The equation of the electric field of an electromagnetic wave propagating through free space is given by: The average power of the electromagnetic wave is The value of is [2026]

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Solution

Q.
The equation of the electric field of an electromagnetic wave propagating through free space is given by:

$E = \sqrt{377} \sin (6.27 \times 10^{3} t - 2.09 \times 10^{- 5} x) N/C$

The average power of the electromagnetic wave is $(\frac{1}{α}) {W/m}^{2} .$ The value of $α$ is _________.

$(Take \sqrt{\frac{μ_{0}}{ε_{0}}} = 377 in SI units)$ [2026]

Ans.
(2)

Here, $v = \frac{ω}{K} = \frac{6.27 \times 10^{3}}{2.09 \times 10^{- 5}} = 3 \times 10^{8}$

So, wave moving in vacuum.

Now, $I = (\frac{1}{2} ε_{0} E_{0}^{2}) c = \frac{1}{2} ε_{0} E_{0}^{2} \frac{1}{\sqrt{μ_{0} ε_{0}}}$

$= \frac{1}{2} \sqrt{\frac{ε_{0}}{μ_{0}}} E_{0}^{2} = \frac{1}{2} \times \frac{1}{377} \times 377$

$\frac{1}{d} = \frac{1}{2}$

$d = 2$

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