A) \[\frac{{{B}^{2}}}{2v{{E}^{2}}}\]
B) \[\frac{2v{{B}^{2}}}{{{E}^{2}}}\]
C) \[\frac{2v{{E}^{2}}}{{{B}^{2}}}\]
D) \[\frac{{{E}^{2}}}{2v{{B}^{2}}}\]
Correct Answer: D
Solution :
Its the electron beam is not deflected then, \[{{F}_{m}}=Ee\] \[Bev=Ee\] \[v=\frac{E}{B}\] According to the law of conservation of energy \[\frac{1}{2}m{{v}^{2}}=eV\] \[v=\sqrt{\frac{2eV}{m}}\] \[\sqrt{\frac{2eV}{m}}=\frac{E}{B}\] \[\frac{e}{m}=\frac{{{E}^{2}}}{2V{{B}^{2}}}\]
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