A) depends on \[v\] and not on \[R\]
B) depends on both \[R\] and \[v\]
C) is independent of both \[R\] and \[v\]
D) depends on \[R\] and not on \[v\]
Correct Answer: C
Solution :
Key Idea To move on circular path in a magnetic field, a centripetal force is provided by the magnetic force. When magnetic field is perpendicular to motion of charged particle, then Centripetal force = magnetic force ie, \[\frac{m{{v}^{2}}}{R}=Bqv\] or \[R=\frac{mv}{Bq}\] Further, time period of the motion \[T=\frac{2\pi R}{v}=\frac{2\pi \left( \frac{mv}{Bq} \right)}{v}\] or \[T=\frac{2\pi m}{Bq}\] It is independent of both R and v.
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