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 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:
- [JEE MAIN 2020]
- 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
$\frac{{3} m v_{0}}{q E_{0}}$
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In the given electromagnetic wave $E_y=600 \sin (\omega t-k x) \mathrm{Vm}^{-1}$, intensity of the associated light beam is (in $\mathrm{W} / \mathrm{m}^2$ ); (Given $\epsilon_0=$ $\left.9 \times 10^{-12} \mathrm{C}^{-2} \mathrm{~N}^{-1} \mathrm{~m}^{-2}\right)$
- [JEE MAIN 2024]
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$(a)$ What is the wavelength and frequency of the wave?
$(b)$ Write an expression for the electric field.
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