A) \[\frac{Be}{{{a}^{2}}}\]
B) \[e{{B}^{2}}a\]
C) \[{{e}^{2}}eB\]
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 \[J=r\times p\] Here, \[J=a\times mv\] Putting value of v from Eq. (i), we get \[J=a\times m\left( \frac{aeB}{m} \right)\] or \[J={{a}^{2}}eB\]
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