A) \[\frac{r}{4}\]
B) \[\frac{r}{2}\]
C) \[r\]
D) \[2\,r\]
Correct Answer: B
Solution :
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, \[{{r}_{p}}:{{r}_{He}}=1:2\]
You need to login to perform this action.
You will be redirected in
3 sec
