The electric field of a plane electromagnetic wave of wave number $k$ and angular frequency $\omega$ is given by $\vec{E} = E_0(\hat{i} + \hat{j}) \sin(kz - \omega t)$. Which of the following gives the direction of the associated magnetic field $\vec{B}$?

$A$ charged particle oscillates about its mean equilibrium position with a frequency of $10^9 \; Hz$. What is the frequency of the electromagnetic waves produced by the oscillator?

Which one of the following statements is correct?

The magnetic field of a plane electromagnetic wave is given by $\vec B = B_0 \hat i \cos(kz - \omega t) + B_1 \hat j \cos(kz - \omega t)$,where $B_0 = 3 \times 10^{-5} \, T$ and $B_1 = 2 \times 10^{-6} \, T$. The rms value of the force experienced by a stationary charge $Q = 10^{-4} \, C$ at $z = 0$ is closest to:

If the electric field intensity of a uniform plane electromagnetic wave is given as $E = -301.6 \sin (kz - \omega t) \hat{a}_{x} + 452.4 \sin (kz - \omega t) \hat{a}_{y} \text{ V/m}$. Then,the magnetic intensity $H$ of this wave in $\text{A/m}$ will be (Given: Speed of light in vacuum $c = 3 \times 10^{8} \text{ m/s}$,permeability of vacuum $\mu_{0} = 4\pi \times 10^{-7} \text{ N/A}^{2}$)

An electromagnetic wave of frequency $1 \times 10^{14} \,Hz$ is propagating along the $z$-axis. The amplitude of the electric field is $4 \,Vm^{-1}$. What is the energy density of the electric field? (Permittivity of free space $\varepsilon_0 = 8.8 \times 10^{-12} \,C^2 \,N^{-1} \,m^{-2}$)