Moving Charges and Magnetism - Result Question 12
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
(a) $1 / R^{2}$
(b) $R^{2}$
(c) $R$
(d) $1 / R$
[2007]
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Answer:
Correct Answer: 12. (a)
Solution:
- (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,
$\therefore \frac{q}{m} \propto \frac{1}{R^{2}}$
