Magnetic Effects Of Current Question 305
Question: A proton, a deuteron and an $ \alpha - $ particle having the same kinetic energy are moving in circular trajectories in a constant magnetic field. If $ r_{p},,r_{d} $ and $ {r_{\alpha }} $ denote respectively the radii of the trajectories of these particles, then [IIT 1997 Re-Exam]
Options:
A) $ {r_{\alpha }}=r_{p}<r_{d} $
B) $ {r_{\alpha }}>r_{d}>r_{p} $
C) $ {r_{\alpha }}=r_{d}>r_{p} $
D) $ r_{p}=r_{d}={r_{\alpha }} $
Show Answer
Answer:
Correct Answer: A
Solution:
Given that $ K_{p}=K_{d}={K_{\alpha }} $ = K (say) We know that mp = m, md = 2m and $ {m_{\alpha }}=4m $ and qp = e, qd = e and $ {q_{\alpha }}=2e $ Further $ r=\frac{\sqrt{2mK}}{qB} $
Þ $ r_{p}=\frac{\sqrt{2mK}}{eB} $ , $ r_{d}=\frac{\sqrt{2( 2m )K}}{eB}=\sqrt{2}r_{p} $ and $ {r_{\alpha }}=\frac{\sqrt{2( 4m )K}}{( 2e )B}=r_{p} $ . Hence $ {r_{\alpha }}=r_{p}<r_{d} $
BETA
