A) \[\sqrt{\frac{Vm}{q{{B}^{2}}}}\]
B) \[\frac{Vm}{q{{B}^{2}}}\]
C) \[\sqrt{\frac{2Vm}{q}}\,\,.\,\left( \frac{1}{B} \right)\]
D) \[\sqrt{\frac{Vm}{q}}\,\,.\,\left( \frac{1}{B} \right)\]
Correct Answer: C
Solution :
The speed of particle just before entering into magnetic field is \[{{v}_{0}}\]. \[\therefore \] \[qV=\frac{1}{2}mv_{0}^{2}\] \[\Rightarrow \] \[{{v}_{0}}=\sqrt{\left( \frac{2qV}{m} \right)}\] \[\therefore \] \[r=\frac{m{{v}_{0}}}{qB}=\frac{m}{qB}\sqrt{\left( \frac{2qV}{m} \right)}=\frac{1}{B}\sqrt{\left( \frac{2mV}{q} \right)}\]
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