An electromagnetic wave travels along the $z$-axis. Which of the following pairs of space and time-varying fields would generate such a wave?

Give the relation between vacuum permittivity $(\epsilon_{0})$, vacuum permeability $(\mu_{0})$, and the speed of light $(c)$.

Suppose that the electric field amplitude of an electromagnetic wave is $E_{0} = 120 \; N/C$ and that its frequency is $\nu = 50.0 \; MHz$.
$(a)$ Determine $B_{0}, \omega, k,$ and $\lambda$.
$(b)$ Find expressions for $E$ and $B$.

The magnetic field of an $\text{E.M.}$ wave is given by $\overrightarrow{ B }=\left(\frac{\sqrt{3}}{2} \hat{ i }+\frac{1}{2} \hat{ j }\right) 30 \sin \left[\omega\left( t -\frac{ z }{ c }\right)\right]$ ($\text{S.I.}$ units). The corresponding electric field in $\text{S.I.}$ units is:

In an $E.M.$ wave,the average energy density is associated with

$A$ plane electromagnetic wave travels in free space along the $z$-axis. At a particular point in space, the electric field along the $x$-axis is $8.7 \ V \ m^{-1}$. The magnetic field along the $y$-axis is: