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) None of these

Correct Answer: D

Solution :

[d]

\[{{a}_{x}}=\frac{{{E}_{0}}q}{m}\]

\[V_{0}^{2}+V_{x}^{2}={{(2\,{{V}_{0}})}^{2}}\]

\[\Rightarrow \,\,{{V}_{x}}=\sqrt{3}{{V}_{0}}={{a}_{x}}t\]

\[\Rightarrow \,\,t=\frac{\sqrt{3}\,{{V}_{0}}m}{{{E}_{0}}q}\]