question_answer

  A particle of mass m and charge q has an initial velocity \[\vec{v}={{v}_{0}}\hat{j}\]. If an electric field \[\vec{E}={{E}_{0}}\hat{i}\] and magnetic field \[\vec{B}={{B}_{0}}\hat{i}\]act on the particle, its speed will double after a time: [JEE MAIN Held on 07-01-2020 Evening]

A) \[\frac{3\,m{{v}_{0}}}{q{{E}_{0}}}\]

B)   \[\frac{\sqrt{3\,}m{{v}_{0}}}{q{{E}_{0}}}\]

C) \[\frac{2\,m{{v}_{0}}}{q{{E}_{0}}}\]       

D) \[\frac{\sqrt{2}\,m{{v}_{0}}}{q{{E}_{0}}}\]

Correct Answer: B

Solution :

[b] \[{{a}_{x}}=\frac{{{E}_{0}}q}{m}\] \[V_{0}^{2}+V_{x}^{2}={{(2\,{{V}_{0}})}^{2}}\] \[\Rightarrow \,\,{{V}_{x}}=\sqrt{3}{{V}_{0}}={{a}_{x}}t\] \[\Rightarrow \,\,t=\frac{\sqrt{3}\,{{V}_{0}}m}{{{E}_{0}}q}\]