An electric charge $+ q$ moves with velocity $\overrightarrow V  = 3\hat i + 4\hat j + \hat k$ in an electromagnetic field given by :  $\overrightarrow E  = 3\hat i + \hat j + 2\hat k$ and $\overrightarrow B  = \hat i + \hat j - 3\hat k$. The $y-$ component of the force experienced by $+ q$ is :-

A mathematical representation of electromagnetic wave is given by the two equations $E = E_{max}\,\, cos (kx -\omega\,t)$ and $B = B_{max} cos\, (kx -\omega\,t),$ where $E_{max}$ is the amplitude of the electric field and $B_{max}$ is the amplitude of the magnetic field. What is the intensity in terms of $E_{max}$ and universal constants $μ_0, \in_0.$

An electromagnetic wave of frequency $3\, GHz$ enters a dielectric medium of relative electric permittivity $2.25$ from vacuum. The wavelength of this wave in that medium will be $.......\,\times 10^{-2} \, cm$

An electromagnetic wave is represented by the electric field $\vec E = {E_0}\hat n\,\sin \,\left[ {\omega t + \left( {6y - 8z} \right)} \right]$. Taking unit vectors in $x, y$ and $z$ directions to be $\hat i,\hat j,\hat k$ ,the direction of propogation $\hat s$, is

An EM wave from air enters a medium. The electric fields are $\overrightarrow {{E_1}}  = {E_{01}}\hat x\;cos\left[ {2\pi v\left( {\frac{z}{c} - t} \right)} \right]$ in air and $\overrightarrow {{E_2}}  = {E_{02}}\hat x\;cos\left[ {k\left( {2z - ct} \right)} \right]$ in medium, where the wave number $k$ and frequency $v$ refer to their values in air. The medium is nonmagnetic. If $\varepsilon {_{{r_1}}}$ and $\varepsilon {_{{r_2}}}$ refer to relative permittivities of air and medium respectively, which of the following options is correct?

The electric field part of an electromagnetic wave in a medium is represented by $E_x = 0\,;$

${E_y} = 2.5\,\frac{N}{C}\,\,\cos \,\left[ {\left( {2\pi \, \times \,{{10}^6}\,\frac{{rad}}{m}} \right)t - \left( {\pi  \times {{10}^{ - 2}}\frac{{rad}}{s}} \right)x} \right];$

$E_z = 0$. The wave is