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8.Electromagnetic waves
medium
A particle of mass $\mathrm{m}$ and charge $\mathrm{q}$ has an initial velocity $\overline{\mathrm{v}}=\mathrm{v}_{0} \hat{\mathrm{j}} .$ If an electric field $\overrightarrow{\mathrm{E}}=\mathrm{E}_{0} \hat{\mathrm{i}}$ and magnetic field $\overrightarrow{\mathrm{B}}=\mathrm{B}_{0} \hat{\mathrm{i}}$ act on the particle, its speed will double after a time:
A
$\frac{{2} m v_{0}}{q E_{0}}$
B
$\frac{\sqrt{2} m v_{0}}{q E_{0}}$
C
$\frac{\sqrt{3} m v_{0}}{q E_{0}}$
D
$\frac{{3} m v_{0}}{q E_{0}}$
(JEE MAIN-2020)
Solution
$\left(2 \mathrm{V}_{0}\right)^{2}=\mathrm{v}_{0}^{2}+\mathrm{v}_{\mathrm{x}}^{2}$
$v_{x}=\sqrt{3} v_{0}$
$\sqrt{3} \mathrm{v}_{0}=0+\frac{\mathrm{qE}_{0}}{\mathrm{m}} \mathrm{t}$
$\mathrm{t}=\frac{\sqrt{3} \mathrm{v}_{0} \mathrm{m}}{\mathrm{q} \mathrm{E}_{0}}$
Standard 12
Physics
