A) \[\sqrt{\frac{2e\,\,V}{m}}\]
B) \[\sqrt{\frac{2V\,m}{e\,{{B}^{2}}}}\]
C) \[\sqrt{\frac{2V\,m}{e\,B}}\]
D) \[\sqrt{\frac{2\,V\,m}{{{e}^{2}}B}}\]
Correct Answer: B
Solution :
Here, force on the charge in the magnetic field that is able to move it on a circular track, is given by \[BeV=\frac{m{{V}^{2}}}{r}\] or \[r=\frac{mV}{Be}=\frac{\sqrt{2Km}}{Be}\] \[\left( as,\,\frac{{{p}^{2}}}{2m}=K \right)\] Where, K == Kinetic energy of the charge As the electron has been accelerated from rest through a potential difference of V volt, then \[K=eV\] \[\therefore \] \[r=\sqrt{\frac{2meV}{{{B}^{2}}{{e}^{2}}}}=\sqrt{\frac{2mV}{{{B}^{2}}e}}\]
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