Q. In a mass spectrometer used to 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 $\left( \frac{charge\ on\ the\ ion}{mass\ of\ the\ ion} \right)$ will be proportional
A) 1/$R$
B) $1/R^{2}$
C) $R^{2}$
D) $R$
Explanation
(b) Radius of path
$R = \frac{1}{B}\sqrt{\frac{2MV}{q}} \Rightarrow \frac{q}{m} = \frac{2V}{B^{2}R^{2}} \Rightarrow \frac{q}{m} \propto \frac{1}{R^{2}}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.