A particle of mass m and charge q has an initial velocity v→=v0j^. If an electric field E→=E0i^ and magnetic field B→=B0i^ act on the particle, its speed will double after a time mvoxqE. Find value of x.

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A particle of mass m and charge q has an initial velocity $\vec{v} = v_{0} \hat{j} . If an electric field \vec{E} = E_{0} \hat{i} and$ $magnetic field \vec{B} = B_{0} \hat{i} act on the particle, its speed will double after a time \frac{m v_{o} \sqrt{x}}{q E} .$ Find value of x.

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Detailed Solution

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

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

$∴ \sqrt{3} v_{0} = 0 + \frac{q E}{m} t; t = \frac{m v_{0} \sqrt{3}}{q E}$

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