A particle of mass m and charge q has an initial velocity . If an electric field and magnetic field act on the particle, its speed will double after a time :

Engineering

Physics

Motion of Charged Particle in Uniform Magnetic Field

Question

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 :

$\frac{\sqrt{2} {mv}_{0}}{{qE}_{0}}$

$\frac{3 {mv}_{0}}{{qE}_{0}}$

$\frac{2 {mv}_{0}}{{qE}_{0}}$

$\frac{\sqrt{3} {mv}_{0}}{{qE}_{0}}$

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As $\vec{v} = v_{0} \hat{j}$ (magnitude of velocity does not change in y–z plane)

${(2 v_{0})}^{2} = v_{0}^{2} + v_{x}^{2}; v_{x} = \sqrt{3} v_{0}$

$∴ \sqrt{3} v_{0} = 0 + \frac{qE}{m} t; t = \frac{{mv}_{0} \sqrt{3}}{qE}$