Question

The dielectric constant of air is $1.006$. The speed of electromagnetic waves traveling in air is $a\times {10}^{8}m{s}^{-1}$, where, $a$ is about

• A. $3$
• B. $3.88$
• C. $3.2$
• D. $2.8$

Answer 1

The correct option is A

$3$

Step 1: Given

The dielectric constant of air is $=1.006$

The speed of electromagnetic waves traveling in air $c=a\times {10}^{8}m{s}^{-1}$

Step 2: Formula

As we know that the speed of the electromagnetic wave,$c=\frac{1}{\sqrt{{\mu }_0{\epsilon }_0}}$

Where ${\mu }_o$is absolute permeability having value $4\pi \times {10}^{-7}Tm{A}^{-1}$

${\epsilon }_o$ is absolute permittivity having value $8.85\times {10}^{-12}{C}^2/N{m}^2$

Step 3: Calculation

For finding the value of $a$ put all the known values into the formula-

That is

$\begin{array}{rcl}a\times {10}^{8}m/s& =& \frac{1}{\sqrt{\left(4\pi \times {10}^{-7}\right)\times \left(8.85\times {10}^{-12}\right)}}\\ a\times {10}^8& =& 3\times {10}^8\\ a& =& 3\end{array}$

Therefore the value of $a$ is $3$.

Hence, option A is the correct answer.