Question 21: EM waves

Question

An electromagnetic wave of frequency 1 $$ 	imes $$ 10
14
hertz is propagating along z - axis.  The amplitude of electric field is 4 V/m. If $$ \in $$
0
= 8.8 $$ 	imes $$ 10
$$-$$12
C
2
/N-m
2
, then average energy density of electric field will be :

Accepted Answer

We have
$$
E=E_0 \sin (\omega t-k x)
$$
Since, energy density is $\mu_{\mathrm{E}}=\frac{1}{2} \varepsilon_0 E^2$
$$
\begin{aligned}
\Rightarrow \bar{\mu}_{\mathrm{E}} & =\frac{1}{2} \varepsilon_0 \bar{E}^2=\frac{1}{2} \varepsilon_0 E_{\mathrm{rms}}^2 \\
& =\frac{1}{2} \varepsilon_0 \frac{E_0^2}{2}=\frac{1}{4} \varepsilon_0 E_0^2 \\
& =\frac{1}{4} 	imes 8.8 	imes 10^{-12} 	imes 4^2=35.2 	imes 10^{-12} \mathrm{~J} / \mathrm{m}^3
\end{aligned}
$$

Answer

35.2 $$ 	imes $$ 10
$$-$$10
J/m
3

Answer

35.2 $$ 	imes $$ 10
$$-$$11
J/m
3

Answer

35.2 $$ 	imes $$ 10
$$-$$12
J/m
3

Answer

35.2 $$ 	imes $$ 10
$$-$$13
J/m
3

EM waves

An electromagnetic wave of frequency 1 $ \times 10 14 hertz is propagating along z - axis. The amplitude of electric field is 4 V/m. If \in 0 = 8.8 \times 10 -$12 C 2 /N-m 2 , then average energy density of electric field will be :

Choose the correct answer: