Question

Two particles of different masses $m_1$ and $m_2$ , different charges $Q_1$ and $Q_2$ , are accelerated through the same potential difference and then enter a uniform magnetic field in a direction perpendicular to the field. If they trace circular paths of same radius, then the ratio of their masses ($m_1$/$m_2$ ) must be :

• A. $Q_2$ / $Q_1$
• B. $Q_1$ / $Q_2$
• C. $(Q_1$ / $Q_2{)}^{1/2}$
• D. $(Q_2$ / $Q_1{)}^{1/2}$

Answer 1

Answer: (B)

$Q_1$ / $Q_2$

$\frac{1}{2}{m}_1{V}_1^2=Q_{1}V$ ,$V_1=\sqrt{\frac{2Q_{1}V}{m_1}}$

And $\frac{1}{2}{m}_2{V}_2^2+Q_{2}V$

$V_2=\sqrt{\frac{2Q_{2}V}{m_2}}$, $r_1=\frac{m_1{V}_1}{Q_{1}B}$

$r_1=\sqrt{\frac{2m_{1}V}{Q_1{B}^2}}$

Similarly,

$r_2=\sqrt{\frac{2m_{2}V}{Q_2{B}^2}}$

given $r_1=r_2$

So $\frac{m_1}{m_2}=\frac{Q_1}{Q_2}$