A) \[f=\frac{qB}{2\,\pi m}\]
B) \[f=\frac{qB}{2\,\pi {{m}^{2}}}\]
C) \[f=\frac{2\,{{\pi }^{2}}m}{qB}\]
D) \[f=\frac{2\,\pi \,m}{qB}\]
Correct Answer: A
Solution :
Lorentz force = centripetal force \[i.e.,\] \[Bq\,v=\frac{m{{v}^{2}}}{r}\] \[\Rightarrow \] \[B\,q=m\,\omega \] \[\Rightarrow \] \[B\,\,q=m2\pi f\] (as \[v=r\,\omega \]) \[\therefore \] \[f=\frac{B\,q}{2\pi m}\]
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