Question

Two particles $ X $ and $ Y $ having equal charges, after being accelerated through the same potential difference enter a region of uniform magnetic field and describe circular paths of radii $ R_1 $ and $ R_2 $ , respectively. The ratio of masses of $ X $ and $ Y $ is

• A. $ \left(\frac{R_{1}}{R_{2}}\right)^{1/2} $
• B. $ \left(\frac{R_{2}}{R_{1}}\right) $
• C. $ \left(\frac{R_{1}}{R_{2}}\right)^{2} $
• D. $ \left(\frac{R_{1}}{R_{2}}\right) $

Answer 1

Answer: (C)

The radius of charged particle in magnetic field,
$r = \frac {mv}{qB} = \frac{\sqrt{2mE_k}}{qB}$
According to question, let $m_x$ and $m_y$ are the masses, $q$ are charges and $B$ magnetic field and $E_K$, kinetic energy. When the charged particles are accelerated at same potential, then $KE$ will be same.
So, radius, $R_{1} = \sqrt{\frac{2m_{x} \times E_{k}}{qB}}$
and $R_{2} = \sqrt{\frac{2 m_{y}E_{k}}{qB}} $
$ \therefore \frac{m_{x}}{m_{y}} = \left(\frac{R_{1}}{R_{2}}\right)^{2}$