$X$-rays,gamma rays and microwaves travelling in vacuum have

For a plane electromagnetic wave,which of the following quantities has an average value of zero?

The electric field of a plane electromagnetic wave of amplitude $2 \, V/m$ varies with time,propagating along the $z$-axis. The average energy density of the magnetic field (in $J/m^3$) is:

Dimension of $\frac{1}{\mu_0 \varepsilon_0}$ should be equal to

$A$ carbon dioxide laser emits a sinusoidal electromagnetic wave that travels in a vacuum in the negative $x-$ direction. The wavelength is $10.6\,\mu m$ and the $\vec E$ field is parallel to the $z-$ axis,with $E_{max} = 1.5 \times 10^6\, V/m$. Then the vector equations for $\vec E$ and $\vec B$ as a function of time and position are:

$A$ plane $EM$ wave travelling along $z-$ direction is described by $\vec E = E_0 \sin(kz - \omega t)\hat i$ and $\vec B = B_0 \sin(kz - \omega t)\hat j$. Show that:
$(i)$ The average energy density of the wave is given by $U_{av} = \frac{1}{4} \epsilon_0 E_0^2 + \frac{1}{4} \frac{B_0^2}{\mu_0}$.
$(ii)$ The time-averaged intensity of the wave is given by $I_{av} = \frac{1}{2} c \epsilon_0 E_0^2$.