A) \[\frac{Be}{{{a}^{2}}}\]
B) \[e{{B}^{2}}a\]
C) \[{{a}^{2}}eB\]
D) \[aeB\]
Correct Answer: C
Solution :
Key Idea Magnetic force provides the necessary centripetal force to the proton to move on circular path. Under uniform magnetic field, force \[evB\]acts on proton and provides the necessary centripetal force\[m{{v}^{2}}/a\] \[\therefore \] \[\frac{m{{v}^{2}}}{a}=evB\] or \[v=\frac{aeB}{m}\] ?(i) Now, angular momentum \[J=r\propto p\] Here, \[J=a\times mv\] Putting value of v from Eq. (i), we get \[J=a\times m\left( \frac{aeB}{m} \right)\] \[={{a}^{2}}eB\]
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