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

For a plane electromagnetic wave, the electric field is given by $\overrightarrow{E} = 90 \sin (0.5 \times 10^{3} x + 1.5 \times 10^{11} t) \hat{k} \text{ V/m}$. The corresponding magnetic field $\vec{B}$ will be

$A$ plane electromagnetic wave of frequency $28 \, MHz$ travels in free space along the positive $x$-direction. At a particular point in space and time, the electric field is $9.3 \, V/m$ along the positive $y$-direction. The magnetic field (in $T$) at that point is:

Given below are two statements:
Statement $I$: $A$ time-varying electric field is a source of a changing magnetic field and vice-versa. Thus,a disturbance in an electric or magnetic field creates $EM$ waves.
Statement $II$: In a material medium,the $EM$ wave travels with speed $v = \frac{1}{\sqrt{\mu_{0} \varepsilon_{0}}}$.
In the light of the above statements,choose the correct answer from the options given below:

The electric and magnetic fields associated with an electromagnetic wave propagating along the $Z$-axis can be represented by:

$A$ plane electromagnetic wave of frequency $25 \text{ MHz}$ travels in free space along the $X$-direction. At a particular point in space and time, the electric field is $\vec{E} = 6.3 \hat{j} \text{ V m}^{-1}$. What is the magnetic field $\vec{B}$ at that point?