therefore \frac{q}{m} \propto \frac{1}{R^{2}}$