Question

A proton and a deutron both having the same kinetic energy, enter perpendicularly into a uniform magnetic field B. For motion of proton and deutron on circular path of radius $R _ { p }$ and $R _ { d }$ respectively, the correct statement is

• A. $R _ { d } = \sqrt { 2 } R _ { p }$
• B. $R _ { d } = R _ { p } / \sqrt { 2 }$
• C. $R _ { d } = R _ { p }$
• D. $R _ { d } = 2 R _ { p }$

Answer 1

Answer: (A)

$R _ { d } = \sqrt { 2 } R _ { p }$

Answer 2

$\frac { m v ^ { 2 } } { R } = q v B$. For proton

$R _ { p } = \frac { m v } { q B } = \frac { \sqrt { 2 m _ { p } E } } { q B }$

and for deuteron $R _ { d } = \frac { \sqrt { 2 m _ { d } E } } { q B }$

$\Rightarrow \frac { R _ { d } } { R _ { p } } = \sqrt { \frac { m _ { d } } { m _ { p } } } = \sqrt { 2 } \Rightarrow R _ { d } = \sqrt { 2 } R _ { p }$