The magnetic field in a plane electromagnetic wave is given by, $B_{y} = 2 \times 10^{-7} \sin (\pi \times 10^{3} x + 3 \pi \times 10^{11} t) \; T$. Calculate the wavelength.

The dimensions of $\frac{1}{{\mu _0}{\varepsilon _0}}$ are .......... .

Which of the following statements is false regarding the properties of electromagnetic waves?

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 $B$.

An electromagnetic wave is propagating in vacuum along $-\hat{j}$ direction. The magnetic field of the wave is given by $\vec{B} = (2 \times 10^{-8}) \cos [\pi \times 10^{15}(t + \frac{y}{c})] \hat{k} \text{ T}$. The electric field $\vec{E}$ of this wave is $(c = \text{speed of light})$

Show that the radiation pressure exerted by an $EM$ wave of intensity $I$ on a surface kept in vacuum is $\frac{I}{c}$.