Question

A double ionized He+2 atom travels at right angles lo a magnetic field of induction 0.4 T at a velocity of 10 m/s describing a circle of radius r. A proton travelling with the same speed in the same direction in the same field will describe a circle radius:

• A. $ \frac{r}{4} $
• B. $ \frac{r}{2} $
• C. $ r $
• D. $ 2\,r $

Answer 1

Answer: (B)

The necessary centripetal force for circular path is provide by magnetic force $ \frac{m{{\mu }^{2}}}{r}=qvB $ $ r=\frac{mv}{qB} $ (Here: velocity is same i.e., $ {{v}_{p}}={{v}_{He}} $ and field is same $ {{B}_{1}}={{B}_{2}}, $ $ {{m}_{He}}=4{{m}_{p}},\,\,{{q}_{_{He}}}=2{{q}_{p}} $ ) $ r\propto \frac{m}{q} $ Hence, $ \frac{{{r}_{He}}}{{{r}_{p}}}=\frac{{{m}_{He}}}{{{m}_{p}}}\times \frac{{{q}_{p}}}{{{q}_{He}}}=\frac{4{{m}_{p}}}{{{m}_{p}}}\times \frac{{{q}_{p}}}{2{{q}_{p}}} $ $ {{r}_{He}}:{{r}_{p}}=2:1 $ Hence, $ {{r}_{p}}:{{r}_{He}}=1:2 $